
import pandas as pd


football = pd.read_csv("football_2.csv", encoding = "ISO-8859-1")
football.head()


football.columns.values.tolist()

['ID',
 'Name',
 'Age',
 'Photo',
 'Nationality',
 'Flag',
 'Overall',
 'Potential',
 'Club',
 'Club Logo',
 'Value',
 'Wage',
 'Special',
 'Preferred Foot',
 'International Reputation',
 'Weak Foot',
 'Skill Moves',
 'Work Rate',
 'Body Type',
 'Real Face',
 'Position',
 'Jersey Number',
 'Joined',
 'Loaned From',
 'Contract Valid Until',
 'Height',
 'Weight',
 'LS',
 'ST',
 'RS',
 'LW',
 'LF',
 'CF',
 'RF',
 'RW',
 'LAM',
 'CAM',
 'RAM',
 'LM',
 'LCM',
 'CM',
 'RCM',
 'RM',
 'LWB',
 'LDM',
 'CDM',
 'RDM',
 'RWB',
 'LB',
 'LCB',
 'CB',
 'RCB',
 'RB',
 'Crossing',
 'Finishing',
 'HeadingAccuracy',
 'ShortPassing',
 'Volleys',
 'Dribbling',
 'Curve',
 'FKAccuracy',
 'LongPassing',
 'BallControl',
 'Acceleration',
 'SprintSpeed',
 'Agility',
 'Reactions',
 'Balance',
 'ShotPower',
 'Jumping',
 'Stamina',
 'Strength',
 'LongShots',
 'Aggression',
 'Interceptions',
 'Positioning',
 'Vision',
 'Penalties',
 'Composure',
 'Marking',
 'StandingTackle',
 'SlidingTackle',
 'GKDiving',
 'GKHandling',
 'GKKicking',
 'GKPositioning',
 'GKReflexes',
 'Release Clause']


football_variables_df = pd.DataFrame(football.columns.values, columns = ["Variables"])
football_variables_df


print(football_variables_df.to_string())

                   Variables
0                         ID
1                       Name
2                        Age
3                      Photo
4                Nationality
5                       Flag
6                    Overall
7                  Potential
8                       Club
9                  Club Logo
10                     Value
11                      Wage
12                   Special
13            Preferred Foot
14  International Reputation
15                 Weak Foot
16               Skill Moves
17                 Work Rate
18                 Body Type
19                 Real Face
20                  Position
21             Jersey Number
22                    Joined
23               Loaned From
24      Contract Valid Until
25                    Height
26                    Weight
27                        LS
28                        ST
29                        RS
30                        LW
31                        LF
32                        CF
33                        RF
34                        RW
35                       LAM
36                       CAM
37                       RAM
38                        LM
39                       LCM
40                        CM
41                       RCM
42                        RM
43                       LWB
44                       LDM
45                       CDM
46                       RDM
47                       RWB
48                        LB
49                       LCB
50                        CB
51                       RCB
52                        RB
53                  Crossing
54                 Finishing
55           HeadingAccuracy
56              ShortPassing
57                   Volleys
58                 Dribbling
59                     Curve
60                FKAccuracy
61               LongPassing
62               BallControl
63              Acceleration
64               SprintSpeed
65                   Agility
66                 Reactions
67                   Balance
68                 ShotPower
69                   Jumping
70                   Stamina
71                  Strength
72                 LongShots
73                Aggression
74             Interceptions
75               Positioning
76                    Vision
77                 Penalties
78                 Composure
79                   Marking
80            StandingTackle
81             SlidingTackle
82                  GKDiving
83                GKHandling
84                 GKKicking
85             GKPositioning
86                GKReflexes
87            Release Clause


print(football.dtypes.to_string())

ID                            int64
Name                         object
Age                           int64
Photo                        object
Nationality                  object
Flag                         object
Overall                       int64
Potential                     int64
Club                         object
Club Logo                    object
Value                         int64
Wage                          int64
Special                       int64
Preferred Foot               object
International Reputation    float64
Weak Foot                   float64
Skill Moves                 float64
Work Rate                    object
Body Type                    object
Real Face                    object
Position                     object
Jersey Number               float64
Joined                       object
Loaned From                  object
Contract Valid Until         object
Height                       object
Weight                       object
LS                           object
ST                           object
RS                           object
LW                           object
LF                           object
CF                           object
RF                           object
RW                           object
LAM                          object
CAM                          object
RAM                          object
LM                           object
LCM                          object
CM                           object
RCM                          object
RM                           object
LWB                          object
LDM                          object
CDM                          object
RDM                          object
RWB                          object
LB                           object
LCB                          object
CB                           object
RCB                          object
RB                           object
Crossing                    float64
Finishing                   float64
HeadingAccuracy             float64
ShortPassing                float64
Volleys                     float64
Dribbling                   float64
Curve                       float64
FKAccuracy                  float64
LongPassing                 float64
BallControl                 float64
Acceleration                float64
SprintSpeed                 float64
Agility                     float64
Reactions                   float64
Balance                     float64
ShotPower                   float64
Jumping                     float64
Stamina                     float64
Strength                    float64
LongShots                   float64
Aggression                  float64
Interceptions               float64
Positioning                 float64
Vision                      float64
Penalties                   float64
Composure                   float64
Marking                     float64
StandingTackle              float64
SlidingTackle               float64
GKDiving                    float64
GKHandling                  float64
GKKicking                   float64
GKPositioning               float64
GKReflexes                  float64
Release Clause               object


football_2 = football[football["Position"] == "ST"] 
football_2.head()


import numpy as np


football_3 = football_2.iloc[:, np.r_[2, 13, 18, 67, 68, 73, 75, 78, 11]]
football_3.head()


# Or simply (if no ranges are used)

football_2.iloc[:, [2, 13, 18, 67, 68, 73, 75, 78, 11]]


from sklearn.model_selection import train_test_split


X = football_3.drop(columns = ["Wage"])
# Get dummies for the caterogical variables

X = pd.get_dummies(X, drop_first = True)

y = football_3["Wage"]

X

y

5         1105
8         2138
18        3875
45        3661
65        2445
         ...  
18181     3399
18184     9389
18188    10780
18190    10121
18203     8358
Name: Wage, Length: 2152, dtype: int64


train_X, valid_X, train_y, valid_y = train_test_split(X, y, test_size = 0.3, random_state = 666)


train_X.head()


len(train_X)

1506


train_y.head()

13946    22512
7711      6760
8402      5377
13651    13711
1625     10521
Name: Wage, dtype: int64


len(train_y)

1506


valid_X.head()


len(valid_X)

646


valid_y.head()

7882      5628
14555    28875
16210     6941
15847    10144
12382    45877
Name: Wage, dtype: int64


len(valid_y)

646


import sklearn
from sklearn.linear_model import LinearRegression


model = LinearRegression()


model.fit(train_X, train_y)

LinearRegression()


train_y_pred = model.predict(train_X)
train_y_pred

array([24239.85483562,  3778.75482905, -4114.30802593, ...,
       18813.39087789, 21533.92321643, 22278.55484414])


train_y_pred_df = pd.DataFrame(train_y_pred, columns = ["Training_Prediction"])
train_y_pred_df


print("model intercept: ", model.intercept_)
print("model coefficients: ", model.coef_)
print("Model score: ", model.score(train_X, train_y))

model intercept:  293888.9838689667
model coefficients:  [-9.16152410e+02  4.85334103e+01  4.63702248e+02  4.80950017e+01
  6.32137998e+02  3.74975144e+02 -2.20174023e+03 -3.55489317e+05
 -3.56667999e+05 -3.57613010e+05]
Model score:  0.4586287207175519


print(pd.DataFrame({"Predictor": train_X.columns, "Coefficient": model.coef_}))

              Predictor    Coefficient
0                   Age    -916.152410
1               Balance      48.533410
2             ShotPower     463.702248
3            Aggression      48.095002
4           Positioning     632.137998
5             Composure     374.975144
6  Preferred Foot_Right   -2201.740231
7        Body Type_Lean -355489.317404
8      Body Type_Normal -356667.999143
9      Body Type_Stocky -357613.009856


mse_train = sklearn.metrics.mean_squared_error(train_y, train_y_pred)
mse_train

261404234.2377431


import math


rmse_train = math.sqrt(mse_train)
rmse_train

16168.000316605116


train_y.describe()

count      1506.000000
mean      12698.381142
std       21981.278007
min        1290.000000
25%        4692.500000
50%        6544.000000
75%       12364.250000
max      407609.000000
Name: Wage, dtype: float64


import dmba
from dmba import regressionSummary


regressionSummary(train_y, train_y_pred)

Regression statistics

                      Mean Error (ME) : 0.0000
       Root Mean Squared Error (RMSE) : 16168.0003
            Mean Absolute Error (MAE) : 8475.7614
          Mean Percentage Error (MPE) : -32.8265
Mean Absolute Percentage Error (MAPE) : 111.6103


train_residuals = train_y - train_y_pred
train_residuals

13946    -1727.854836
7711      2981.245171
8402      9491.308026
13651   -16051.024484
1625     -5183.772118
             ...     
12759    -3215.715396
17284   -15227.772659
1016     -7666.390878
16984    -9871.923216
16744     4022.445156
Name: Wage, Length: 1506, dtype: float64


type(train_residuals)

pandas.core.series.Series


import matplotlib.pyplot as plt
plt.hist(train_residuals, bins = 30)
plt.title("Residuals for Training")
plt.show()


train_residuals_df = train_residuals.to_frame(name = "Wage_Residuals")
train_residuals_df


import matplotlib.pyplot as plt

plt.hist(train_residuals_df["Wage_Residuals"], bins = 30)
plt.title("Residuals for Training")
plt.show()


import numpy as np
from scipy.stats import shapiro

shapiro(train_y)

ShapiroResult(statistic=0.38412952423095703, pvalue=0.0)


shapiro(train_residuals)

ShapiroResult(statistic=0.5784118175506592, pvalue=0.0)


from statsmodels.stats.outliers_influence import variance_inflation_factor

vif_df = pd.DataFrame()

vif_df["features"] = train_X.columns
vif_df["VIF"] = [variance_inflation_factor(train_X.values, i) for i in range(train_X.shape[1])]

print(vif_df)

               features         VIF
0                   Age   48.741902
1               Balance   33.364691
2             ShotPower  155.270485
3            Aggression   18.482052
4           Positioning  184.558829
5             Composure  115.774481
6  Preferred Foot_Right    7.714600
7        Body Type_Lean   32.118906
8      Body Type_Normal   59.412529
9      Body Type_Stocky   11.108926


