Multicollinearity
import pandas as pd import numpy as np import seaborn as sns import matplotlib.pyplot as plt from statsmodels.stats.outliers_influence import variance_inflation_factor from numpy.linalg import eig from sklearn.decomposition import PCA from sklearn.model_selection import train_test_split from sklearn.linear_model import LinearRegression, Ridge from sklearn.metrics import mean_squared_error, r2_score np.random.seed(73) num_players = 200 batting_average = np.random.normal(0.28, 0.05, num_players) batting_average = np.clip(batting_average, 0.2, 0.4) AB = np.random.randint(300, 700, num_players) # At-bats for the season H = AB * batting_average dividing the total number of bases a player records by their total number of at-bats
maybe replace this with something else?
height = np.random.normal(72, 6, num_players) Wind = np.random.uniform(-1.5, 1.5, num_players) # Average wind factor affecting performance (AB * 0.02) + (height * 0.01) + (Wind * 7) + np.random.normal(0, 10, num_players) RBIs_rounded = np.round(RBIs) H_rounded = np.round(H) AB_rounded = np.round(AB) # Create the DataFrame data = pd.DataFrame({ 'AB': AB_rounded, # At-Bats 'H': H_rounded, # Hits 'Height': height, # Slugging Percentage 'Wind': Wind, # Wind Factor 'RBIs': RBIs_rounded # Runs Batted In (Target) }) print(data.head()) 
X = data[['AB', 'H', 'Height', 'Wind']] y = data['RBIs'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) lr = LinearRegression() lr.fit(X_train, y_train) 
y_pred = lr.predict(X_test) mse_before = mean_squared_error(y_test, y_pred) r2_before = r2_score(y_test, y_pred) print("Regression Coefficients (Before):", lr.coef_) 
print("Mean Squared Error (Before):", mse_before) 
print("R^2 (Before):", r2_before) 
CORRELATION MATRIX
correlation_matrix = X.corr() # Visualize the correlation matrix sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', fmt=".2f") plt.title("Correlation Matrix") plt.show() 
VIF
vif_data = pd.DataFrame() vif_data["Feature"] = X.columns vif_data["VIF"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])] print(vif_data) 
Instead of using raw height, you might normalize or categorize height into bins, which could reduce the numerical interdependence.
Calculate Condition Index (CI)
features = data[['AB', 'H', 'Height', 'Wind']] normalized_features = (features - features.mean()) / features.std() cov_matrix = np.cov(normalized_features.T) eigenvalues, _ = np.linalg.eig(cov_matrix) condition_indices = np.sqrt(eigenvalues.max() / eigenvalues) ci_data = pd.DataFrame({ "Condition Index": condition_indices }) print(ci_data) 
How to address Multicollinearity
Drop a Feature (At Bats)
X_reduced = X[['H', 'Height', 'Wind']] look at corr matrix
correlation_matrix = X_reduced.corr() # Visualize the correlation matrix sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', fmt=".2f") plt.title("Correlation Matrix") plt.show() 
VIF
vif_data_2 = pd.DataFrame() vif_data_2["Feature"] = X_reduced.columns vif_data_2["VIF"] = [variance_inflation_factor(X_reduced.values, i) for i in range(X_reduced.shape[1])] print(vif_data_2) 
lr_reduced = LinearRegression() lr_reduced.fit(X_train[['H', 'Height', 'Wind']], y_train) 
y_pred_reduced = lr_reduced.predict(X_test[['H', 'Height', 'Wind']]) mse_reduced = mean_squared_error(y_test, y_pred_reduced) r2_reduced = r2_score(y_test, y_pred_reduced) print("Regression Coefficients (Reduced):", lr_reduced.coef_) 
print("Mean Squared Error (Reduced):", mse_reduced) 
print("R^2 (Reduced):", r2_reduced) 
Perform PCA
pca = PCA(n_components=3) # Reduce to 3 components X_train_pca = pca.fit_transform(X_train) X_test_pca = pca.transform(X_test) lr_pca = LinearRegression() lr_pca.fit(X_train_pca, y_train) 
y_pred_pca = lr_pca.predict(X_test_pca) mse_pca = mean_squared_error(y_test, y_pred_pca) r2_pca = r2_score(y_test, y_pred_pca) print("Regression Coefficients (PCA):", lr_pca.coef_) 
print("Mean Squared Error (PCA):", mse_pca) 
print("R^2 (PCA):", r2_pca) 
Ridge Regression
Ridge regression reduces the impact of multicollinearity by adding an L2 penalty to the regression coefficients.
ridge = Ridge(alpha=1.0) ridge.fit(X_train, y_train) 
y_pred_ridge = ridge.predict(X_test) mse_ridge = mean_squared_error(y_test, y_pred_ridge) r2_ridge = r2_score(y_test, y_pred_ridge) print("Regression Coefficients (Ridge):", ridge.coef_) 
print("Mean Squared Error (Ridge):", mse_ridge) 
print("Mean Squared Error (Ridge):", r2_ridge) 
