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True and False Statement

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 Xj

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.

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