valid_y_pred = model.predict(valid_X)
valid_y_pred

array([ 2.66530045e+03,  2.39448807e+04,  1.52116766e+04,  2.42079729e+04,
        2.96013138e+04,  1.24219313e+04,  7.03030428e+03,  1.95690670e+04,
        1.65262949e+04, -1.47780320e+03,  1.30968036e+04,  1.46015036e+04,
        1.65416124e+04,  1.23451712e+04,  2.41133395e+04,  3.44640274e+04,
        1.67102936e+04,  1.29909076e+04,  3.97181605e+03,  2.20783678e+04,
        5.38322832e+03,  2.09776571e+04,  2.08805388e+04,  2.34148863e+04,
        1.06999140e+04, -5.56234183e+03,  1.17865372e+04,  2.23538133e+04,
        1.43890326e+04,  1.75954292e+04, -1.22354489e+02,  1.29628192e+04,
        8.41552263e+03,  2.27889941e+04,  2.31121184e+03,  1.94168827e+04,
       -6.96486103e+03,  1.37996432e+04,  3.27861195e+03,  2.86742008e+04,
        2.97875564e+04, -6.32773021e+03,  2.31928580e+04,  3.04579799e+03,
        1.54775276e+04,  2.42101352e+04, -5.84285114e+03, -1.29340208e+03,
        4.06247257e+03,  1.80227373e+04,  2.17889372e+04,  9.70873486e+03,
        8.02344053e+03,  1.92883880e+04,  1.77181908e+04,  2.18037493e+04,
       -4.33997863e+03,  1.56144785e+04,  9.71271318e+03,  2.05954475e+04,
        4.75178565e+03,  2.30383707e+04,  1.02677166e+04,  2.35779602e+04,
        9.87039872e+03,  1.68866474e+04, -1.31118203e+03,  8.87430877e+03,
        3.24007684e+03,  3.23350289e+04,  1.53211409e+04,  1.07576794e+03,
        1.62358353e+03,  1.73480299e+04,  1.79438503e+04,  2.49372041e+04,
        2.00529623e+04,  1.68100187e+04,  8.56136513e+03,  3.46264372e+04,
        2.54399862e+04,  4.68426335e+04,  9.91675364e+03,  1.83355436e+04,
        3.54108387e+04,  1.70138955e+04,  1.46236932e+04,  1.02365282e+04,
        1.62242848e+04,  2.37720957e+04,  3.08256560e+04,  1.59745648e+04,
        1.59032676e+04,  3.19791193e+04,  2.04379622e+04,  1.55905542e+04,
        2.37955466e+04,  1.04128105e+04,  9.19329209e+03,  4.21540077e+04,
        1.27777969e+04,  2.41864412e+04,  2.14468738e+04,  8.06144737e+03,
        2.36390151e+04,  1.44857796e+04,  2.78377031e+04,  2.65205841e+04,
        2.38842489e+03,  4.01141506e+04,  1.19248133e+04,  1.74026797e+04,
       -3.55892891e+03,  1.72208335e+04,  1.22610883e+04, -5.54908320e+03,
        9.56791282e+03,  3.64233850e+03,  3.18218976e+04,  1.47101698e+04,
        3.73624918e+03,  5.33297175e+03,  2.29637658e+04,  2.10020910e+03,
        2.39209825e+04,  4.18162608e+04,  3.26198242e+04,  3.84999758e+04,
        2.36460768e+03,  2.00953034e+03,  2.70110133e+04, -2.01391023e+03,
       -2.20258250e+03,  1.69663027e+04,  3.12074612e+04,  2.05483828e+02,
       -3.60379347e+03,  1.35194619e+03, -2.64933746e+03,  8.64132573e+03,
        1.58664227e+04,  1.67561284e+04,  1.34151485e+04,  3.70881499e+03,
        4.13986671e+03,  3.08144727e+04,  1.23279327e+04, -2.22148139e+01,
        5.57685656e+03,  2.56361861e+04,  2.59934302e+04,  1.34265919e+03,
        2.65983638e+04,  1.18370810e+04,  1.09183425e+04,  1.43909810e+04,
        3.88503740e+03, -2.33173138e+03,  2.02760295e+04,  1.87326850e+04,
        1.96038255e+04, -9.93766117e+03,  7.47558360e+03,  1.66588172e+04,
        1.16956311e+04,  3.90959788e+03,  7.51416417e+03,  2.06412445e+04,
        1.75336594e+04,  1.33414610e+04,  1.96836251e+03, -4.82880254e+03,
       -3.71099746e+02,  7.66629848e+03,  6.14881071e+03,  1.23687003e+04,
        1.21231323e+04,  1.35733402e+04,  1.83551007e+04,  1.70539379e+04,
        3.02524002e+04, -1.07159337e+04,  6.01304553e+03,  1.14180403e+04,
       -3.34690338e+03,  1.00622718e+04,  2.06918571e+04,  1.73350758e+04,
        2.29914945e+04, -5.50771205e+03,  2.85330575e+04,  1.98521492e+03,
        1.06942632e+04,  1.73230322e+04,  2.49513789e+03, -2.79106246e+03,
        4.39038348e+04,  1.43537643e+04,  1.85450045e+04, -6.16542967e+03,
        1.63629421e+04,  2.79125830e+04,  1.73431638e+04,  3.14934519e+04,
        4.66349422e+03,  1.16135024e+04,  3.35813201e+04,  4.53795643e+03,
        3.03687846e+04,  5.61531696e+03,  7.07152851e+03,  3.18497487e+04,
        1.53772460e+04,  2.67107658e+03,  2.33955389e+04,  2.40698188e+04,
       -4.75904102e+03, -3.45112153e+03,  2.41953892e+04,  1.23263230e+04,
        2.13734730e+04,  4.57129895e+03,  4.79790380e+03,  3.16235504e+04,
        2.16213142e+04,  1.75585724e+04,  5.23850275e+03,  1.36123705e+04,
        1.30277524e+04,  1.95346600e+04,  2.84475997e+03,  2.44038322e+04,
        7.41182434e+03,  1.37544881e+04, -7.02660112e+02,  1.64984689e+04,
        1.11341685e+04,  7.89961221e+03,  2.46923901e+04,  1.76240587e+04,
        8.96931690e+03,  6.48185568e+03, -1.26222354e+03, -1.69218974e+03,
        2.57214042e+03,  1.61502589e+04,  1.28138050e+04,  9.60814203e+03,
        1.63259753e+04,  6.50911760e+03, -9.95762340e+03,  3.42057372e+02,
        1.02190745e+04,  1.67276920e+04,  2.21600760e+04,  4.65490924e+03,
        1.25402256e+04,  1.61009022e+04,  1.90925692e+04,  1.98924863e+04,
        1.10061114e+04,  5.83648195e+03,  1.70692595e+04,  1.45910951e+04,
        2.66219412e+04,  8.48576063e+03,  1.69487687e+04,  2.99414092e+03,
        1.80086237e+04,  1.87362018e+04,  3.54003722e+04, -3.68164534e+02,
        2.37253161e+04,  2.03710982e+04,  1.20499329e+04,  2.47400389e+04,
       -7.52342461e+03,  2.49023341e+04,  6.50286770e+03,  4.85828603e+03,
        9.87788899e+03,  1.49300957e+04,  9.99666283e+03,  2.42095834e+04,
        2.23392492e+03,  3.87104769e+03,  1.84381152e+04,  1.99189419e+04,
        2.88502679e+04,  2.95576858e+03,  1.02739668e+04,  8.61212517e+03,
        3.79011769e+04,  1.18256155e+04,  6.26209526e+03,  2.04705359e+04,
        8.36627864e+03,  1.49795212e+03,  1.96112157e+04,  1.25041470e+04,
        3.33043822e+03,  8.02272601e+03,  6.30190884e+01,  1.38667489e+04,
       -2.66181757e+03,  2.41768675e+02,  1.19301758e+04,  1.17904093e+04,
        2.05007501e+04, -1.68721187e+04,  2.41243743e+04,  3.72096058e+03,
        6.75666851e+03,  1.58471520e+04,  1.94148247e+04,  1.48026594e+03,
        1.31713425e+04,  2.98162207e+04, -4.06148613e+03,  2.23375583e+04,
        1.19660384e+04,  2.43317954e+04,  5.31000984e+04,  1.79335761e+04,
        1.34151909e+04, -4.84794752e+03,  1.87710521e+04,  1.87750241e+04,
        2.12204070e+04,  2.20818928e+04,  1.15592485e+03, -1.04175449e+04,
       -3.17875690e+03,  2.90112257e+04,  1.69765732e+04,  2.60161382e+04,
        2.43898074e+04,  8.39128773e+02,  1.63886547e+04, -7.37612923e+03,
        5.62485527e+03,  6.74975491e+03,  1.22944936e+04,  1.33810595e+04,
        5.46762848e+03,  1.28159578e+04,  1.08639469e+04,  1.03348099e+03,
        1.63132754e+03,  1.44072810e+04,  1.84246280e+04, -2.47909605e+03,
        1.95474530e+04,  1.99982066e+04,  2.25021690e+04,  1.32872506e+04,
        3.28203363e+03,  9.06686227e+03,  2.45238371e+04,  1.33661644e+04,
       -1.14433324e+03,  1.01026574e+04,  2.07442960e+04,  1.01544218e+04,
        1.47549186e+04,  1.99151083e+04,  1.84707327e+04,  2.91420465e+03,
        1.55694684e+04,  1.98216015e+04,  7.22538464e+03,  1.59688520e+04,
        8.82264506e+03, -5.57106659e+03, -3.61325599e+03,  1.66954298e+04,
        6.04080018e+03,  5.64313195e+03,  2.34846318e+04,  4.95252927e+03,
        1.17609615e+04,  2.73460395e+02,  4.62524003e+04,  1.94219123e+04,
        2.67636958e+03,  7.99161270e+02,  3.45401861e+04,  2.59576995e+03,
        1.89228641e+04,  3.42841898e+04,  4.15955289e+03,  3.50195062e+04,
        2.12903857e+04, -5.06633274e+03,  1.72083042e+04,  1.09837661e+04,
        9.35620710e+03,  1.39696572e+04,  2.02365913e+04,  2.01273692e+04,
        4.92787054e+03,  2.75630232e+04,  1.94245386e+04,  1.78279991e+04,
        2.49990535e+04,  2.22097084e+04,  8.43216129e+03,  8.92326875e+02,
        5.49338576e+03,  1.95493159e+04,  1.06933156e+04,  1.17082833e+04,
        2.25027856e+04,  1.45716041e+04,  4.09754472e+03,  9.19128351e+03,
        7.77620947e+03,  1.90177070e+04,  1.96619616e+04,  4.66622488e+04,
        3.67881827e+03,  5.08111933e+03,  5.38303692e+03,  1.24476702e+04,
        1.84716579e+04, -1.31531118e+03,  2.03243896e+04,  1.86851668e+04,
        3.77256684e+03,  1.01734030e+04,  3.06560978e+04,  2.34528445e+04,
        1.83387120e+04,  1.40144687e+04,  1.65206404e+04,  3.96428102e+04,
        1.04960032e+04, -4.15137281e+03,  1.05653584e+04,  3.39106609e+04,
        2.97230029e+04,  1.53912380e+04,  1.11446062e+04,  2.24223425e+04,
        2.68597465e+04,  1.22405459e+04, -2.66504745e+03,  1.20825230e+04,
        2.03241862e+04, -3.92528017e+03,  5.56118121e+03, -5.96828907e+03,
        1.60675081e+04,  8.47372390e+03,  1.66574753e+04, -1.08819482e+04,
        2.20162527e+04,  1.36954201e+04,  1.52982927e+04,  2.86445902e+04,
        2.15596058e+04,  3.72854768e+03,  6.01809567e+03,  2.62442863e+04,
        1.78847640e+04,  2.60260009e+04,  2.21141255e+04, -2.91738379e+03,
        2.81612491e+04,  4.74778654e+04,  8.43042557e+03,  2.17905824e+04,
        1.78861898e+04,  2.81132855e+04,  2.24379049e+04,  4.87238954e+03,
        3.48894848e+04,  1.06339999e+04,  4.88834577e+03,  2.37027527e+04,
        2.77041377e+04,  1.67256495e+04, -1.23767615e+03,  2.45406129e+04,
       -6.73009778e+03, -3.71221165e+03,  1.87645554e+04,  3.45908317e+03,
        9.69112280e+03,  9.79096864e+03, -6.92458269e+03,  3.78754518e+03,
       -3.03440938e+03,  2.51852102e+04, -4.47402223e+03,  3.98987083e+04,
        2.19649914e+04,  1.91549960e+04,  8.60118620e+03,  2.05626620e+04,
       -3.69035608e+03,  1.48537949e+04,  4.04843946e+03,  3.16774267e+04,
        1.70576259e+04,  1.73557586e+03,  3.20480351e+04,  1.56235213e+04,
        5.63278927e+03,  2.32403127e+04,  2.46781892e+04,  7.00114435e+03,
       -3.58186265e+03,  2.21807504e+04, -6.37439516e+03,  7.92053004e+03,
        5.22713559e+03,  3.85323630e+03,  1.61069767e+04,  1.75678237e+04,
        1.81873006e+04,  1.00464058e+04,  8.84400565e+03,  1.72847394e+04,
        5.17322566e+02,  2.56655118e+04,  2.62752003e+04,  1.07591937e+04,
        1.51229379e+04,  1.93102802e+04,  9.00728050e+03,  2.97264751e+03,
       -1.65027255e+03,  1.94821918e+04, -4.41337726e+03,  1.89499469e+04,
        3.01911889e+01,  1.34545696e+04,  5.57215010e+03,  4.50681337e+02,
        3.92060784e+04,  1.32187052e+04,  1.10678007e+04,  1.06085720e+04,
       -4.72793002e+03,  2.23111111e+04,  4.89426890e+03,  1.58645569e+04,
       -4.78889524e+03,  2.36842533e+03,  3.30683841e+04,  4.89473966e+02,
        1.38929836e+04,  2.39812906e+04, -8.08396068e+03,  1.55943106e+04,
        2.26993605e+04,  3.51540327e+04,  3.59982676e+04,  2.57322782e+04,
        2.85020030e+04,  1.23762047e+04,  1.77077060e+04,  6.05218625e+02,
        2.12468521e+04,  1.98247308e+03,  9.75425736e+03,  1.91635760e+04,
        1.11030216e+04,  2.59148087e+04,  1.04661967e+04,  3.23588749e+04,
        3.13942429e+03, -4.08853810e+03,  1.52620187e+04, -1.58765960e+04,
        1.92577674e+04,  2.37955347e+04,  1.31788779e+04,  1.08961748e+04,
        1.81281065e+04,  1.83373496e+04,  9.36618933e+03,  2.37138764e+04,
        1.44469600e+04,  2.24502896e+02,  1.87964914e+04,  1.71068838e+04,
       -1.06577785e+03,  1.00160136e+04,  1.60681170e+04,  3.22133872e+04,
        2.30064316e+04,  6.75391713e+03,  1.60378128e+04,  1.32996181e+04,
       -1.49122318e+02,  8.22587441e+03,  3.26499372e+04,  1.85186487e+04,
       -4.30577382e+03,  1.16753828e+04,  5.05871265e+03,  4.04057843e+04,
        7.68904389e+03,  1.82256266e+04, -2.70297307e+03,  2.81515606e+04,
       -5.27176698e+03,  1.86762020e+04,  1.06676760e+04,  3.22475566e+04,
       -5.52105925e+03,  2.62373303e+04,  1.44986397e+04, -4.73905063e+03,
        3.65046624e+04,  4.02480572e+03,  8.28482915e+03,  1.95814608e+04,
        8.41202780e+03, -3.84857827e+03,  8.40586509e+03,  1.03176404e+04,
        2.43958443e+04,  1.38968987e+04,  3.67708230e+04,  1.72569153e+04,
        6.03696891e+03, -1.43788106e+03,  3.32488578e+04,  1.62319091e+04,
        1.61211529e+04,  4.90873986e+03,  9.34189590e+03, -5.86994130e+03,
        1.42400588e+04,  3.39109284e+02,  3.07350763e+03,  1.75517998e+04,
        1.60393277e+04,  5.81477513e+02, -1.61141500e+03,  2.06980825e+04,
        1.15261767e+04,  3.04436687e+04])


valid_y_pred_df = pd.DataFrame(valid_y_pred, columns = ["Validation_Prediction"])
valid_y_pred_df


mse_valid = sklearn.metrics.mean_squared_error(valid_y, valid_y_pred)
mse_valid

380956622.57514906


# As before
# import math

rmse_valid = math.sqrt(mse_valid)
rmse_valid

19518.110117917386


valid_y.describe()

count       646.000000
mean      13535.160991
std       23624.770667
min        1105.000000
25%        4708.750000
50%        6750.500000
75%       12827.750000
max      301070.000000
Name: Wage, dtype: float64


# As before:

# If using the dmba package:

# pip install dmba


# Done earlier. Just for illustration
# import dmba
# from dmba import regressionSummary

regressionSummary(valid_y, valid_y_pred)

Regression statistics

                      Mean Error (ME) : 91.4105
       Root Mean Squared Error (RMSE) : 19518.1101
            Mean Absolute Error (MAE) : 9319.7708
          Mean Percentage Error (MPE) : -43.3987
Mean Absolute Percentage Error (MAPE) : 118.8390


valid_residuals = valid_y - valid_y_pred
valid_residuals.head()

7882      2962.699548
14555     4930.119329
16210    -8270.676647
15847   -14063.972902
12382    16275.686201
Name: Wage, dtype: float64


import matplotlib.pyplot as plt
plt.hist(valid_residuals, bins = 30)
plt.title("Residuals for Validation")
plt.show()


valid_residuals_df = valid_residuals.to_frame(name = "Wage_Residuals")
valid_residuals_df


import matplotlib.pyplot as plt

plt.hist(valid_residuals_df["Wage_Residuals"], bins = 30)
plt.title("Residuals for Validation")
plt.show()


import statsmodels.api as sm


model_statsmodels = sm.OLS(train_y, train_X)


results = model_statsmodels.fit()
print(results.summary())

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                   Wage   R-squared (uncentered):                   0.515
Model:                            OLS   Adj. R-squared (uncentered):              0.512
Method:                 Least Squares   F-statistic:                              159.1
Date:                Sat, 18 Feb 2023   Prob (F-statistic):                   4.36e-227
Time:                        13:25:45   Log-Likelihood:                         -16865.
No. Observations:                1506   AIC:                                  3.375e+04
Df Residuals:                    1496   BIC:                                  3.380e+04
Df Model:                          10                                                  
Covariance Type:            nonrobust                                                  
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
Age                   -852.0938    127.623     -6.677      0.000   -1102.432    -601.756
Balance                151.9979     40.583      3.745      0.000      72.392     231.604
ShotPower              633.7931     85.723      7.393      0.000     465.642     801.944
Aggression              15.2246     36.329      0.419      0.675     -56.037      86.486
Positioning            716.7647     94.926      7.551      0.000     530.562     902.968
Composure              382.7540     81.366      4.704      0.000     223.151     542.357
Preferred Foot_Right  -493.9671   1360.831     -0.363      0.717   -3163.306    2175.372
Body Type_Lean       -8.622e+04   4538.366    -18.999      0.000   -9.51e+04   -7.73e+04
Body Type_Normal     -8.807e+04   4632.299    -19.011      0.000   -9.72e+04    -7.9e+04
Body Type_Stocky     -8.937e+04   4906.471    -18.216      0.000    -9.9e+04   -7.97e+04
==============================================================================
Omnibus:                     2072.969   Durbin-Watson:                   1.959
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           660076.649
Skew:                           7.548   Prob(JB):                         0.00
Kurtosis:                     104.446   Cond. No.                     2.46e+03
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 2.46e+03. This might indicate that there are
strong multicollinearity or other numerical problems.


new_players_df = pd.read_csv("new_players.csv")
new_players_df


new_records_players_pred = model.predict(new_players_df)
new_records_players_pred

array([29318.86943019, 20847.31938856, 29120.84519698])


# As before
# import pandas as pd

new_records_players_pred_df = pd.DataFrame(new_records_players_pred, columns = ["Prediction"])
new_records_players_pred_df

# to export
# new_records_players_pred_df.to_csv("whatever_name.csv")


alpha = 0.05
ci = np.quantile(train_residuals, 1 - alpha)
ci

17225.89938935508


def generate_results_confint(preds, ci):
    df = pd.DataFrame()
    df["Prediction"] = preds
    if ci >= 0:
        df["upper"] = preds + ci
        df["lower"] = preds - ci
    else:
        df["upper"] = preds - ci
        df["lower"] = preds + ci
        
    return df


new_records_players_pred_confint_df = generate_results_confint(new_records_players_pred, ci)
new_records_players_pred_confint_df


train_X.dtypes

Age                       int64
Balance                 float64
ShotPower               float64
Aggression              float64
Positioning             float64
Composure               float64
Preferred Foot_Right      uint8
Body Type_Lean            uint8
Body Type_Normal          uint8
Body Type_Stocky          uint8
dtype: object


train_X_variables_df = pd.DataFrame(train_X.columns.values, columns = ["Variables"])
train_X_variables_df


train_X_log10 = np.log10(train_X.iloc[:,0:6])
train_X_log10.head()


train_X2 = pd.concat((train_X_log10, train_X.iloc[:,6:10]), axis = 1)
train_X2.head()


valid_X_log10 = np.log10(valid_X.iloc[:,0:6])
valid_X_log10.head()


valid_X2 = pd.concat((valid_X_log10, valid_X.iloc[:,6:10]), axis = 1)
valid_X2.head()


train_y2 = np.log10(train_y)
train_y2

13946    4.352414
7711     3.829947
8402     3.730540
13651    4.137069
1625     4.022057
           ...   
12759    4.345805
17284    3.818556
1016     4.047158
16984    4.066773
16744    4.419972
Name: Wage, Length: 1506, dtype: float64


valid_y2 = np.log10(valid_y)
valid_y2

7882     3.750354
14555    4.460522
16210    3.841422
15847    4.006209
12382    4.661595
           ...   
8620     3.780821
10786    3.643354
16154    4.535775
4990     3.535800
14654    4.214764
Name: Wage, Length: 646, dtype: float64


import sklearn
from sklearn.linear_model import LinearRegression


model2 = LinearRegression()


model2.fit(train_X2, train_y2)

