Select True or False from each pull-down menu, depending on whether the correspo
ID: 3251152 • Letter: S
Question
Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false. In multiple regression, the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression, since the F-test combines these t-tests into a single test. In regression analysis, the total variation in the dependent variable y measured by Sum(y_i - y^bar)^2, can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE. In multiple regression, the standard error of estimate is defined by S_elementof = Squareroot SSE/(n - k), where n is the sample size and k is the number of independent variables. In multiple regression, and because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not nearly related to the dependent variable when in fact they are.Explanation / Answer
1) FALSE
Multicollinearity refers to independent variables that are correlated with each other. Multicollinearity causes standard errors for the regression coefficients to be too high, which, in turn, causes the t-statistics to be too low. However,multicollinearity has no effect on the F-statistic.
2) TRUE
We know that TSS=SSR+SSE, hence true.
3) TRUE.
This is the actual formula for standard error of the estimate.
4) TRUE