If the number of PLS components equals the number of predictors in OLS, the forecasted values from both methods are what?

If the number of PLS components equals the number of predictors in OLS, the forecasted values from both methods are what?

• A. The same
• B. The opposite
• C. PLS superior
• D. OLS superior

Answer: (A)

When you use as many PLS components as there are predictors, the latent variables span the entire predictor space. If the predictor matrix has full column rank, OLS has a unique linear relationship between X and Y, and PLS with a full set of components can reproduce that same relationship. In this case, the fitted values from PLS and OLS are identical because both methods are effectively representing the same linear mapping from X to Y.

When you use as many PLS components as there are predictors, the latent variables span the entire predictor space. If the predictor matrix has full column rank, OLS has a unique linear relationship between X and Y, and PLS with a full set of components can reproduce that same relationship. In this case, the fitted values from PLS and OLS are identical because both methods are effectively representing the same linear mapping from X to Y.