LinearRegression()


train_y2_pred = model2.predict(train_X2)
train_y2_pred

array([4.16670693, 3.70430495, 3.5309925 , ..., 4.08446948, 4.07971215,
       4.12972782])


train_y2_pred_df = pd.DataFrame(train_y2_pred, columns = ["Training_Prediction"])
train_y2_pred_df


print("model intercept: ", model2.intercept_)
print("model coefficients: ", model2.coef_)
print("Model score: ", model2.score(train_X2, train_y2))

model intercept:  -2.8669058840786708
model coefficients:  [-0.74070881  0.14474169  1.64201441  0.09668163  1.83662843  1.15205982
  0.00265055 -0.95251776 -0.96819688 -0.9947823 ]
Model score:  0.4981172727732758


print(pd.DataFrame({"Predictor": train_X2.columns, "Coefficient": model2.coef_}))

              Predictor  Coefficient
0                   Age    -0.740709
1               Balance     0.144742
2             ShotPower     1.642014
3            Aggression     0.096682
4           Positioning     1.836628
5             Composure     1.152060
6  Preferred Foot_Right     0.002651
7        Body Type_Lean    -0.952518
8      Body Type_Normal    -0.968197
9      Body Type_Stocky    -0.994782


mse_train_2 = sklearn.metrics.mean_squared_error(train_y2, train_y2_pred)
mse_train_2

0.06356591642873398


import math


rmse_train_2 = math.sqrt(mse_train_2)
rmse_train_2

0.25212282012688575


train_y2.describe()

count    1506.000000
mean        3.904520
std         0.356004
min         3.110590
25%         3.671404
50%         3.815843
75%         4.092168
max         5.610244
Name: Wage, dtype: float64


import dmba
from dmba import regressionSummary


regressionSummary(train_y2, train_y2_pred)

Regression statistics

                      Mean Error (ME) : -0.0000
       Root Mean Squared Error (RMSE) : 0.2521
            Mean Absolute Error (MAE) : 0.1955
          Mean Percentage Error (MPE) : -0.3879
Mean Absolute Percentage Error (MAPE) : 4.9901


import numpy as np
from scipy.stats import shapiro

shapiro(train_y2)

ShapiroResult(statistic=0.9299247860908508, pvalue=5.641337850676267e-26)


train_residuals_2 = train_y2 - train_y2_pred
train_residuals_2

13946    0.185707
7711     0.125642
8402     0.199548
13651   -0.091927
1625     0.051814
           ...   
12759    0.150935
17284   -0.266274
1016    -0.037311
16984   -0.012939
16744    0.290244
Name: Wage, Length: 1506, dtype: float64


shapiro(train_residuals_2)

ShapiroResult(statistic=0.9941757917404175, pvalue=1.2548777704068925e-05)


from statsmodels.stats.outliers_influence import variance_inflation_factor

vif_df_2 = pd.DataFrame()

vif_df_2["features"] = train_X.columns
vif_df_2["VIF"] = [variance_inflation_factor(train_X2.values, i) for i in range(train_X2.shape[1])]

print(vif_df_2)

               features          VIF
0                   Age   503.047038
1               Balance   392.228433
2             ShotPower  2230.845164
3            Aggression   224.646809
4           Positioning  2688.086015
5             Composure  1657.030037
6  Preferred Foot_Right     7.725654
7        Body Type_Lean   234.209226
8      Body Type_Normal   421.031902
9      Body Type_Stocky    71.646782


valid_y2_pred = model2.predict(valid_X2)
valid_y2_pred

array([3.76367355, 4.15529918, 4.02761799, 4.17061134, 4.27664223,
       3.90982955, 3.86919134, 4.05394802, 4.07575135, 3.58962247,
       3.90714578, 3.99290823, 3.95256648, 3.85413803, 4.19055898,
       4.3770946 , 4.06555802, 4.0018328 , 3.71793422, 4.15389889,
       3.75427973, 4.11372724, 4.04790165, 4.16199766, 3.81913817,
       3.45592807, 3.85618089, 4.11258275, 4.01680881, 4.0156488 ,
       3.57791354, 3.92013811, 3.93333019, 4.15243617, 3.64206255,
       4.05268594, 3.55963358, 3.93038411, 3.65549926, 4.26277204,
       4.2957239 , 3.407724  , 4.0802973 , 3.71756546, 4.01320061,
       4.15470805, 3.43053436, 3.58982582, 3.77744561, 4.05297243,
       4.1264634 , 3.86412457, 3.80646696, 4.10663088, 4.0277011 ,
       4.10682818, 3.4907613 , 3.9930389 , 3.7844055 , 4.07632993,
       3.74574599, 4.13168887, 3.93609012, 4.15447129, 3.8351393 ,
       3.98164635, 3.70036723, 3.83283241, 3.6957984 , 4.32483198,
       3.97680842, 3.64890098, 3.68376159, 4.02159597, 4.04864317,
       4.17927691, 4.07174931, 3.99436296, 3.89363006, 4.35326354,
       4.1946218 , 4.55669742, 3.83271191, 4.02022325, 4.38496503,
       3.99722499, 3.93647576, 3.89577843, 3.99995635, 4.17175375,
       4.29133548, 4.0160841 , 3.98917806, 4.31295093, 4.10110026,
       4.01077971, 4.15171613, 3.93406065, 3.92381907, 4.47762954,
       3.86056946, 4.14341326, 4.10795381, 3.78488352, 4.13184288,
       3.96830151, 4.22809601, 4.17370611, 3.70893568, 4.41445846,
       3.9860071 , 4.03624456, 3.54130701, 3.97681342, 3.93321275,
       3.40274183, 3.77377519, 3.7484716 , 4.31232063, 3.99361937,
       3.709269  , 3.76580361, 4.12616882, 3.62756573, 4.10717141,
       4.4300846 , 4.26733575, 4.42559001, 3.68110372, 3.63376597,
       4.20690577, 3.55348096, 3.58817486, 4.0028743 , 4.31354532,
       3.60417179, 3.46791211, 3.63460305, 3.52797995, 3.80240164,
       3.99804681, 4.07003803, 3.96740854, 3.67782452, 3.7088948 ,
       4.29154294, 3.91117274, 3.68003573, 3.72960344, 4.20021854,
       4.16794103, 3.68047068, 4.24551816, 3.89801283, 3.85297611,
       3.93996911, 3.79674516, 3.5260676 , 4.08968162, 4.04203417,
       4.08326129, 3.31249389, 3.78856385, 4.03608251, 3.97750166,
       3.73639092, 3.89686649, 4.08641956, 4.02202326, 3.95785434,
       3.66121658, 3.47142139, 3.68216025, 3.79270249, 3.74367342,
       3.90196004, 3.99075541, 3.9180192 , 4.06335476, 4.00007676,
       4.27009768, 3.31072324, 3.74364683, 3.93199629, 3.66915503,
       3.86109118, 4.12719138, 4.02302088, 4.12066631, 3.46212247,
       4.24516929, 3.60772261, 3.86266376, 4.0068775 , 3.64991768,
       3.57821803, 4.51164804, 3.86884302, 4.02278378, 3.40892806,
       4.00929465, 4.27441749, 4.04650643, 4.31664087, 3.79570229,
       3.87387915, 4.33204612, 3.73025151, 4.26612984, 3.739114  ,
       3.79062207, 4.35863673, 3.9667509 , 3.65394184, 4.08544516,
       4.21615412, 3.61137378, 3.47775978, 4.18257474, 3.94734872,
       4.09660859, 3.86340944, 3.76653697, 4.28916253, 4.12961482,
       4.01531056, 3.73242103, 3.92353868, 4.01528881, 4.05693391,
       3.64922279, 4.13251124, 3.78851204, 3.96812818, 3.60234792,
       4.02649726, 3.87836136, 3.78527889, 4.17130734, 4.01839531,
       3.87736521, 3.84803085, 3.56809734, 3.53356624, 3.74931027,
       3.93071361, 3.92688701, 3.82006385, 3.99352542, 3.78762902,
       3.3088708 , 3.6389334 , 3.85878766, 3.99660732, 4.15405735,
       3.77264981, 3.96080938, 4.00249334, 4.06460802, 4.07503455,
       3.92041065, 3.77078081, 4.00051175, 4.01299821, 4.22032504,
       3.83147516, 4.01829502, 3.77217185, 4.04027499, 4.04894302,
       4.37009593, 3.66198416, 4.16404301, 4.07537538, 3.81702852,
       4.18393764, 3.38560675, 4.15056587, 3.76938473, 3.66133542,
       3.83298873, 3.96379047, 3.88700295, 4.11912182, 3.76007694,
       3.6960155 , 4.1211959 , 4.04400082, 4.21272665, 3.69404658,
       3.87553024, 3.82367299, 4.44392643, 3.90035329, 3.82670037,
       4.09651587, 3.81539836, 3.62901484, 4.12364698, 3.87491952,
       3.60137225, 3.8373793 , 3.60737549, 4.02177599, 3.50538178,
       3.6237138 , 3.95906308, 3.93927344, 4.0979651 , 3.06117595,
       4.11487814, 3.71943094, 3.7607101 , 4.00325951, 4.07500449,
       3.63075039, 3.90162744, 4.24153272, 3.55020114, 4.11677891,
       3.9519506 , 4.19331594, 4.64906177, 4.08705043, 3.91322188,
       3.4643572 , 4.07389286, 4.01613118, 4.13090872, 4.12330112,
       3.67620387, 3.3069908 , 3.50331655, 4.22838468, 4.06350805,
       4.23418359, 4.16447788, 3.6789202 , 3.97233518, 3.39431118,
       3.83794578, 3.83635319, 3.94286729, 3.9122974 , 3.85503556,
       3.92286221, 3.86449427, 3.61902976, 3.64006414, 3.9710172 ,
       4.06949047, 3.51857609, 4.06396503, 4.08485153, 4.16137828,
       3.96409872, 3.72730472, 3.92930897, 4.18743676, 3.9411608 ,
       3.66906524, 3.85038249, 4.04403355, 3.91918519, 4.06720527,
       4.12111189, 4.01383475, 3.61697527, 3.97950546, 4.08334525,
       3.78934118, 3.959101  , 3.80638364, 3.45757572, 3.49770466,
       4.0626396 , 3.71218504, 3.8107466 , 4.14436282, 3.74999602,
       3.92760265, 3.58786307, 4.53483917, 4.02076808, 3.79226698,
       3.70145343, 4.35696259, 3.60565745, 4.05148097, 4.35182707,
       3.69722441, 4.35512404, 4.10090967, 3.44589242, 3.94972836,
       3.88857535, 3.93084888, 3.98319886, 4.12587376, 4.06091435,
       3.76180862, 4.22510036, 4.04137816, 4.0553892 , 4.19899674,
       4.09319953, 3.78428264, 3.64991702, 3.8155647 , 4.08733891,
       3.9064268 , 3.90981766, 4.119122  , 3.95709316, 3.80575735,
       3.83523119, 3.79857318, 4.045406  , 4.0474044 , 4.56175315,
       3.75433912, 3.82384601, 3.81895492, 3.98409788, 4.04380715,
       3.56992826, 4.08171437, 4.09281733, 3.62415787, 3.89357785,
       4.32357572, 4.16051063, 4.0979448 , 3.97747216, 3.96721426,
       4.43209841, 3.89480226, 3.49403115, 3.85021414, 4.31085473,
       4.26492488, 3.96203775, 3.96303963, 4.13080105, 4.2010063 ,
       3.9434954 , 3.55218052, 3.90594563, 4.11490189, 3.53312359,
       3.86513143, 3.46451959, 3.95465407, 3.80188125, 4.02308478,
       3.27226357, 4.15753532, 3.94023949, 4.01913372, 4.22553447,
       4.07815829, 3.74204974, 3.81970664, 4.2039179 , 4.02616824,
       4.13984176, 4.1229543 , 3.55495757, 4.21420044, 4.56258001,
       3.88078398, 4.1247032 , 4.04834385, 4.27668304, 4.12747814,
       3.76683153, 4.33579598, 3.93189263, 3.72548763, 4.18447111,
       4.23916186, 4.03404372, 3.61674952, 4.17929048, 3.41112525,
       3.49051379, 4.09164834, 3.77737006, 3.82334394, 3.8455094 ,
       3.40492441, 3.70119257, 3.53003948, 4.18349422, 3.47598818,
       4.44548399, 4.07921488, 4.03500231, 3.78440745, 4.10491587,
       3.47807912, 3.92702743, 3.612196  , 4.24948279, 4.05430833,
       3.63814312, 4.31071604, 4.02682925, 3.79727886, 4.17466371,
       4.1356379 , 3.72467379, 3.67319298, 4.14294685, 3.40578843,
       3.8218298 , 3.80856988, 3.69074869, 3.97580986, 4.05361426,
       4.06683376, 3.93669446, 3.90456332, 3.99560591, 3.66866854,
       4.13639514, 4.1891806 , 3.89513874, 4.00730782, 4.06946615,
       3.86813897, 3.75452134, 3.55861187, 4.12137531, 3.44527625,
       4.08483195, 3.5823102 , 4.00056343, 3.81471346, 3.59462776,
       4.41776481, 3.90334739, 3.94811114, 3.93948265, 3.37279971,
       4.09378912, 3.71299135, 3.94671423, 3.49139588, 3.66989535,
       4.34275382, 3.58419407, 3.98424773, 4.15901486, 3.38451984,
       3.92587981, 4.11555836, 4.35077569, 4.33447151, 4.18984644,
       4.20444188, 3.98738318, 4.02013942, 3.6510333 , 4.14290566,
       3.63184601, 3.90346708, 4.05734256, 3.89546729, 4.20709072,
       3.91355501, 4.30099848, 3.65052262, 3.45561065, 3.93542772,
       3.1519519 , 4.09416062, 4.12392262, 3.90775453, 3.85970599,
       4.02417249, 3.98409722, 3.85601473, 4.18887768, 3.9512208 ,
       3.63514546, 4.04710009, 3.94807166, 3.5565326 , 3.84958316,
       3.98819984, 4.3147352 , 4.14870834, 3.79284242, 3.9958641 ,
       3.95117854, 3.69148335, 3.82822223, 4.30014425, 4.06913287,
       3.50836167, 3.8211041 , 3.8298556 , 4.42267047, 3.84580223,
       4.06574794, 3.47712171, 4.18324774, 3.55245306, 4.05191393,
       3.91601428, 4.32217236, 3.42756651, 4.19186723, 3.97225306,
       3.55904222, 4.39020702, 3.78896984, 3.87030635, 4.06807547,
       3.82900839, 3.41678228, 3.79877734, 3.886422  , 4.17168873,
       3.89690427, 4.38305566, 4.01866806, 3.78008935, 3.62017101,
       4.3320427 , 3.96860992, 4.02460072, 3.73670569, 3.83703631,
       3.42525497, 3.93023985, 3.58773105, 3.68050587, 4.01015867,
       4.00341998, 3.66600645, 3.52794768, 4.10312619, 3.88325128,
       4.26631878])


valid_y2_pred_df = pd.DataFrame(valid_y2_pred, columns = ["Validation_Prediction"])
valid_y2_pred_df


mse_valid_2 = sklearn.metrics.mean_squared_error(valid_y2, valid_y2_pred)
mse_valid_2

0.06790509555931858


# As before
# import math

rmse_valid_2 = math.sqrt(mse_valid_2)
rmse_valid_2

0.2605860617134358


valid_y2.describe()

count    646.000000
mean       3.915194
std        0.373620
min        3.043362
25%        3.672905
50%        3.829336
75%        4.108147
max        5.478667
Name: Wage, dtype: float64


