statistics regression

II. 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

j

b

ˆ

depends on the R2 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.

III. 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()=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.