PCR, PLS, and Lasso Regression

This chapter begins by introducing the problem of multicollinearity, which occurs when predictor variables are highly correlated with each other. Multicollinearity can lead to unreliable coefficient estimates and inflated standard errors in methods, such as multiple linear regression. This issue is particularly problematic in high-dimensional datasets, where some predictors are likely to be strongly correlated. To address these challenges, we will explore how principal component regression and partial least squares regression combine highly correlated predictors, as well as how to compute confidence intervals using bootstrapping. This chapter ends with Lasso regression, a regularization technique that can shrink parameter estimates to zero. When multiple features are highly correlated, Lasso may randomly select one and discard the others.