# As before:

# If using the dmba package:

# pip install dmba


# Done earlier. Just for illustration
# import dmba
# from dmba import regressionSummary

regressionSummary(valid_y2, valid_y2_pred)

Regression statistics

                      Mean Error (ME) : -0.0105
       Root Mean Squared Error (RMSE) : 0.2606
            Mean Absolute Error (MAE) : 0.2020
          Mean Percentage Error (MPE) : -0.7122
Mean Absolute Percentage Error (MAPE) : 5.1776


new_players_df


new_players_df_log10 = np.log10(new_players_df.iloc[:,0:6])
new_players_df_log10.head()


new_players_df_2 = pd.concat((new_players_df_log10, new_players_df.iloc[:,6:10]), axis = 1)
new_players_df_2


new_records_players_pred_2 = model2.predict(new_players_df_2)
new_records_players_pred_2

array([4.25518124, 4.07711107, 4.17585671])


# As before
# import pandas as pd

new_records_players_pred_df_2 = pd.DataFrame(new_records_players_pred_2, columns = ["Prediction"])
new_records_players_pred_df_2

# to export
# new_records_players_pred_df.to_csv("whatever_name.csv")


alpha = 0.05
ci_2 = np.quantile(train_residuals_2, 1 - alpha)
ci_2

0.43633371119162057


# as before

def generate_results_confint_2(preds, ci_2):
    df = pd.DataFrame()
    df["Prediction"] = preds
    if ci >= 0:
        df["upper"] = preds + ci_2
        df["lower"] = preds - ci_2
    else:
        df["upper"] = preds - ci_2
        df["lower"] = preds + ci_2
    return df


new_records_players_pred_2_confint_df = generate_results_confint_2(new_records_players_pred_2, ci_2)
new_records_players_pred_2_confint_df


def exp10(x):
    return 10**x
 
# execute the function
new_records_players_pred_df_2_exp = new_records_players_pred_2_confint_df.apply(exp10)
new_records_players_pred_df_2_exp


train_X3 = train_X.copy()
train_y3 = train_y.copy()
valid_X3 = valid_X.copy()
valid_y3 = valid_y.copy()


from sklearn.linear_model import Ridge

model_ridge = Ridge(alpha = 1.0)
model_ridge.fit(train_X3, train_y3)

Ridge()


from sklearn.linear_model import Ridge

model_ridge = Ridge(alpha = 1.0)
model_ridge.fit(train_X3, train_y3)

Ridge()


train_y3_pred = model_ridge.predict(train_X3)
train_y3_pred

array([25188.51155671,  3860.14487559, -4188.44855596, ...,
       19245.95968925, 21417.50420002, 23004.19110446])


train_y3_pred_df = pd.DataFrame(train_y3_pred, columns = ["Training_Prediction"])
train_y3_pred_df


print("model intercept: ", model_ridge.intercept_)
print("model coefficients: ", model_ridge.coef_)
print("Model score: ", model_ridge.score(train_X3, train_y3))

model intercept:  20081.83125341736
model coefficients:  [-9.27897306e+02  5.45457726e+01  5.02883492e+02  2.41877047e+01
  6.53156518e+02  4.20617179e+02 -1.86591933e+03 -8.72301759e+04
 -8.86049391e+04 -8.90541217e+04]
Model score:  0.3608967032383109


print(pd.DataFrame({"Predictor": train_X3.columns, "Coefficient": model_ridge.coef_}))

              Predictor   Coefficient
0                   Age   -927.897306
1               Balance     54.545773
2             ShotPower    502.883492
3            Aggression     24.187705
4           Positioning    653.156518
5             Composure    420.617179
6  Preferred Foot_Right  -1865.919332
7        Body Type_Lean -87230.175924
8      Body Type_Normal -88604.939142
9      Body Type_Stocky -89054.121691


mse_train_3 = sklearn.metrics.mean_squared_error(train_y3, train_y3_pred)
mse_train_3

308594700.68349236


import math


rmse_train_3 = math.sqrt(mse_train_3)
rmse_train_3

17566.86371221375


train_y3.describe()

count      1506.000000
mean      12698.381142
std       21981.278007
min        1290.000000
25%        4692.500000
50%        6544.000000
75%       12364.250000
max      407609.000000
Name: Wage, dtype: float64


import dmba
from dmba import regressionSummary


regressionSummary(train_y3, train_y3_pred)

Regression statistics

                      Mean Error (ME) : -0.0000
       Root Mean Squared Error (RMSE) : 17566.8637
            Mean Absolute Error (MAE) : 8938.7057
          Mean Percentage Error (MPE) : -31.3821
Mean Absolute Percentage Error (MAPE) : 117.8144


import numpy as np
from scipy.stats import shapiro

shapiro(train_y3)

ShapiroResult(statistic=0.38412952423095703, pvalue=0.0)


train_residuals_3 = train_y3 - train_y3_pred
train_residuals_3

13946    -2676.511557
7711      2899.855124
8402      9565.448556
13651   -16284.100230
1625     -5588.083754
             ...     
12759    -4657.388840
17284   -16198.529768
1016     -8098.959689
16984    -9755.504200
16744     3296.808896
Name: Wage, Length: 1506, dtype: float64


shapiro(train_residuals_3)

ShapiroResult(statistic=0.5465858578681946, pvalue=0.0)


from statsmodels.stats.outliers_influence import variance_inflation_factor

vif_df_3 = pd.DataFrame()

vif_df_3["features"] = train_X3.columns
vif_df_3["VIF"] = [variance_inflation_factor(train_X3.values, i) for i in range(train_X3.shape[1])]

print(vif_df_3)

               features         VIF
0                   Age   48.741902
1               Balance   33.364691
2             ShotPower  155.270485
3            Aggression   18.482052
4           Positioning  184.558829
5             Composure  115.774481
6  Preferred Foot_Right    7.714600
7        Body Type_Lean   32.118906
8      Body Type_Normal   59.412529
9      Body Type_Stocky   11.108926


valid_y3_pred = model_ridge.predict(valid_X3)
valid_y3_pred

array([ 2.64972256e+03,  2.52642557e+04,  1.64240635e+04,  2.53329585e+04,
        3.10955126e+04,  1.29528286e+04,  6.70941044e+03,  2.04919113e+04,
        1.67847671e+04, -1.77608909e+03,  1.37232569e+04,  1.48205527e+04,
        1.60211714e+04,  1.10493542e+04,  2.52134500e+04,  3.59934836e+04,
        1.78365347e+04,  1.32628212e+04,  4.48094205e+03,  2.29869164e+04,
        4.96584554e+03,  2.16229676e+04,  2.09228408e+04,  2.42567025e+04,
        1.03654164e+04, -6.30245310e+03,  1.23663735e+04,  2.36282687e+04,
        1.49069805e+04,  1.72923603e+04, -1.41187798e+03,  1.21934953e+04,
        8.99116266e+03,  2.36012248e+04,  2.03620098e+03,  1.97430366e+04,
       -7.88156562e+03,  1.42296144e+04,  3.02349161e+03,  2.98615135e+04,
        3.17155746e+04, -7.45185605e+03,  2.36998503e+04,  2.10088321e+03,
        1.55835468e+04,  2.53623215e+04, -6.50981532e+03, -1.76196097e+03,
        3.62986525e+03,  1.82776299e+04,  2.19955432e+04,  9.56082725e+03,
        7.90816856e+03,  1.95834541e+04,  1.78544369e+04,  2.23809073e+04,
       -4.90366027e+03,  1.54642694e+04,  9.31753268e+03,  2.15480020e+04,
        4.57990856e+03,  2.33541602e+04,  1.11657541e+04,  2.46551380e+04,
        9.84817425e+03,  1.63822774e+04, -1.80807030e+03,  8.69464783e+03,
        2.72496530e+03,  3.43697545e+04,  1.59330718e+04,  9.17012681e+02,
        1.66581487e+03,  1.76629155e+04,  1.83800182e+04,  2.65577927e+04,
        2.01509977e+04,  1.71244262e+04,  8.74705677e+03,  3.58738523e+04,
        2.65122746e+04,  5.00604302e+04,  9.64618370e+03,  1.90684929e+04,
        3.70800559e+04,  1.66337474e+04,  1.47011831e+04,  1.01626727e+04,
        1.62589786e+04,  2.47699032e+04,  3.16840751e+04,  1.74982126e+04,
        1.63608869e+04,  3.31509430e+04,  2.07902205e+04,  1.64597306e+04,
        2.47251371e+04,  1.04628862e+04,  9.57437075e+03,  4.42431055e+04,
        1.26561720e+04,  2.55199260e+04,  2.23256682e+04,  8.14743820e+03,
        2.45764795e+04,  1.48054501e+04,  2.85598619e+04,  2.72748441e+04,
        1.65894359e+03,  4.17885584e+04,  1.22392050e+04,  1.80790225e+04,
       -4.47457671e+03,  1.78499306e+04,  1.31001658e+04, -6.64508399e+03,
        9.19121426e+03,  3.15130742e+03,  3.35840483e+04,  1.53441534e+04,
        3.51981089e+03,  5.40674384e+03,  2.42962197e+04,  1.77612088e+03,
        2.46176244e+04,  4.35989119e+04,  3.41348306e+04,  4.02437061e+04,
        1.66983814e+03,  2.16856079e+03,  2.83205082e+04, -2.41088911e+03,
       -2.36682760e+03,  1.76805901e+04,  3.30181153e+04, -3.41788605e+02,
       -4.42985144e+03,  9.78417778e+02, -3.41201914e+03,  8.68924567e+03,
        1.65537818e+04,  1.72906353e+04,  1.33560660e+04,  3.40153805e+03,
        4.03253553e+03,  3.19964770e+04,  1.20998236e+04, -8.26064462e+02,
        5.55617913e+03,  2.71488508e+04,  2.68272814e+04,  1.14432826e+03,
        2.83124624e+04,  1.15858075e+04,  1.08250398e+04,  1.51075765e+04,
        3.30687121e+03, -2.76195568e+03,  2.12094054e+04,  1.88687090e+04,
        2.04936705e+04, -1.09126099e+04,  7.30930490e+03,  1.67882716e+04,
        1.15685907e+04,  3.14702931e+03,  7.35938167e+03,  2.13262354e+04,
        1.84566066e+04,  1.42514599e+04,  1.65441942e+03, -5.65924431e+03,
       -1.00778426e+03,  7.51549323e+03,  5.67264855e+03,  1.22640084e+04,
        1.33564333e+04,  1.36739531e+04,  1.90346104e+04,  1.79189151e+04,
        3.18978213e+04, -1.20856433e+04,  5.73937028e+03,  1.16894482e+04,
       -3.87423563e+03,  1.00288060e+04,  2.20562707e+04,  1.74938502e+04,
        2.37843794e+04, -6.23145484e+03,  2.94267502e+04,  1.48092211e+03,
        9.80861441e+03,  1.81335960e+04,  1.85554394e+03, -3.94264372e+03,
        4.56839001e+04,  1.39029242e+04,  1.91594303e+04, -7.49391130e+03,
        1.66476248e+04,  2.94697109e+04,  1.76200685e+04,  3.27957846e+04,
        4.31614870e+03,  1.19215192e+04,  3.51546196e+04,  4.07900156e+03,
        3.19670958e+04,  5.19281830e+03,  7.22590148e+03,  3.36253366e+04,
        1.55881255e+04,  2.49167421e+03,  2.48504689e+04,  2.55159442e+04,
       -4.77474929e+03, -4.42846792e+03,  2.59056546e+04,  1.26388624e+04,
        2.15742548e+04,  4.08688167e+03,  5.14702418e+03,  3.31563915e+04,
        2.27265145e+04,  1.79822987e+04,  4.88434587e+03,  1.41505327e+04,
        1.41902561e+04,  2.02603488e+04,  2.05241854e+03,  2.55923095e+04,
        7.44893187e+03,  1.39030195e+04, -2.08543587e+03,  1.76049436e+04,
        1.16541566e+04,  7.37981695e+03,  2.52979520e+04,  1.82726281e+04,
        8.90597823e+03,  6.23015687e+03, -1.55508696e+03, -2.63008981e+03,
        2.13902693e+03,  1.61152051e+04,  1.22182585e+04,  9.64623645e+03,
        1.63859443e+04,  6.14276618e+03, -1.11170706e+04,  2.10258398e+02,
        9.68578502e+03,  1.69246037e+04,  2.31236071e+04,  3.64414735e+03,
        1.25187206e+04,  1.70574873e+04,  1.90115826e+04,  2.04687259e+04,
        1.10294579e+04,  6.15333543e+03,  1.71130713e+04,  1.49853247e+04,
        2.73762381e+04,  8.27010205e+03,  1.71023730e+04,  2.89285921e+03,
        1.92188863e+04,  1.92121483e+04,  3.67284627e+04, -6.07554785e+02,
        2.50715536e+04,  2.16535634e+04,  1.15711762e+04,  2.61352627e+04,
       -8.60774818e+03,  2.55153591e+04,  6.52033108e+03,  3.83335571e+03,
        1.01184551e+04,  1.49659750e+04,  1.01356377e+04,  2.50175606e+04,
        1.87688328e+03,  3.39055929e+03,  1.94403783e+04,  2.04072294e+04,
        2.95313635e+04,  1.93304405e+03,  1.03166764e+04,  8.90465883e+03,
        4.03368608e+04,  1.15774038e+04,  6.91783988e+03,  2.08803031e+04,
        7.72041122e+03,  7.47676798e+02,  2.04555233e+04,  1.13323091e+04,
        2.19823569e+03,  8.45970953e+03, -1.60356018e+02,  1.51640672e+04,
       -3.23890555e+03, -5.41129809e+02,  1.18993186e+04,  1.17328722e+04,
        2.14902835e+04, -1.84628171e+04,  2.48351686e+04,  3.78260306e+03,
        6.02224315e+03,  1.64688353e+04,  1.97621129e+04,  9.78325175e+02,
        1.26317064e+04,  3.04878019e+04, -5.12399165e+03,  2.35210556e+04,
        1.21487080e+04,  2.50761478e+04,  5.54846852e+04,  1.81841465e+04,
        1.40340286e+04, -5.67563080e+03,  1.93854989e+04,  1.91248164e+04,
        2.23340938e+04,  2.27299834e+04,  5.01194389e+02, -1.15661438e+04,
       -3.77023194e+03,  3.00930391e+04,  1.72765208e+04,  2.69024012e+04,
        2.54266342e+04,  7.74975266e+02,  1.64742338e+04, -8.23238191e+03,
        4.84693210e+03,  6.87596180e+03,  1.32836570e+04,  1.37999954e+04,
        5.47063742e+03,  1.32036417e+04,  1.09850059e+04,  7.52434673e+02,
        1.40420709e+03,  1.45256380e+04,  1.92371576e+04, -2.95672651e+03,
        1.96692843e+04,  2.09792274e+04,  2.30787686e+04,  1.31057062e+04,
        2.81278489e+03,  9.19501376e+03,  2.54078773e+04,  1.39056907e+04,
       -1.48998032e+03,  9.43590431e+03,  2.08441471e+04,  1.08298218e+04,
        1.57316997e+04,  2.06514061e+04,  1.89700762e+04,  1.97035528e+03,
        1.53088095e+04,  2.05240124e+04,  6.72708804e+03,  1.60869486e+04,
        8.65837159e+03, -7.18089848e+03, -4.26694157e+03,  1.76287093e+04,
        5.62502207e+03,  4.82475782e+03,  2.42722486e+04,  3.59591071e+03,
        1.17751784e+04, -2.93829377e+02,  4.80477917e+04,  1.93483751e+04,
        2.38544972e+03,  6.92000223e+02,  3.60260896e+04,  1.49467166e+03,
        2.00469931e+04,  3.58091380e+04,  3.22001833e+03,  3.60920606e+04,
        2.20140015e+04, -6.37074328e+03,  1.72028120e+04,  1.08869315e+04,
        9.15671520e+03,  1.41010720e+04,  2.11844206e+04,  2.12523380e+04,
        5.05986592e+03,  2.87168385e+04,  1.98271066e+04,  1.78028470e+04,
        2.55563086e+04,  2.26937924e+04,  7.65953819e+03,  1.14027031e+03,
        4.95056974e+03,  2.05747082e+04,  1.06161080e+04,  1.19372254e+04,
        2.38570744e+04,  1.47834347e+04,  3.92652328e+03,  9.07837512e+03,
        7.70710391e+03,  1.95896382e+04,  1.98514394e+04,  4.87556054e+04,
        3.65470215e+03,  5.10325452e+03,  5.10605410e+03,  1.25633366e+04,
        1.87506241e+04, -2.57565109e+03,  2.06597667e+04,  1.95280430e+04,
        2.73315802e+03,  1.03630664e+04,  3.26718614e+04,  2.44039167e+04,
        1.88165479e+04,  1.41204917e+04,  1.67221228e+04,  4.06206105e+04,
        1.07958563e+04, -4.61966557e+03,  1.04215163e+04,  3.49053711e+04,
        3.06430420e+04,  1.54659743e+04,  1.22507073e+04,  2.29838211e+04,
        2.80689352e+04,  1.24090610e+04, -3.49672644e+03,  1.25655413e+04,
        2.05060764e+04, -4.41494270e+03,  6.23406765e+03, -6.70792866e+03,
        1.56835455e+04,  8.79905672e+03,  1.70954798e+04, -1.20006299e+04,
        2.32764489e+04,  1.39722455e+04,  1.62556336e+04,  2.90585260e+04,
        2.22614474e+04,  3.44931672e+03,  6.56518945e+03,  2.80309304e+04,
        1.89065022e+04,  2.66251273e+04,  2.24008904e+04, -3.46664344e+03,
        2.98405605e+04,  4.99986035e+04,  8.12192118e+03,  2.32108496e+04,
        1.87207048e+04,  2.94864225e+04,  2.30635700e+04,  4.03739664e+03,
        3.64064534e+04,  1.05239389e+04,  4.49418032e+03,  2.46542703e+04,
        2.88372647e+04,  1.76145821e+04, -1.20502662e+03,  2.61923258e+04,
       -7.61830669e+03, -4.50469220e+03,  1.91039876e+04,  2.80859861e+03,
        9.02589549e+03,  9.54643401e+03, -7.87782051e+03,  2.77553648e+03,
       -3.96550627e+03,  2.63663828e+04, -5.16826783e+03,  4.16443749e+04,
        2.25535536e+04,  2.04084092e+04,  8.41693418e+03,  2.05492947e+04,
       -4.22402137e+03,  1.48464457e+04,  3.01046448e+03,  3.28672702e+04,
        1.73061251e+04,  4.24882811e+02,  3.43642557e+04,  1.57630928e+04,
        5.52028075e+03,  2.43579326e+04,  2.52115136e+04,  6.67538351e+03,
       -4.19654223e+03,  2.29247760e+04, -7.01731014e+03,  7.45820243e+03,
        5.35308176e+03,  2.97321929e+03,  1.56642176e+04,  1.85091797e+04,
        1.85282979e+04,  1.03320994e+04,  8.86594198e+03,  1.79533622e+04,
       -3.54957681e+01,  2.62175580e+04,  2.70939411e+04,  1.06984674e+04,
        1.61454223e+04,  1.97848288e+04,  9.28741712e+03,  2.35441972e+03,
       -2.59330284e+03,  2.06180656e+04, -5.18959023e+03,  1.93485397e+04,
       -9.71407235e+02,  1.40957274e+04,  5.84901372e+03,  1.73548488e+02,
        4.09526861e+04,  1.36427385e+04,  1.16803204e+04,  1.11871214e+04,
       -5.65502163e+03,  2.31504982e+04,  3.75366145e+03,  1.57885881e+04,
       -6.34163254e+03,  2.26687996e+03,  3.40943947e+04,  9.97980536e+00,
        1.50604487e+04,  2.44857791e+04, -9.35765870e+03,  1.52885189e+04,
        2.41150212e+04,  3.73041735e+04,  3.70898660e+04,  2.74715032e+04,
        2.87226250e+04,  1.26741468e+04,  1.79040878e+04,  4.60183007e+02,
        2.23109943e+04,  1.78538625e+03,  9.02557010e+03,  2.01956331e+04,
        1.05164678e+04,  2.69007396e+04,  1.03669063e+04,  3.37218711e+04,
        2.89384174e+03, -4.98294404e+03,  1.62006981e+04, -1.68883107e+04,
        2.00918359e+04,  2.40758274e+04,  1.38033618e+04,  1.06915559e+04,
        1.88552352e+04,  1.85701688e+04,  8.58962927e+03,  2.44692265e+04,
        1.44986629e+04, -8.81666640e+02,  1.98617818e+04,  1.72889990e+04,
       -2.38132445e+03,  1.00666818e+04,  1.61490980e+04,  3.37592177e+04,
        2.35518465e+04,  6.69464349e+03,  1.62140691e+04,  1.33486771e+04,
       -7.37100276e+02,  7.64119851e+03,  3.38947073e+04,  1.90228970e+04,
       -5.14680564e+03,  1.16282656e+04,  5.24410508e+03,  4.22266653e+04,
        7.46513445e+03,  1.92853443e+04, -2.96787795e+03,  2.83142670e+04,
       -5.67270244e+03,  1.87006172e+04,  1.06228110e+04,  3.40462412e+04,
       -6.17229472e+03,  2.76193489e+04,  1.46349742e+04, -5.40404007e+03,
        3.87923821e+04,  4.26609772e+03,  9.17012026e+03,  1.98957880e+04,
        8.87239181e+03, -4.78964782e+03,  8.28162370e+03,  1.00649189e+04,
        2.54524277e+04,  1.36966510e+04,  3.83869347e+04,  1.74591469e+04,
        5.91810624e+03, -2.20336374e+03,  3.44185013e+04,  1.68850384e+04,
        1.63163285e+04,  4.39716151e+03,  9.59128260e+03, -7.16391412e+03,
        1.45834243e+04, -9.00687687e+02,  2.64116608e+03,  1.75427015e+04,
        1.66920621e+04,  5.42307771e+02, -3.37066104e+03,  2.15759581e+04,
        1.15776922e+04,  3.14873465e+04])


