Which of the followings is correct when selecting a best subset in a multiple li

Question

Which of the followings is correct when selecting a best subset in a multiple linear regression? Choose all correct answers.

a. Missing one or more important predictor does not yield biased regression coefficients and biased predictions of the response.

b. Missing one or more important predictor yields wider confidence intervals than it should.

c. A regression model that contains one or more extraneous variables that are neither related to the response yields biased predictions of the response, and a biased MSE.

d. Confidence intervals tend to be wider in a regression model that contains one or more extraneous variables that are neither related to the response.

e. Important predictor variables observed within a narrow range of values may turn out to be statistically nonsignificant.

Explanation / Answer

The problem of selecting the best subset or subsets of independent variables in a multiple linear regression analysis is two-fold. The first, and most important problem is the development of criterion for choosing between two contending subsets. Applying these criteria to all possible subsets, if the number of independent variables is large, may not be economically feasible and so the second problem is concerned with decreasing the computational effort.

b and d

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