import pandas as pd import numpy as np from sklearn.linear_model import LinearRegression from sklearn.model_selection import cross_validate

nba_data = pd.read_csv('NBA.csv') nba_data.head()

X = nba_data[['win_rating']] y = nba_data['mp'] model = LinearRegression() cv_results = cross_validate(model, X, y, cv=5) cv_score = cv_results['test_score'].mean() cv_score

import matplotlib.pyplot as plt from sklearn.model_selection import learning_curve

train_sizes = np.linspace(100, 3200, 32, dtype='int') train_sizes, train_scores, test_scores = learning_curve(estimator=LinearRegression(), X=X, y=y, train_sizes=train_sizes, cv=5) train_scores_mean = np.mean(train_scores, axis=1) test_scores_mean = np.mean(test_scores, axis=1) plt.figure(figsize=(10,6)) plt.plot(train_sizes, train_scores_mean, label='training score') plt.plot(train_sizes, test_scores_mean, label='test score') plt.ylabel('r2 score') plt.xlabel('training set size') plt.legend();

X = nba_data[['mp', 'poss', 'do_ratio', 'pacing']] y = nba_data['win_rating'] model = LinearRegression() cross_val = cross_validate(model, X, y, cv=5) score_added_features = cross_val['test_score'].mean() score_added_features

train_sizes = np.linspace(100, 3200, 32, dtype='int') train_sizes, train_scores, test_scores = learning_curve(estimator=LinearRegression(), X=X, y=y, train_sizes=train_sizes, cv=5) train_scores_mean = np.mean(train_scores, axis=1) test_scores_mean = np.mean(test_scores, axis=1) plt.figure(figsize=(10,6)) plt.plot(train_sizes, train_scores_mean, label='training score') plt.plot(train_sizes, test_scores_mean, label='test score') plt.ylabel('r2 score') plt.xlabel('training set size') plt.legend();

import seaborn as sns sns.scatterplot(data=nba_data, x='mp', y='win_rating', alpha=0.5);

from sklearn.model_selection import train_test_split # training the model model = LinearRegression() X = nba_data[['mp']] y = nba_data['win_rating'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1) model.fit(X_train, y_train) # scoring the model lin_reg_score = model.score(X_test, y_test) print("Model R2:", lin_reg_score) # extracting the coefficients and regression function regression = model.coef_[0] * nba_data['mp'] + model.intercept_ # plotting the data and learned regression function sns.scatterplot(data=nba_data, x='mp', y='win_rating', alpha=0.5) plt.plot(nba_data['mp'], regression, color='red', linewidth=3);

from sklearn.preprocessing import PolynomialFeatures polynomial_features = PolynomialFeatures(degree=2, include_bias=False) # we don't want to add a column of 1's X_poly = polynomial_features.fit_transform(X) X_poly = pd.DataFrame(X_poly) # turning it back into a DataFrame for easier manipulation X_poly.head()

sorted_df = nba_data.sort_values('mp') X = sorted_df[['mp']] y = sorted_df['win_rating'] poly_features = PolynomialFeatures(degree=2, include_bias=False) X_poly = poly_features.fit_transform(X) model.fit(X_poly, y) predictions = model.predict(X_poly) sns.scatterplot(x=X['mp'], y=y, alpha=0.5) plt.plot(X['mp'], predictions, linewidth=3, color='r');

X = nba_data[['mp', 'poss', 'do_ratio', 'pacing']] y = nba_data['win_rating'] polynomial_features = PolynomialFeatures(degree=2, include_bias=False) X_poly = polynomial_features.fit_transform(pd.DataFrame(X)) model = LinearRegression() cv_results = cross_validate(model, X_poly, y, cv=5) cv_results['test_score'].mean()

