True and False Statement

Question

Discuss the following statements and explain why they are true or false:

a)      Increasing the number of predictor variables will never decrease the R²

b)      Multicollinearity affects the interpretation of the regression coefficients

c)      The variance inflation factor of βj depends on the R² of the regression of the response variable Y on the regressor variable X_j

d)     A high leverage point is always highly influential

e)      Standardized residuals are always smaller than the ordinary residuals.

 

Indicate whether the following statements are true or false

a)      A Durbin-Watson statistic of zero indicates that all regressors are insignificant in predicting the response variable

b)      If a qualitative X variable has two levels/classes, then defining two indicator variables will make the X'X matrix invertible

c)      If the variance of the error term is proportional to X², ie, Var(e)=kX², the appropriate weights are w=k/X² for performing weighted least squares.

d)     Ridge regression estimate is a biased estimator with a smaller MSE than the least squares estimate.