valid_y3_pred_df = pd.DataFrame(valid_y3_pred, columns = ["Validation_Prediction"])
valid_y3_pred_df


mse_valid_3 = sklearn.metrics.mean_squared_error(valid_y3, valid_y3_pred)
mse_valid_3

377856956.3335032


# As before
# import math

rmse_valid_3 = math.sqrt(mse_valid_3)
rmse_valid_3

19438.543060978187


valid_y3.describe()

count       646.000000
mean      13535.160991
std       23624.770667
min        1105.000000
25%        4708.750000
50%        6750.500000
75%       12827.750000
max      301070.000000
Name: Wage, dtype: float64


# As before:

# If using the dmba package:

# pip install dmba


# Done earlier. Just for illustration
# import dmba
# from dmba import regressionSummary

regressionSummary(valid_y3, valid_y3_pred)

Regression statistics

                      Mean Error (ME) : -146.0444
       Root Mean Squared Error (RMSE) : 19438.5431
            Mean Absolute Error (MAE) : 9585.2762
          Mean Percentage Error (MPE) : -42.4877
Mean Absolute Percentage Error (MAPE) : 124.7749


new_players_df


new_records_players_pred_3 = model_ridge.predict(new_players_df)
new_records_players_pred_3

array([30907.21640178, 21909.60027727, 30847.24918278])


# As before
# import pandas as pd

new_records_players_pred_df_3 = pd.DataFrame(new_records_players_pred_3, columns = ["Prediction"])
new_records_players_pred_df_3

# to export
# new_records_players_pred_df.to_csv("whatever_name.csv")


alpha = 0.05
ci_3 = np.quantile(train_residuals_3, 1 - alpha)
ci_3

17045.478790700115


def generate_results_confint_3(preds, ci_3):
    df = pd.DataFrame()
    df["Prediction"] = preds
    if ci >= 0:
        df["upper"] = preds + ci_3
        df["lower"] = preds - ci_3
    else:
        df["upper"] = preds - ci_3
        df["lower"] = preds + ci_3
    return df


new_records_players_pred_confint_df_3 = generate_results_confint_3(new_records_players_pred_3, ci_3)
new_records_players_pred_confint_df_3


train_X4 = train_X.copy()
train_y4 = train_y.copy()
valid_X4 = valid_X.copy()
valid_y4 = valid_y.copy()


from sklearn import linear_model

model_lasso = linear_model.Lasso(alpha = 0.5, tol = 2, max_iter = 10)
model_lasso.fit(train_X4, train_y4)

Lasso(alpha=0.5, max_iter=10, tol=2)


train_y4_pred = model_lasso.predict(train_X4)
train_y4_pred

array([23664.75129721,  7309.43845012,  1682.14259148, ...,
       25528.99628982, 23094.83450666, 23317.79242772])


train_y4_pred_df = pd.DataFrame(train_y4_pred, columns = ["Training_Prediction"])
train_y4_pred_df


print("model intercept: ", model_lasso.intercept_)
print("model coefficients: ", model_lasso.coef_)
print("Model score: ", model_lasso.score(train_X4, train_y4))

model intercept:  -86996.1156468611
model coefficients:  [  878.5716549     73.05446438   860.5312622    -13.47353083
   257.41231334    32.58020897 -2105.20659376  3767.57721845
  -518.43939572 -1578.14026859]
Model score:  0.18302583344714407


print(pd.DataFrame({"Predictor": train_X4.columns, "Coefficient": model_lasso.coef_}))

              Predictor  Coefficient
0                   Age   878.571655
1               Balance    73.054464
2             ShotPower   860.531262
3            Aggression   -13.473531
4           Positioning   257.412313
5             Composure    32.580209
6  Preferred Foot_Right -2105.206594
7        Body Type_Lean  3767.577218
8      Body Type_Normal  -518.439396
9      Body Type_Stocky -1578.140269


mse_train_4 = sklearn.metrics.mean_squared_error(train_y4, train_y4_pred)
mse_train_4

394480672.6408317


import math


rmse_train_4 = math.sqrt(mse_train_4)
rmse_train_4

19861.537519558544


train_y4.describe()

count      1506.000000
mean      12698.381142
std       21981.278007
min        1290.000000
25%        4692.500000
50%        6544.000000
75%       12364.250000
max      407609.000000
Name: Wage, dtype: float64


import dmba
from dmba import regressionSummary


regressionSummary(train_y4, train_y4_pred)

Regression statistics

                      Mean Error (ME) : 0.0000
       Root Mean Squared Error (RMSE) : 19861.5375
            Mean Absolute Error (MAE) : 10701.9033
          Mean Percentage Error (MPE) : -31.7885
Mean Absolute Percentage Error (MAPE) : 145.9077


import numpy as np
from scipy.stats import shapiro

shapiro(train_y4)

ShapiroResult(statistic=0.38412952423095703, pvalue=0.0)


train_residuals_4 = train_y4 - train_y4_pred
train_residuals_4

13946    -1152.751297
7711      -549.438450
8402      3694.857409
13651   -11901.713391
1625    -12379.953559
             ...     
12759    -6257.116142
17284     1801.187590
1016    -14381.996290
16984   -11432.834507
16744     2983.207572
Name: Wage, Length: 1506, dtype: float64


shapiro(train_residuals_4)

ShapiroResult(statistic=0.5732489824295044, pvalue=0.0)


from statsmodels.stats.outliers_influence import variance_inflation_factor

vif_df_4 = pd.DataFrame()

vif_df_4["features"] = train_X4.columns
vif_df_4["VIF"] = [variance_inflation_factor(train_X4.values, i) for i in range(train_X4.shape[1])]

print(vif_df_4)

               features         VIF
0                   Age   48.741902
1               Balance   33.364691
2             ShotPower  155.270485
3            Aggression   18.482052
4           Positioning  184.558829
5             Composure  115.774481
6  Preferred Foot_Right    7.714600
7        Body Type_Lean   32.118906
8      Body Type_Normal   59.412529
9      Body Type_Stocky   11.108926


