from jupyterthemes.stylefx import set_nb_theme set_nb_theme('gruvboxd')

#Importing useful libraries import pandas as pd import numpy as np import matplotlib.pyplot as plt import seaborn as sns from copy import deepcopy from scipy.stats import shapiro from statsmodels.graphics.gofplots import qqplot from statsmodels.stats.outliers_influence import variance_inflation_factor from statsmodels.tools.tools import add_constant from sklearn.linear_model import LinearRegression from xgboost import XGBRegressor from sklearn.model_selection import train_test_split from sklearn.preprocessing import RobustScaler from sklearn.metrics import mean_squared_error from sklearn.metrics import r2_score from sklearn.metrics import mean_absolute_error from warnings import filterwarnings filterwarnings(action = 'ignore') %matplotlib inline

raw = pd.read_csv('surveyofbodyfat.csv') df = deepcopy(raw)

#Features with above +-0.5 of correlation coefficient affect the most df.corr()['BodyFat'].to_frame().sort_values(by='BodyFat', ascending=False).iloc[1:].T

sns.displot(df['BodyFat'], bins=20, color='grey') plt.show()

def normality_visual(data): for column in data.columns: fig = qqplot(data[column], line = '45', fit=True) ax = plt.gca() fig.set_size_inches(15, 8) ax.set_xlabel('Theoretical Quantiles', fontsize=13) ax.set_ylabel(f'Sample Quantiles of the {column} column', fontsize=13) plt.show()

normality_visual(df)

sns.set(rc={'figure.figsize':(10,7)}) mask = np.triu(np.ones_like(df.corr(), dtype=bool)) sns.heatmap(df.corr(), mask=mask, annot=True) plt.show()

df.describe().iloc[2,:].reset_index().T #standard deviations

df.duplicated().sum()

class handle_vif(): def __init__(self, data): self.data = data def compute_vif(self, considered_features: list): self.considered_features = considered_features X = self.data[self.considered_features] X['intercept'] = 1 self.vif = pd.DataFrame() self.vif["Variable"] = X.columns self.vif["VIF"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])] self.vif = self.vif[self.vif['Variable']!='intercept'] return self.vif def drop_high_vif(self): self.vif_table = self.vif.sort_values(by='VIF', ascending=False).reset_index(drop=True) while self.vif_table['VIF'].iloc[0]>5: self.data.drop(self.vif_table['Variable'][0], axis=1, inplace=True) computed = compute_vif([col for col in df.columns if col!='BodyFat']) self.vif_table = computed.sort_values(by='VIF', ascending=False).reset_index(drop=True) return self.data.head()

vif = handle_vif(df)

vif.compute_vif([col for col in df.columns if col!='BodyFat'])

vif.drop_high_vif()

df.corr()['BodyFat'].to_frame().sort_values(by='BodyFat', ascending=False).iloc[1:].T

df = df[[f for f in df.columns if abs(df[f].corr(df['BodyFat']))>0.5]]

df = pd.concat([df.iloc[:,1:], df.iloc[:,0]], axis=1)

X = df.iloc[:,:-1] y = df['BodyFat']

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)

scaler = RobustScaler() X_train = scaler.fit_transform(X_train) X_train = pd.DataFrame(X_train) scaler = RobustScaler() X_test = scaler.fit_transform(X_test) X_test = pd.DataFrame(X_test)

lin_mod = LinearRegression() lin_mod.fit(X_train, y_train) preds = lin_mod.predict(X_test)

rmse = np.sqrt(mean_squared_error(y_test, preds)) rmse

r2_score(y_test, preds)

mean_absolute_error(y_test, preds)

normalized_rmse = rmse/(47.5-0) #rmse divided by the range normalized_rmse