A8 (b) Its value is in the interval [0,1] (c) It does not decrease as more varia

Question

A8

(b) Its value is in the interval [0,1] (c) It does not decrease as more variables are added to the model (d) R2 near zero implies that the response variable and the explanatory variables are unrelated A8. The manager of a college wanted to model the response variable GPA (grade point average after one year of college) using three independent variables Xi, X) and Xj, based on 100 observations. He tries all possible combinations of predictors and finds the top four combinations. In the following, these four combinations and the corresponding sums of squares for regression and error are shown. SSE 26.0 14.6 20.0 386.0 14.0 Variables in Model SSR 74.0 385.4 80.0 Which predictors should be included in the model according to the adjusted R' criterion? (a) X (b) X and X (c) X and X (d)X,X and X 8 9 5 6 7

Explanation / Answer

Formula for R2adj = 1 - MSE / MST where MSE = SSE/(n-p-1) and SST/(n-1) where n is number of observations and p number of predictors in equation.

based on adjusted r square criterion we will go with x1,x2 and x3 model as its adj r square is highest

SSR SSE SST n p Adj R square x1 374 26 400 100 1 0.934336735 x1,x2 385.4 14.6 400 100 2 0.962747423 x1,x3 380 20 400 100 2 0.948969072 x1,x2,x3 386 14 400 100 3 0.96390625

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