valid_y4_pred = model_lasso.predict(valid_X4)
valid_y4_pred

array([ 1.60888749e+04,  2.28658032e+04,  2.29165150e+04,  2.02857565e+04,
        2.62424904e+04,  6.67204751e+03,  1.81177179e+04,  6.41889523e+03,
        2.69140122e+04, -7.34359467e+02,  5.62294937e+03,  1.95665783e+04,
        9.67738388e+03,  9.83296597e+03,  2.64396039e+04,  4.10728682e+04,
        2.39865085e+04,  2.42018735e+04,  3.60388275e+03,  2.61979797e+04,
       -3.97585033e+02,  2.19805171e+04,  1.57147085e+04,  2.50387186e+04,
        3.52740625e+03, -1.12435316e+04,  1.47258031e+04,  1.39643707e+04,
        2.22710897e+04,  1.26309930e+04,  6.54265365e+03,  1.94652956e+04,
        2.87796041e+04,  2.27009351e+04,  8.02049536e+03,  1.78417813e+04,
        6.09700927e+03,  2.07105507e+03, -5.74940302e+03,  2.73190544e+04,
        3.13813566e+04, -1.75414133e+04,  1.87993583e+04,  9.10826540e+03,
        1.60578541e+04,  2.73955332e+04, -4.58333255e+03,  7.19872200e+03,
        8.04411300e+03,  2.02694381e+04,  2.27172953e+04,  6.53840561e+03,
        2.07694645e+03,  2.72765691e+04,  1.09033157e+04,  1.36896612e+04,
        4.27639965e+02,  1.41412401e+04,  2.05011614e+03,  1.40974560e+04,
        1.93406089e+04,  2.99152387e+04,  2.31520588e+04,  2.47631286e+04,
        3.43348748e+03,  2.36939432e+04,  1.36181766e+04,  2.76957840e+03,
       -2.03776570e+03,  3.47129067e+04,  1.89990075e+04, -1.75023659e+03,
        3.01520525e+02,  1.04627448e+04,  2.62403265e+04,  2.66132919e+04,
        1.41224816e+04,  9.59158193e+03,  1.85603403e+04,  2.66950059e+04,
        2.84043835e+04,  4.37907666e+04,  2.37083249e+03,  1.77106111e+04,
        3.50975309e+04,  1.32232907e+04,  6.92081485e+03,  1.71187991e+04,
        1.76364337e+04,  2.49008126e+04,  2.65661978e+04,  1.80388153e+04,
        1.04781396e+04,  2.81083442e+04,  2.38637678e+04,  1.87402022e+04,
        1.39745881e+04,  2.37620749e+04,  2.04038056e+04,  3.04591318e+04,
        1.59192615e+04,  1.39363677e+04,  3.32839738e+04,  5.53410122e+03,
        3.21413922e+04,  1.80982290e+04,  1.87306118e+04,  2.29560836e+04,
        6.99944165e+03,  4.06076710e+04,  2.33133879e+04,  1.35916222e+04,
        8.33711061e+03,  2.26958161e+04,  1.23702955e+04, -1.27709895e+04,
        5.75901385e+03,  4.88970659e+03,  2.78235806e+04,  1.96004174e+04,
        4.59367928e+02,  3.03766150e+03,  1.88247776e+04, -5.49801173e+03,
        2.54392756e+04,  3.50776464e+04,  2.84189046e+04,  3.34495332e+04,
       -3.74478093e+02,  7.17734196e+03,  2.04475163e+04, -3.90257396e+03,
        8.51705656e+03,  1.20419618e+04,  3.12936781e+04, -1.77652605e+03,
       -8.15480142e+03,  2.55030846e+02, -1.07168959e+04, -3.92066826e+03,
        1.78793280e+04,  2.65900919e+04,  1.79857707e+04, -1.88812413e+03,
       -9.21307823e+01,  2.66310360e+04,  1.42427135e+04,  8.90525482e+03,
        5.06681050e+02,  2.36865409e+04,  2.85556930e+04,  6.71464963e+03,
        3.38685951e+04,  5.50140701e+03,  1.44291766e+04,  2.44361591e+03,
        1.10923943e+04, -4.79461466e+03,  1.73182301e+04,  9.19798343e+03,
        1.98289424e+04, -1.67570552e+04,  4.75537493e+03,  2.17511075e+04,
        3.07270871e+04,  7.54793161e+03,  2.42095051e+04,  2.55495164e+04,
        2.34050760e+04,  1.55194262e+04, -2.44420941e+03, -1.38997798e+04,
        1.51027652e+04, -1.57547089e+03,  5.54208650e+03,  7.37557579e+02,
        2.25591142e+04,  1.15972177e+04,  2.25169608e+04,  1.48101737e+04,
        2.60619906e+04, -7.11529825e+03,  4.41655556e+02,  1.90016427e+04,
        2.06300472e+04,  4.45581728e+03,  2.72346581e+04,  2.26692972e+04,
        1.66070388e+04, -3.34656643e+03,  2.37028391e+04, -6.99913025e+03,
        6.39434938e+03,  4.35908400e+03, -2.06729861e+03, -5.58996134e+02,
        3.86144201e+04,  2.78935579e+03,  9.37102135e+03, -6.97122364e+03,
        1.37569537e+04,  3.73297127e+04,  2.42269396e+04,  3.06369603e+04,
        1.84434748e+04,  1.17156680e+04,  3.35720256e+04, -1.91862641e+03,
        2.16452938e+04, -4.88260091e+03,  4.62975862e+03,  4.09837158e+04,
        1.79503901e+04,  3.64415514e+02,  1.66633135e+04,  3.32423824e+04,
        1.13084337e+04, -1.24435223e+04,  2.96966921e+04,  1.85483604e+04,
        2.14978785e+04,  2.60371649e+04,  1.67770907e+04,  2.17863454e+04,
        2.80850844e+04,  2.05488151e+04,  2.84596132e+03,  1.56514499e+04,
        2.50457505e+04,  1.53038368e+04, -2.10420470e+03,  1.04771486e+04,
        1.08202903e+04,  1.64081414e+04,  5.38762075e+02,  1.94600342e+04,
        1.33156332e+04, -6.62094416e+03,  1.69535139e+04,  1.18997505e+04,
        1.65717592e+04,  1.82224667e+04, -7.01880524e+03, -8.02125460e+03,
        1.12112209e+04,  1.01939541e+04,  1.53144871e+04, -3.68156802e+03,
        6.95021475e+03,  1.07493781e+04, -1.55063158e+04,  7.23664071e+03,
        4.68077893e+03,  1.14209803e+04,  2.44929255e+04,  1.98843194e+04,
        1.74738019e+04,  1.25251769e+04,  1.79250166e+04,  1.97538995e+04,
        1.87939890e+04,  9.63343492e+03,  1.09965060e+04,  2.35214579e+04,
        2.41829656e+04,  2.43581552e+03,  1.64577593e+04,  1.27118398e+04,
        1.63961883e+04,  1.32278591e+04,  2.88379301e+04,  8.91057395e+03,
        2.35511830e+04,  1.76595572e+04,  6.99332839e+02,  2.18978660e+04,
       -1.42876612e+04,  1.58988435e+04,  4.42680677e+03,  3.91184834e+03,
        1.22576103e+04,  7.34186242e+03,  1.09420656e+04,  1.76738855e+04,
        1.33831337e+04, -6.37160171e+03,  3.69193289e+04,  2.15356035e+04,
        2.54768158e+04,  4.52041538e+03,  8.74892408e+03,  9.59495112e+03,
        4.62705394e+04,  1.37422401e+04,  1.28107742e+04,  2.11039601e+04,
        3.17852399e+03, -7.60302984e+03,  2.68399444e+04, -7.46115997e+02,
       -8.61116274e+03,  8.46258726e+03,  3.18954628e+03,  2.44497263e+04,
       -9.00470385e+03,  2.75658141e+03,  1.88641332e+04,  1.48955244e+04,
        1.62578564e+04, -1.98085164e+04,  2.51306804e+04, -3.47888573e+02,
       -3.83135545e+03,  1.40263929e+04,  1.52814340e+04, -6.69429127e+03,
        1.29184076e+04,  3.20941758e+04,  4.06613399e+01,  1.25995833e+04,
        1.91431660e+04,  2.63589862e+04,  3.81945715e+04,  2.34658540e+04,
        5.49099238e+03, -1.40751599e+04,  1.85026469e+04,  1.97590221e+04,
        2.31917144e+04,  1.58724974e+04, -7.87105665e+02, -1.45681988e+04,
       -6.66176802e+03,  3.21785679e+04,  2.45184042e+04,  3.24873271e+04,
        2.56065571e+04,  6.87115371e+03,  5.40968391e+03, -9.39165633e+03,
        1.41752250e+04,  1.72407072e+04,  1.89420324e+04,  5.72073480e+03,
        2.14517630e+04,  7.61933028e+03,  4.86244567e+03,  6.05864416e+03,
        6.23672050e+03,  1.35262705e+04,  2.10523162e+04, -2.44342898e+03,
        3.05601701e+04,  1.53326377e+04,  2.74806751e+04,  1.44554675e+04,
        3.73210805e+03,  2.26703966e+04,  2.43727356e+04,  1.48885122e+04,
        1.10605836e+04,  2.51943385e+03,  1.98587479e+04,  1.67562321e+04,
        3.32498668e+04,  2.52278618e+04,  6.87409114e+03,  6.15607398e+03,
        1.86627647e+04,  1.84280274e+04,  2.28444296e+03,  1.58605452e+04,
        6.46186369e+02, -8.97251493e+03, -3.72358569e+03,  2.27231350e+04,
        4.88534470e+03,  1.11998861e+04,  1.82165976e+04,  1.32147369e+04,
        1.36947600e+04, -5.80173138e+03,  2.69399308e+04,  1.91517860e+04,
        1.93484166e+04,  1.54226866e+04,  3.60286200e+04,  4.47914169e+02,
        1.37536816e+04,  3.46808670e+04, -6.93837922e+03,  2.30809413e+04,
        2.01956160e+04, -1.63418067e+04,  1.01373639e+04,  6.34659526e+03,
        2.18460500e+04,  2.07755790e+04,  2.92644227e+04,  1.63887211e+04,
        4.28153755e+03,  2.67536540e+04,  9.02755879e+03,  2.38623679e+04,
        2.64816130e+04,  2.39299875e+04,  2.00292678e+03,  2.06038174e+03,
        1.12373667e+04,  2.36371608e+04,  1.32021048e+04,  1.51747075e+04,
        1.99552447e+04,  6.79833775e+03,  2.18167688e+04,  9.01418537e+03,
       -9.99352663e+02,  1.67641319e+04,  1.16662632e+04,  4.24323517e+04,
        1.12985080e+04,  1.60572403e+04,  2.44525141e+04,  2.27511222e+04,
        2.08737879e+04, -5.82400428e+03,  2.82174294e+04,  3.11551420e+04,
       -4.69698911e+03,  1.19888693e+04,  3.73228426e+04,  2.13593987e+04,
        2.55976493e+04,  2.24854620e+04,  5.41969148e+03,  2.81381425e+04,
        1.15023507e+04, -3.86262187e+03, -1.19446767e+03,  3.45223441e+04,
        2.58357274e+04,  9.23895335e+03,  2.11859025e+04,  2.86370512e+04,
        1.97167704e+04,  1.40977758e+04,  8.05747461e+03,  1.57975645e+04,
        2.52698900e+04, -2.99220337e+03,  2.27021369e+04, -7.34827734e+03,
        9.42477370e+03,  7.44978350e+03,  1.58720826e+04, -1.95381434e+04,
        2.68251362e+04,  9.47770452e+03,  2.32776944e+04,  3.04295550e+04,
        8.78853438e+03,  7.18708126e+03,  1.62088849e+04,  2.37940551e+04,
        8.85774288e+03,  1.25139539e+04,  2.21013450e+04, -1.78983235e+03,
        2.39546348e+04,  3.58780279e+04,  1.61462498e+04,  1.79346638e+04,
        1.52933406e+04,  3.30664727e+04,  1.53642916e+04,  6.37359615e+03,
        2.86878854e+04,  2.37880945e+04, -4.94550903e+03,  3.00543561e+04,
        2.90182003e+04,  2.52515789e+04,  4.78106890e+03,  3.20769640e+04,
       -7.30460403e+03, -1.25622268e+04,  2.29174987e+04,  1.39012875e+04,
       -3.06930042e+03,  1.11624990e+04, -1.48666371e+04,  3.06589123e+03,
        6.72357884e+02,  2.47464704e+04, -6.77626185e+03,  3.14378530e+04,
        2.07278930e+04,  2.72607806e+04,  1.04486112e+04,  2.56922422e+04,
       -1.02766329e+04,  2.35137439e+04,  9.62746024e+02,  2.79983466e+04,
        2.21216593e+04,  9.20928565e+03,  3.03490668e+04,  1.99912055e+04,
        1.20438670e+04,  3.00985832e+04,  2.28445373e+04,  2.53193368e+03,
        1.28598758e+04,  2.14288904e+04, -1.23016386e+04,  1.16536355e+04,
        1.51943815e+04, -6.95738781e+03,  1.94049429e+04,  1.82144135e+04,
        2.10293876e+04,  2.42393706e+04,  1.88700518e+04,  3.12614580e+03,
        6.68480328e+03,  2.11872995e+04,  1.88734202e+04,  8.00493699e+03,
        1.93347662e+04,  1.96450720e+04,  1.34064991e+04,  1.64068990e+04,
       -6.94743474e+03,  2.56211052e+04, -8.41223183e+03,  2.58562216e+04,
       -6.85420116e+03,  2.64068791e+04,  1.73265562e+04, -4.01980007e+03,
        3.76516850e+04,  1.56277151e+04,  2.01996049e+04,  2.65081750e+04,
       -1.05868509e+04,  2.59287853e+04, -4.96806088e+03,  1.32000523e+04,
       -7.10351398e+03,  2.88477413e+03,  4.24803109e+04, -6.84345017e+03,
        1.98806772e+04,  2.45388299e+04, -8.16594535e+03,  8.36178352e+03,
        1.78555867e+04,  2.28804969e+04,  2.42634875e+04,  2.74984963e+04,
        2.46513003e+04,  2.17666350e+04,  1.44914746e+04,  3.12145127e+03,
        3.04987095e+04, -2.02211535e+03,  1.98677231e+04,  1.96423504e+04,
        8.90696985e+03,  3.07026025e+04,  1.48978513e+04,  2.84487445e+04,
       -4.97523053e+03, -8.66521484e+02,  1.29763444e+04, -7.99536222e+03,
        2.75359156e+04,  2.86476834e+04,  7.53286174e+03,  6.11551173e+03,
        1.73268105e+04,  1.96363681e+04,  1.78118381e+04,  2.83903425e+04,
        4.65014871e+03,  1.02605521e+03,  2.17578611e+04,  5.42991734e+03,
       -1.24515281e+04,  1.86704096e+04,  1.35216557e+04,  3.17605101e+04,
        1.94115740e+04,  9.94811501e+03,  1.81044663e+04,  1.13553424e+04,
        1.05495804e+04,  8.14530718e+03,  2.54853869e+04,  3.39594266e+04,
        3.59410210e+03,  6.61478785e+03,  1.69307324e+04,  4.05745556e+04,
        1.83727980e+04,  2.44659292e+04, -1.38422062e+04,  2.39812839e+04,
        6.30206872e+03,  1.70565923e+04,  1.52304237e+04,  3.31359512e+04,
       -1.06537963e+04,  2.39127251e+04,  1.32528237e+04,  6.41677453e+03,
        2.82429089e+04,  1.84240516e+04,  2.39529817e+04,  1.49468820e+04,
        1.41015024e+04, -3.23017246e+03, -5.59277267e+03,  1.63212296e+04,
        2.42808217e+04,  1.24670307e+04,  3.15458260e+04,  2.17338233e+04,
        8.28983452e+03,  1.41617551e+04,  2.69616326e+04,  1.10601573e+04,
        1.65777186e+04,  5.50576865e+03,  5.76146552e+03, -9.76252428e+03,
        1.17118783e+04,  1.21399049e+03, -1.46113543e+03,  4.59854240e+03,
        1.31693546e+04,  4.99593646e+03, -1.02712169e+04,  1.74376599e+04,
        1.21050714e+04,  1.22957991e+04])


valid_y4_pred_df = pd.DataFrame(valid_y4_pred, columns = ["Validation_Prediction"])
valid_y4_pred_df


mse_valid_4 = sklearn.metrics.mean_squared_error(valid_y4, valid_y4_pred)
mse_valid_4

445185876.78789973


# As before
# import math

rmse_valid_4 = math.sqrt(mse_valid_4)
rmse_valid_4

21099.428352159204


valid_y4.describe()

count       646.000000
mean      13535.160991
std       23624.770667
min        1105.000000
25%        4708.750000
50%        6750.500000
75%       12827.750000
max      301070.000000
Name: Wage, dtype: float64


# As before:

# If using the dmba package:

# pip install dmba


# Done earlier. Just for illustration
# import dmba
# from dmba import regressionSummary

regressionSummary(valid_y4, valid_y4_pred)

Regression statistics

                      Mean Error (ME) : -213.0518
       Root Mean Squared Error (RMSE) : 21099.4284
            Mean Absolute Error (MAE) : 11072.2334
          Mean Percentage Error (MPE) : -48.3380
Mean Absolute Percentage Error (MAPE) : 152.1841


new_players_df


new_records_players_pred_4 = model_lasso.predict(new_players_df)
new_records_players_pred_4

array([24044.91108935, 14502.47793021, 23347.2433213 ])


# As before
# import pandas as pd

new_records_players_pred_df_4 = pd.DataFrame(new_records_players_pred_4, columns = ["Prediction"])
new_records_players_pred_df_4

# to export
# new_records_players_pred_df.to_csv("whatever_name.csv")


alpha = 0.05
ci_4 = np.quantile(train_residuals_4, 1 - alpha)
ci_4

19771.787699952376


def generate_results_confint_4(preds, ci_4):
    df = pd.DataFrame()
    df["Prediction"] = preds
    if ci >= 0:
        df["upper"] = preds + ci_4
        df["lower"] = preds - ci_4
    else:
        df["upper"] = preds - ci_4
        df["lower"] = preds + ci_4
    return df


new_records_players_pred_confint_df_4 = generate_results_confint_4(new_records_players_pred_4, ci_4)
new_records_players_pred_confint_df_4


from sklearn.linear_model import ElasticNet
from sklearn.datasets import make_regression


train_X5 = train_X.copy()
train_y5 = train_y.copy()
valid_X5 = valid_X.copy()
valid_y5 = valid_y.copy()


train_X5, train_y5 = make_regression(n_features = 10, random_state = 666)
model_elastic = ElasticNet(random_state = 666)
model_elastic.fit(train_X5, train_y5)

