RegressionAnalysis-FIFA2019-OverallRating

Predicting Overall Rating for FIFA 2019 Dataset using only Linear Regression based techniques

Link to DataSet

Used All Numerical Features except Potential Rating for predicting Overall Rating.

Scores :

Adjusted R^2 = 0.90
RMSE = 0.11

Link to Kaggle R Notebook

Visualize first 100 Predictions :

Process :

Removed Multicollinear Features, tested Global and Individual Significance Hypotheses.
Residual Analysis Plots - 1. Residuals vs Fitted 2. QQ Plot 3. Scale Location 4. Residuals vs Leverage
Residuals Look like Normal Distribution, but Shapiro-Wilk test rejects it. Shown that this is expected by simulating Shapiro-Wilk Test that rejects Random Normal Variables with slight deviation for n=5000 dataset.
Used the BoxCox transformation on y to stabilize variance, removing Outliers detected using Leverage, Cook's Distance, DFBETAS, DFFITS, and COVRATIO techniques, then retrained model.
Also implemented olssr Model Selection Techniques- Backward Elimination, Stepwise Elimination, Step Back AIC, Step Forward AIC.