X = nba_data[['mp', 'poss', 'do_ratio', 'pacing']] y = nba_data['win_rating'] degrees = list(range(1,11)) scores = []

for i in degrees: polynomial_features = PolynomialFeatures(degree=i, include_bias=False) X_poly = polynomial_features.fit_transform(X) model = LinearRegression() cv_results = cross_validate(model, X_poly, y, cv=5) scores.append(cv_results['test_score'].mean())

scores

# Transform our X to include polynomial features poly_features = PolynomialFeatures(degree=5, include_bias=False) X_poly = poly_features.fit_transform(X) # Get train scores, train sizes, and validation scores using `learning_curve`, r2 score train_sizes, train_scores, test_scores = learning_curve( estimator = LinearRegression(), X = X_poly, y = y, train_sizes = train_sizes, cv = 5 ) # Take the mean of cross-validated train scores and test scores train_scores_mean = np.mean(train_scores, axis=1) test_scores_mean = np.mean(test_scores, axis=1) # Plot the learning curves! plt.figure(figsize=(10,6)) plt.plot(train_sizes, train_scores_mean, label = 'Training score') plt.plot(train_sizes, test_scores_mean, label = 'Test score') plt.ylabel('r2 score', fontsize = 14) plt.xlabel('Training set size', fontsize = 14) plt.title('Learning curves', fontsize = 18, y = 1.03) plt.ylim(0,1) plt.legend();

# create the training size slices train_sizes = np.linspace(100, 3200, 32, dtype='int') X_poly = PolynomialFeatures(degree=2, include_bias=False).fit_transform(X) # Get train scores, train sizes, and validation scores using `learning_curve`, r2 score train_sizes, train_scores, test_scores = learning_curve(estimator = LinearRegression(), X = X_poly, y = y, train_sizes = train_sizes, cv = 5) # Take the mean of cross-validated train scores and validation scores train_scores_mean = np.mean(train_scores, axis=1) test_scores_mean = np.mean(test_scores, axis=1) # Plot the learning curves! plt.figure(figsize=(10,6)) plt.plot(train_sizes, train_scores_mean, label = 'training score') plt.plot(train_sizes, test_scores_mean, label = 'test score') plt.ylabel('r2 score', fontsize = 14) plt.xlabel('Training set size', fontsize = 14) plt.title('Learning curves', fontsize = 18, y = 1.03) plt.legend();

# Plotting the learning curves plt.figure(figsize=(10,6)) plt.plot(train_sizes, train_scores_mean, label = 'training score') plt.plot(train_sizes, test_scores_mean, label = 'test score') plt.ylabel('r2 score', fontsize = 14) plt.xlabel('Training set size', fontsize = 14) plt.title('Learning curves', fontsize = 18, y = 1.03) # Plotting a line where difference of train and test score becomes <1% plt.axvline(1400, linestyle='--', c='black') plt.annotate('Past this line:\ntrain_score - test_score <= 0.01', xy=(1450, 0.7)) # Comparing test scores at that line and at max training data (80% of data) plt.scatter(train_sizes[14], test_scores_mean[14], c='orange', s=50) plt.annotate(f"R2: {round(test_scores_mean[14],2)}", xy=(train_sizes[14] + 50, test_scores_mean[14] - 0.03), fontsize=12, c='orange') plt.scatter(train_sizes[31], test_scores_mean[31], c='orange', s=50) plt.annotate(f"R2: {round(test_scores_mean[31],2)}", xy=(train_sizes[31] - 200, test_scores_mean[31] - 0.03), fontsize=12, c='orange') plt.legend();

# preparing the features and target X = nba_data[['mp', 'poss', 'do_ratio', 'pacing']] y = nba_data.win_rating # instantiating a linear regression model model = LinearRegression() # fitting the model model.fit(X, y) # calculating the MSE reg_score = np.mean((model.predict(X) - y) ** 2) print("Regular model MSE:", round(reg_score, 2)) ### 2nd Model ### # preparing the features and target X = nba_data[['mp', 'poss', 'do_ratio', 'pacing']] y = nba_data.win_rating # transforming the features with degree-3 polynomial features poly_features = PolynomialFeatures(degree=2, include_bias=False) X_poly = poly_features.fit_transform(X) # instantiating a linear regression model model = LinearRegression() # fitting the model model.fit(X_poly, y) # calculating the MSE poly_score = np.mean((model.predict(X_poly) - y) ** 2) print("Degree-2 polynomial feature model MSE", round(poly_score, 2))