ElasticNet(random_state=666)


type(train_X5)

numpy.ndarray


type(train_y5)

numpy.ndarray


train_y5_pred = model_elastic.predict(train_X5)
train_y5_pred

array([-239.89702287,   30.20471618,  146.41102948,   62.35336983,
        177.08753921, -209.59344487, -159.0879793 , -242.38244857,
         54.87544413,  -26.34258741,  231.11945687,  309.32913489,
          5.68659987, -102.16230273,    1.22670383,  -59.4133525 ,
        -85.15133799,  -98.99056433,  -87.74329659,   44.51773042,
        159.3243627 ,  117.5443711 , -164.62941892,  125.34439908,
          8.90255763, -114.7913873 ,  291.75693957, -202.28642913,
        171.71712251,   -3.92022359, -143.08624391,  -89.08740894,
       -106.63397392, -194.63807216, -244.85791217,  122.01268078,
         57.49586543,  175.80148181, -154.49993083,  -41.72967953,
        239.68753594,    8.39230607,   67.89458582,  203.52636571,
        -15.51052836,   97.53529516,   56.9366598 , -368.15724976,
        -26.46591475, -116.38192221, -129.1303425 ,  277.99750842,
       -217.03245809,  110.77806504,  -98.47472604,  -37.8287712 ,
        211.12887163,  -41.54899521, -114.55327138,   33.64785209,
         -3.58899371,   34.09284041,   60.20734999, -252.26679574,
        154.37071339,  -62.95584088,  127.81457702, -220.9094447 ,
       -287.99704049,   42.56795837, -160.11760685,   42.74309451,
         42.01724616,   44.95060293, -171.09356266, -143.00605263,
       -128.79839338, -158.04057611,   23.3411471 , -208.12593485,
        -60.49186376,  -97.30339631,  254.14383238,  -93.8974994 ,
        301.25260918,    9.89642346,  -62.83757572, -130.10642815,
         89.3330917 ,   19.50624336,   -2.98545981,  -72.02696057,
        -39.62413746,  -93.51527208,  141.07669442,   91.93363588,
         51.80867706,  -34.02927417,  -75.6741745 ,   95.76213508])


train_y5_pred_df = pd.DataFrame(train_y5_pred, columns = ["Training_Prediction"])
train_y5_pred_df


print("model intercept: ", model_elastic.intercept_)
print("model coefficients: ", model_elastic.coef_)
print("Model score: ", model_elastic.score(train_X5, train_y5))

model intercept:  -6.133468616184231
model coefficients:  [24.3065105   1.72597924 32.79853103 11.29839994 57.71459241 60.51954808
 50.97607045 46.07791909 55.01341304 60.31821326]
Model score:  0.8825434233397067


mse_train_5 = sklearn.metrics.mean_squared_error(train_y5, train_y5_pred)
mse_train_5

5476.117116636182


import math


rmse_train_5 = math.sqrt(mse_train_5)
rmse_train_5

74.00079132439181


np.std(train_y5)

215.9223978114257


import dmba
from dmba import regressionSummary


regressionSummary(train_y5, train_y5_pred)

Regression statistics

                      Mean Error (ME) : 0.0000
       Root Mean Squared Error (RMSE) : 74.0008
            Mean Absolute Error (MAE) : 59.4893
          Mean Percentage Error (MPE) : -12.6902
Mean Absolute Percentage Error (MAPE) : 82.0362


import numpy as np
from scipy.stats import shapiro

shapiro(train_y5)

ShapiroResult(statistic=0.9933440089225769, pvalue=0.907919704914093)


train_residuals_5 = train_y5 - train_y5_pred
train_residuals_5

array([-115.87355838,   20.55225498,  105.29541848,   70.33789465,
         85.10534445, -119.32838286,  -90.17104944,  -94.61626251,
         49.49931428,  -13.57318615,  134.61766684,  121.55259874,
          6.61723475,  -38.86744747,   -8.05409341,   15.02212719,
        -43.36458565,   -2.26900164,  -44.19868389,   31.22462816,
         83.89791053,   62.4307288 ,  -81.24968022,   65.54643487,
          7.05336542,  -61.84098657,  168.23587577,  -74.16622347,
        116.40139242,   22.32224043,  -57.88069139,  -14.05995462,
        -10.96375877,  -95.15789269, -151.64687109,   53.23292199,
         35.31233236,   90.27628713,  -94.06304233,   25.63635158,
        112.03495283,    3.70977227,   33.8162091 ,   88.91654268,
        -31.254995  ,   39.51105913,   29.7090374 , -167.38446484,
         25.89299222,  -48.92758299,  -84.58876275,  148.84402504,
       -114.49031964,   76.21986696,  -62.0456898 ,  -20.23421487,
         89.04950568,   -1.57350087,  -56.13256276,    1.78988291,
        -26.7977081 ,   44.23729077,    0.6689099 , -131.99698805,
         77.07876543,  -25.64571667,   48.77518018,  -94.01834119,
       -157.90006355,   23.29664651,  -77.19246555,   55.45884587,
          5.61274092,   33.90949488,  -80.64159432,  -67.74133301,
        -52.99278782,  -43.69628765,   12.47426646, -108.35823508,
        -17.70919494,  -57.74881675,  135.72993831,  -51.58580114,
        185.07822914,    8.27717559,  -31.0038929 ,  -66.45850356,
         27.76413165,   36.8337016 ,   -6.4878831 ,  -19.69525644,
         -9.7356234 ,  -32.31802903,   81.7506021 ,   51.2448407 ,
         36.8203488 ,  -16.76202468,   14.50928694,   75.27942723])


shapiro(train_residuals_5)

ShapiroResult(statistic=0.9953042268753052, pvalue=0.9822211861610413)


valid_y5_pred = model_elastic.predict(valid_X5)
valid_y5_pred

C:\Users\byeo\Anaconda3\lib\site-packages\sklearn\base.py:443: UserWarning: X has feature names, but ElasticNet was fitted without feature names
  warnings.warn(

array([10352.05910353, 12105.44069022, 12255.07200558, 12134.3868721 ,
       13147.61617235, 10243.06386701, 11313.32224233, 11032.09564747,
       12791.92844967,  8908.74659791, 10387.15719227, 11464.07362857,
       10906.60311722, 10608.97750665, 12831.67428293, 14471.71294576,
       12320.35842574, 12052.28358989,  9515.58499339, 12535.33345669,
       10151.37624276, 12170.51937152, 11334.90749268, 12147.7654329 ,
        9794.85597288,  8467.82894156, 10686.93646591, 12472.92965584,
       11986.96867404, 11006.64046664,  9411.96610806, 11355.46901679,
       12196.38602963, 12709.13983713,  8970.73975657, 11031.00275534,
       10464.23712765, 10808.36750752,  8957.50677167, 13141.91778899,
       13576.62603385,  8444.99670939, 11176.32407544,  9902.04169514,
       12083.37100625, 12948.20034059,  8122.52822429,  9119.78689569,
       10840.40275917, 11571.32309035, 12138.15395455, 10521.20361808,
        9795.8311031 , 12483.43309484, 11418.35024528, 11595.3768299 ,
        8463.55143622, 11243.80020398,  9690.64626627, 11292.38087084,
       10254.85268662, 12809.3242474 , 11854.75627534, 12182.38536325,
        9764.61970382, 11595.34411481, 10976.90641622, 10068.74833515,
        9401.38304107, 13545.93970676, 10717.11283639,  9233.12389415,
       10440.76178304, 11229.62273501, 12312.2758096 , 12193.72842343,
       11397.17414624, 10716.94611653, 11713.08899622, 13630.14063311,
       13003.82337793, 15368.58879639,  9761.59161119, 12149.79714464,
       14078.54221453, 11085.17724553, 10721.85414481, 11104.99277646,
       12101.6610874 , 12476.05627164, 13347.31622935, 11723.9698162 ,
       10614.75795541, 13080.32887597, 11901.4709434 , 11840.69140093,
       11466.01742385, 12048.83126325, 11536.50027683, 14044.74049154,
        9899.55146143, 11766.23338592, 12373.55297498,  9485.01408948,
       12152.60672717, 11011.72078307, 12035.81933079, 12523.09261077,
       10044.86099962, 13679.61907932, 12119.19426514, 11555.1113625 ,
        9195.81690137, 11059.13270076, 11291.64505669,  8129.2754332 ,
        9453.67669073, 10438.16486942, 13496.484549  , 11713.15135056,
        9565.65875894, 10127.63828516, 11211.25847167,  8730.46393144,
       11464.48238118, 13992.42592753, 12680.9219006 , 13920.38074777,
        9548.5274636 ,  8889.91531046, 11755.34749597,  9125.06800726,
        9121.30409183, 10794.18810957, 13345.27496844,  8959.37264987,
        8194.45885751,  9090.65510799,  8559.99299338,  9895.62335948,
       11191.77979577, 12314.54463745, 11448.29771524,  9160.53378102,
        9156.10331445, 12909.91829704, 10859.31073101, 10070.28886388,
        9204.80176842, 12178.93635149, 12830.08269192,  9876.61311764,
       13882.44657459, 10469.0559072 , 10375.89184879, 10857.74933212,
       11568.49556747,  8363.05241204, 11656.17277285, 11071.47688265,
       11524.56418679,  7851.60146357,  9697.27927879, 12111.67380638,
       12002.93630653, 10001.97324197, 11498.83815181, 12221.96067723,
       10924.12307689, 11378.00042588,  9283.17597152,  8606.10583163,
        9978.55170431,  9736.45350326,  9331.35800275, 10215.8221707 ,
       12561.04023405, 11107.05957564, 11581.62588877, 10522.64186496,
       12798.60222989,  8118.80733405,  9598.93135701, 11417.7759794 ,
       10414.19744897, 10118.95520032, 12950.08051071, 12077.26462182,
       11444.33982293,  8538.05715103, 13014.41184658,  9024.42345157,
       10577.58323199, 10824.73004598,  8959.15622165,  9534.11628987,
       14733.93676839,  9631.46855787, 10754.48023068,  8142.09307727,
       11148.02085278, 13941.64646087, 11565.43884066, 13632.35722122,
       10554.12980061, 10130.09110264, 12728.87927866, 10110.23841177,
       12104.07799694,  9800.3472128 ,  9850.34126804, 14501.1381244 ,
       11385.27675579,  8917.82199634, 11768.23753761, 13311.39581984,
        9936.86455837,  9051.59327363, 12573.05898577, 11060.07161974,
       11961.10514464, 11593.11161466,  9832.93259552, 12492.82402189,
       12478.95319134, 11784.66170994,  9689.1675903 , 10556.50773932,
       12768.75650148, 11101.65276867,  8914.20026887, 11882.03457769,
        9807.98637367, 11884.85828607,  9353.19048249, 11777.48423306,
       10074.44938971, 10161.97810891, 12287.35960953, 10605.23222895,
       10756.1904017 , 11152.64050382,  8884.06056659,  8762.31273865,
       10444.39992637, 10519.90297765, 10906.78681814,  9985.65571416,
       11319.41523747, 10209.02622837,  7658.66885234,  9269.95118605,
       10448.99818541, 10603.75092298, 13021.66467132, 10954.2872683 ,
       12007.53026353, 11106.66541944, 12126.05183304, 11685.5686955 ,
       10998.1895253 ,  9623.88504223, 10508.47416779, 11800.44219586,
       12881.95959803, 10789.33550312, 11631.22698844, 10747.60354427,
       11463.68774696, 11661.68780507, 13924.20457518,  9646.73076185,
       13060.49409883, 11382.35314513,  9819.18444803, 12535.12146765,
        8264.88828232, 12032.72088507,  9717.07893981,  9153.073164  ,
       10643.48540969, 11153.4817259 , 10863.82417413, 11734.51629157,
       10654.21132183,  9483.72026011, 12745.64816369, 11552.51173636,
       12392.31644634,  9622.34634275, 10327.2845096 ,  9968.3212924 ,
       14767.08367069, 10554.27373735, 10679.54042274, 12297.78539478,
       10002.89591453,  8926.61180675, 12718.1118005 , 10785.41060887,
        8502.21359245, 10366.58046846,  8884.93706053, 12147.61982551,
        8540.44564116,  9568.2296874 , 11746.79516293, 11430.09696906,
       12074.74703264,  6932.90638676, 11701.53820379,  9766.42011926,
        9550.75765528, 11329.59590192, 12041.51349855,  8855.99875912,
       10934.37560517, 12682.62925959,  9339.65202606, 11163.52806206,
       11360.37063843, 13075.13477091, 15304.40279194, 12964.4931213 ,
       10251.0757177 ,  8353.81395642, 11892.10702604, 12101.18330051,
       12283.95447085, 12177.44514571, 10274.42117972,  7787.09898337,
        8360.20426381, 13258.87581233, 12259.53250973, 13261.76167787,
       13009.05294426,  9592.56570422, 10496.55630757,  8346.13613016,
       11649.80655946, 10817.12275202, 11465.9587795 , 10268.55390299,
       11161.97842404, 10441.96006572,  9975.27498703,  8804.15908119,
        8864.31669839, 11066.63683321, 12374.1176849 ,  8449.18106432,
       12293.82925208, 11690.10907326, 12722.85412665, 11682.91566374,
       10062.56357869, 11832.5551472 , 13531.39222571, 11224.24260704,
        9967.5888109 , 10225.76056374, 12254.50939371, 11769.97854703,
       13159.58425392, 12658.84164177, 10618.01908829,  9012.0754734 ,
       11188.27492229, 11814.17928184, 10130.3801664 , 10889.78883617,
        9807.04788674,  8530.3089394 ,  8433.50363483, 12328.56321367,
        9267.9742972 , 11014.41671047, 12236.77969102, 10760.96746641,
       11495.89420143,  8713.55480494, 14191.9125366 , 11861.89064184,
       10929.37940198,  9852.93814648, 13532.24549513,  8975.74784107,
       11950.50064859, 13922.89647561,  9206.669179  , 13480.56012939,
       11824.1702701 ,  8428.99332366, 10280.62786165, 10761.27083749,
       11888.92838727, 11404.13078614, 12723.24363395, 10964.34822915,
        9976.53263002, 12442.64820484, 11015.48251927, 11818.12250712,
       13363.67455221, 12625.19385989,  9711.13491179,  9743.68379298,
       11080.78110568, 11987.06609374, 11063.27187731, 10935.10091144,
       11435.63005305, 10717.67824628, 10668.92756333,  9858.02067596,
        9759.03261078, 11732.14060299, 10895.69565095, 15186.2229698 ,
       10398.41151905, 10895.39018223, 11743.04593773, 12011.69427789,
       11413.31377267,  8920.81218442, 12100.64853017, 12142.685605  ,
        8669.94306172, 10863.2632574 , 13842.42029289, 12295.14895607,
       12776.83092699, 11786.50872889, 11064.71718986, 13794.76181894,
       10717.36420635,  8572.96565498,  9687.30808491, 13931.27732276,
       12540.69681497, 11384.08531118, 11878.75612326, 11876.75124707,
       11945.06229399, 11271.79918663,  8897.90743476, 10371.35173223,
       12415.0924782 ,  8863.66537364, 11616.70456178,  8607.00880655,
       10581.63405677,  9719.38670152, 11385.44425347,  7473.04793819,
       13022.48744777, 11396.35349915, 11882.66746664, 13018.94540275,
       10950.96681061, 10055.39106399, 10465.06848606, 13096.17154433,
       10664.92517367, 11846.69946251, 11920.63555508,  8848.83944817,
       11676.45409336, 14680.38429109, 11238.51192127, 12484.13530186,
       11623.46332236, 13694.25618208, 11908.87620961, 10457.15701494,
       12367.81699053, 11605.92559126,  9909.44232993, 12650.86097834,
       12503.35314765, 11754.6511254 ,  9521.76644665, 12951.99522976,
        8300.87555145,  8129.5321238 , 12482.49265728, 10729.17565091,
        9704.17957748, 10108.01493561,  8040.68551843,  9459.58537563,
        8875.6548931 , 12545.83598965,  8120.71763799, 13381.77370333,
       11457.21936677, 12149.08982721, 10114.53871164, 12604.93300858,
        8408.49356248, 10492.56132372,  8800.45969315, 12572.50219925,
       12052.52606993,  9558.83283931, 13302.16550826, 12140.71994083,
       10561.94991113, 13252.63075741, 12361.08207867,  9293.17586843,
       10773.29517317, 12575.22191801,  8150.31728555, 10158.31730872,
       10498.21211411,  9294.11718509, 11512.22492837, 12086.95191814,
       11905.58951226, 12056.21979514, 11783.55043798, 10381.87249236,
        9614.51471077, 11982.33598525, 11563.37704148, 10979.23136041,
       11899.11945894, 12037.11036324, 11125.77367072, 10586.4840021 ,
        8706.95283703, 13711.34439512,  8070.54339278, 12049.8503929 ,
        9027.25424165, 12085.50782813, 10705.38046147,  8717.6062918 ,
       14370.0903199 , 11037.30558497, 11487.37476506, 11322.71420903,
        8033.28239732, 12002.20514018,  9264.05699996, 11466.35549296,
        8942.4513159 ,  9025.74462322, 13902.44326097,  8893.78707802,
       11567.77257344, 12551.09105077,  8402.89606438, 10930.78799594,
       11648.91542521, 12917.56854583, 12713.15335777, 11814.65224847,
       12958.12124841, 12158.03067397, 11179.37678291,  9278.12924163,
       12640.02543852,  8546.49534972, 11348.10962545, 11072.99129439,
       11023.97942909, 12601.76271511, 11570.97552015, 13563.39314908,
        8976.9451948 ,  8887.12914342, 11164.12997477,  7349.59801436,
       12297.6377403 , 12003.38087139, 11077.40788284, 10127.2837807 ,
       10759.46387563, 10649.04178383, 10796.07837745, 13048.04448806,
       10464.6499887 ,  9455.36973093, 11106.23404978, 10223.40089743,
        8676.97838846, 10877.06833973, 10786.72331017, 13232.87131753,
       12560.65966486, 10129.57959853, 11762.86563682, 11213.62427294,
       10723.83478156, 10323.19110693, 12887.51244029, 12165.12147262,
        9067.67034924,  9815.91069961, 10922.34608037, 14307.36191062,
       10816.18660139, 12202.81147321,  8499.88212335, 12350.43882535,
        9230.93735655, 11370.61611376, 11200.67622136, 13770.79491507,
        8330.06371747, 11742.99846727, 11046.85775595,  9297.32581794,
       12799.89408687, 10574.64858958, 11423.39836545, 11315.90253714,
       10307.65262234,  7893.2361795 ,  9870.0870919 , 10938.20075926,
       12948.14320036, 10814.20903472, 14047.97609045, 11302.41790933,
        9946.63323734,  9500.22293708, 14010.0340521 , 10282.6559869 ,
       11970.80623827,  9874.12347864,  9971.93112213,  8493.84065595,
       10388.7205472 ,  8966.89519204,  9195.00539556, 10897.77393112,
       11058.80252548,  9508.46221552,  8710.25832147, 12042.05594272,
       10221.49974833, 12455.93087572])


valid_y5_pred_df = pd.DataFrame(valid_y5_pred, columns = ["Validation_Prediction"])
valid_y5_pred_df


mse_valid_5 = sklearn.metrics.mean_squared_error(valid_y5, valid_y5_pred)
mse_valid_5

