Discuss the following statements and explain why they are true or false:
a) Increasing the number of predictor variables will never decrease the R^2.
b) Multicollinearity affects the interpretation of the regression coefficients.
c) The variance inflation factor of Bhat depends on the R^2 of the regression of the response variable Y on the regressor variable Xj.
d) A high leverage point is always highly influential.
e) Standardized residuals are always smaller than the ordinary residuals.