A data science team is developing a multiple linear regression model to forecast monthly energy consumption. Diagnostic checks show a Pearson correlation of 0.96 between the predictors "heated_area_sqft" and "total_floor_area_sqft" and Variance Inflation Factors near 25 for both variables. When the model is refit on different random training samples, the coefficients for these two predictors vary widely even though the model's R² remains stable. Domain experts require that both predictors stay in the model. Which modeling adjustment is most likely to mitigate the multicollinearity problem while retaining both variables and without creating new synthetic features?
Increase the training-set size by appending several additional months of data before refitting the ordinary least-squares model.
Standardize all predictors to mean-zero, unit-variance and refit ordinary least squares.
Fit a ridge regression model and tune the L2 penalty (λ) by cross-validation.
Add an interaction term heated_area_sqft × total_floor_area_sqft to capture their joint effect.
Ridge regression (L2-regularized linear regression) adds a penalty proportional to the squared magnitude of the coefficients. Shrinkage reduces the variance of highly correlated coefficients, lowering their VIFs and stabilizing estimates while allowing all original predictors to remain in the model. Scaling predictors to z-scores improves numerical conditioning but does not eliminate the underlying correlation, so multicollinearity largely persists. Adding an interaction term usually increases, rather than decreases, multicollinearity because the product term is itself highly correlated with the main effects. Simply enlarging the data set can modestly reduce coefficient variance, but it does not address the near-exact linear relationships that produce high VIFs, so the issue may remain even with more observations.
Ask Bash
Bash is our AI bot, trained to help you pass your exam. AI Generated Content may display inaccurate information, always double-check anything important.
What is multicollinearity in regression models?
Open an interactive chat with Bash
How does ridge regression address multicollinearity?
Open an interactive chat with Bash
What is the role of the L2 penalty (λ) in ridge regression?