529003242.8305753


# As before
# import math

rmse_valid_5 = math.sqrt(mse_valid_5)
rmse_valid_5

23000.070496208817


np.std(valid_y5)

23606.478158841604


# As before:

# If using the dmba package:

# pip install dmba


# Done earlier. Just for illustration
# import dmba
# from dmba import regressionSummary

regressionSummary(valid_y5, valid_y5_pred)

Regression statistics

                      Mean Error (ME) : 2498.2800
       Root Mean Squared Error (RMSE) : 23000.0705
            Mean Absolute Error (MAE) : 9245.0033
          Mean Percentage Error (MPE) : -69.6001
Mean Absolute Percentage Error (MAPE) : 93.7624


new_players_df


#new_players_df = make_regression(n_features = 1, random_state = 666)


new_records_players_pred_5 = model_elastic.predict(new_players_df)
new_records_players_pred_5

C:\Users\byeo\Anaconda3\lib\site-packages\sklearn\base.py:443: UserWarning: X has feature names, but ElasticNet was fitted without feature names
  warnings.warn(

array([13308.1034435 , 11652.42206796, 11237.31927071])


new_records_players_pred_5_df = pd.DataFrame(new_records_players_pred_5, columns = ["Prediction"])
new_records_players_pred_5_df


alpha = 0.05
ci_5 = np.quantile(train_residuals_5, 1 - alpha)
ci_5

122.20585214240019


def generate_results_confint_5(preds, ci_5):
    df = pd.DataFrame()
    df["Prediction"] = preds
    if ci >= 0:
        df["upper"] = preds + ci_5
        df["lower"] = preds - ci_5
    else:
        df["upper"] = preds - ci_5
        df["lower"] = preds + ci_5
    return df


new_records_players_pred_confint_df_5 = generate_results_confint_5(new_records_players_pred_5, ci_5)
new_records_players_pred_confint_df_5

	Validation_Prediction
0	2665.300452
1	23944.880671
2	15211.676647
3	24207.972902
4	29601.313799
...	...
641	581.477513
642	-1611.414995
643	20698.082536
644	11526.176711
645	30443.668736

	Prediction	upper	lower
0	29318.869430	46544.768820	12092.970041
1	20847.319389	38073.218778	3621.419999
2	29120.845197	46346.744586	11894.945808

	Age	Balance	ShotPower	Aggression	Positioning	Composure
13946	1.414973	1.838849	1.851258	1.806180	1.857332	1.857332
7711	1.342423	1.929419	1.838849	1.799341	1.672098	1.748188
8402	1.397940	1.812913	1.716003	1.342423	1.740363	1.716003
13651	1.414973	1.770852	1.880814	1.903090	1.875061	1.857332
1625	1.447158	1.740363	1.845098	1.740363	1.785330	1.851258

	Age	Balance	ShotPower	Aggression	Positioning	Composure	Preferred Foot_Right	Body Type_Lean	Body Type_Normal	Body Type_Stocky
13946	1.414973	1.838849	1.851258	1.806180	1.857332	1.857332	1	1	0	0
7711	1.342423	1.929419	1.838849	1.799341	1.672098	1.748188	1	0	0	1
8402	1.397940	1.812913	1.716003	1.342423	1.740363	1.716003	1	1	0	0
13651	1.414973	1.770852	1.880814	1.903090	1.875061	1.857332	0	0	1	0
1625	1.447158	1.740363	1.845098	1.740363	1.785330	1.851258	0	1	0	0

	Age	Balance	ShotPower	Aggression	Positioning	Composure
7882	1.477121	1.770852	1.826075	1.591065	1.799341	1.716003
14555	1.380211	1.740363	1.903090	1.770852	1.851258	1.812913
16210	1.505150	1.785330	1.845098	1.716003	1.875061	1.826075
15847	1.380211	1.778151	1.875061	1.690196	1.851258	1.845098
12382	1.431364	1.826075	1.880814	1.740363	1.892095	1.886491

Regression¶

Goal! Goal! Goal!¶

1. Load Data¶

1.1 Libraries¶

1.2 Data¶

1.3 Filter required records and variables¶

2. Regression¶

2.1 Training-Validation Split¶

2.2 Training the Regression Model¶

2.2.1 Model Evaluation on Training¶

2.3 Predict Validation Set¶

2.3.1 Model Evaluation on Validation¶

2.3.2 Traditional model evaluation¶

3. New Records¶

4. Non-Linear Regression¶

4.1 Log transformation¶

4.2 Training the Log Regression Model¶

4.2.1 Model Evaluation on Training (Log Regression)¶

4.3 Predict Validation Set (Log Regression)¶

4.3.1 Model Evaluation on Validation (Log Regression)¶

4.4 Predict New Records (Log Regression)¶

5. Ridge Regression¶

5.1 Transformation¶

5.2 Training the Ridge Regression Model¶

5.2.1 Model Evaluation on Training (Ridge Regression)¶

5.3 Predict Validation Set (Ridge Regression)¶

5.3.1 Model Evaluation on Validation (Ridge Regression)¶

5.4 Predict New Records (Ridge Regression)¶

6. Lasso Regression¶

6.1 Transform¶

6.2.1 Model Evaluation on Training (Lasso Regression)¶

6.3 Predict Validation Set (Lasso Regression)¶

6.3.1 Model Evaluation on Validation (Lasso Regression)¶

6.4 Predict New Records (Lasso Regression)¶

7. Elastic Net¶

7.1 Transformation¶

7.2.1 Model Evaluation on Training (Elastic Regression)¶

7.3 Predict Validation Set (Elastic Regression)¶

7.3.1 Model Evaluation on Validation (elastic Regression)¶

7.4 Predict New Records (Elastic Regression)¶

	ID	Name	Age	Photo	Nationality	Flag	Overall	Potential	Club	Club Logo	...	Composure	Marking	StandingTackle	SlidingTackle	GKDiving	GKHandling	GKKicking	GKPositioning	GKReflexes	Release Clause
0	207439	L. Paredes	24	https://cdn.sofifa.org/players/4/19/207439.png	Argentina	https://cdn.sofifa.org/flags/52.png	80	85	NaN	https://cdn.sofifa.org/flags/52.png	...	74.0	73.0	75.0	72.0	9.0	14.0	6.0	9.0	10.0	NaN
1	156713	A. Granqvist	33	https://cdn.sofifa.org/players/4/19/156713.png	Sweden	https://cdn.sofifa.org/flags/46.png	80	80	NaN	https://cdn.sofifa.org/flags/46.png	...	78.0	82.0	83.0	79.0	7.0	9.0	12.0	10.0	15.0	NaN
2	229909	A. Lunev	26	https://cdn.sofifa.org/players/4/19/229909.png	Russia	https://cdn.sofifa.org/flags/40.png	79	81	NaN	https://cdn.sofifa.org/flags/40.png	...	69.0	18.0	20.0	12.0	80.0	73.0	65.0	77.0	85.0	NaN
3	187347	I. Smolnikov	29	https://cdn.sofifa.org/players/4/19/187347.png	Russia	https://cdn.sofifa.org/flags/40.png	79	79	NaN	https://cdn.sofifa.org/flags/40.png	...	73.0	76.0	76.0	80.0	7.0	12.0	10.0	8.0	15.0	NaN
4	153260	Hilton	40	https://cdn.sofifa.org/players/4/19/153260.png	Brazil	https://cdn.sofifa.org/flags/54.png	78	78	Montpellier HSC	https://cdn.sofifa.org/teams/2/light/70.png	...	70.0	83.0	77.0	76.0	12.0	7.0	11.0	12.0	13.0	NaN

	Variables
0	ID
1	Name
2	Age
3	Photo
4	Nationality
...	...
83	GKHandling
84	GKKicking
85	GKPositioning
86	GKReflexes
87	Release Clause

	ID	Name	Age	Photo	Nationality	Flag	Overall	Potential	Club	Club Logo	...	Composure	Marking	StandingTackle	SlidingTackle	GKDiving	GKHandling	GKKicking	GKPositioning	GKReflexes	Release Clause
5	187607	A. Dzyuba	29	https://cdn.sofifa.org/players/4/19/187607.png	Russia	https://cdn.sofifa.org/flags/40.png	78	78	NaN	https://cdn.sofifa.org/flags/40.png	...	70.0	21.0	15.0	19.0	15.0	12.0	11.0	11.0	8.0	NaN
8	183389	G. Sio	29	https://cdn.sofifa.org/players/4/19/183389.png	Ivory Coast	https://cdn.sofifa.org/flags/108.png	77	77	NaN	https://cdn.sofifa.org/flags/108.png	...	72.0	40.0	18.0	12.0	15.0	9.0	10.0	15.0	16.0	NaN
18	245683	K. Fofana	26	https://cdn.sofifa.org/players/4/19/245683.png	Ivory Coast	https://cdn.sofifa.org/flags/108.png	75	75	NaN	https://cdn.sofifa.org/flags/108.png	...	83.0	23.0	37.0	46.0	7.0	11.0	7.0	11.0	14.0	NaN
45	190461	B. SigurÌ¡arson	27	https://cdn.sofifa.org/players/4/19/190461.png	Iceland	https://cdn.sofifa.org/flags/24.png	73	74	NaN	https://cdn.sofifa.org/flags/24.png	...	76.0	31.0	39.0	24.0	9.0	12.0	10.0	15.0	16.0	NaN
65	225900	J. Sambenito	26	https://cdn.sofifa.org/players/4/19/225900.png	Paraguay	https://cdn.sofifa.org/flags/58.png	71	74	NaN	https://cdn.sofifa.org/flags/58.png	...	74.0	15.0	16.0	16.0	15.0	16.0	15.0	7.0	7.0	NaN

	Age	Preferred Foot	Body Type	Balance	ShotPower	Aggression	Positioning	Composure	Wage
5	29	Right	Stocky	32.0	78.0	75.0	78.0	70.0	1105
8	29	Left	Normal	73.0	77.0	77.0	76.0	72.0	2138
18	26	Right	Normal	60.0	78.0	67.0	72.0	83.0	3875
45	27	Right	Normal	76.0	68.0	73.0	73.0	76.0	3661
65	26	Right	Lean	64.0	73.0	49.0	75.0	74.0	2445

	Age	Balance	ShotPower	Aggression	Positioning	Composure	Preferred Foot_Right	Body Type_Lean	Body Type_Normal	Body Type_Stocky
13946	26	69.0	71.0	64.0	72.0	72.0	1	1	0	0
7711	22	85.0	69.0	63.0	47.0	56.0	1	0	0	1
8402	25	65.0	52.0	22.0	55.0	52.0	1	1	0	0
13651	26	59.0	76.0	80.0	75.0	72.0	0	0	1	0
1625	28	55.0	70.0	55.0	61.0	71.0	0	1	0	0

	Training_Prediction
0	24239.854836
1	3778.754829
2	-4114.308026
3	29762.024484
4	15704.772118
...	...
1501	25387.715396
1502	21812.772659
1503	18813.390878
1504	21533.923216
1505	22278.554844

	Wage_Residuals
13946	-1727.854836
7711	2981.245171
8402	9491.308026
13651	-16051.024484
1625	-5183.772118
...	...
12759	-3215.715396
17284	-15227.772659
1016	-7666.390878
16984	-9871.923216
16744	4022.445156

	Wage_Residuals
7882	2962.699548
14555	4930.119329
16210	-8270.676647
15847	-14063.972902
12382	16275.686201
...	...
8620	5455.522487
10786	6010.414995
16154	13639.917464
4990	-8092.176711
14654	-14046.668736

	Training_Prediction
0	4.166707
1	3.704305
2	3.530993
3	4.228996
4	3.970243
...	...
1501	4.194870
1502	4.084830
1503	4.084469
1504	4.079712
1505	4.129728

	Validation_Prediction
0	3.763674
1	4.155299
2	4.027618
3	4.170611
4	4.276642
...	...
641	3.666006
642	3.527948
643	4.103126
644	3.883251
645	4.266319

	Prediction
0	4.255181
1	4.077111
2	4.175857

	Prediction	upper	lower
0	4.255181	4.691515	3.818848
1	4.077111	4.513445	3.640777
2	4.175857	4.612190	3.739523

	Prediction	upper	lower
0	17996.217938	49149.030458	6589.425204
1	11942.935088	32617.057784	4372.978686
2	14991.900984	40944.013939	5489.376187

	Training_Prediction
0	25188.511557
1	3860.144876
2	-4188.448556
3	29995.100230
4	16109.083754
...	...
1501	26829.388840
1502	22783.529768
1503	19245.959689
1504	21417.504200
1505	23004.191104

	Validation_Prediction
0	2649.722558
1	25264.255715
2	16424.063481
3	25332.958518
4	31095.512607
...	...
641	542.307771
642	-3370.661042
643	21575.958067
644	11577.692233
645	31487.346512

	Prediction	upper	lower
0	30907.216402	47952.695192	13861.737611
1	21909.600277	38955.079068	4864.121487
2	30847.249183	47892.727973	13801.770392

	Training_Prediction
0	23664.751297
1	7309.438450
2	1682.142591
3	25612.713391
4	22900.953559
...	...
1501	28429.116142
1502	4783.812410
1503	25528.996290
1504	23094.834507
1505	23317.792428

	Validation_Prediction
0	16088.874881
1	22865.803237
2	22916.515027
3	20285.756474
4	26242.490423
...	...
641	4995.936456
642	-10271.216895
643	17437.659872
644	12105.071401
645	12295.799079

	Prediction	upper	lower
0	24044.911089	43816.698789	4273.123389
1	14502.477930	34274.265630	-5269.309770
2	23347.243321	43119.031021	3575.455621

	Training_Prediction
0	-239.897023
1	30.204716
2	146.411029
3	62.353370
4	177.087539
...	...
95	91.933636
96	51.808677
97	-34.029274
98	-75.674174
99	95.762135

	Validation_Prediction
0	10352.059104
1	12105.440690
2	12255.072006
3	12134.386872
4	13147.616172
...	...
641	9508.462216
642	8710.258321
643	12042.055943
644	10221.499748
645	12455.930876

	Prediction	upper	lower
0	13308.103443	13430.309296	13185.897591
1	11652.422068	11774.627920	11530.216216
2	11237.319271	11359.525123	11115.113419