A7. Which of the following statements about the coefficient of multiple determin

Question

A7. Which of the following statements about the coefficient of multiple determination R' in a multiple regression model is NOT true? (a) It is a measure of the proportion of variance explained by the fitted regression model (b) Its value is in the interval [0,1] (e) It does not decrease as more variables are added to the model (d) R 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 X. X, and X, 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. Variables in Model SSR SSE -374.0 26.0 385.414.6 20.0 386.0 14.0 380.0 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, A9. Consider the model with transformed response variable ./Y! = 0 + .xa + .xi2 + Ei (i = 1,2, ,n). This model is fitted to a set of data and gives For an individual whose explanatory variables Xi and X, have values of I and 2 respectively, the value of the observed untransformed response was actually 5.0. For this individual, the predicted value of the untransformed response variable and the associated residual are (a) 16,-11 (b) 16, 11 (c) 4, 1 (d) 4,-1 (e) None of these choices A 10. Consider the model Y = 0 + ,Ka + .x2 + q (i = 1,2, . . . ,n). Suppose that based on a sample of size n, the estimated variance-covariance matrix, Var(), of the least squares estimator is calculated to be | 1 3 0 |, what is the estimate of the variance of ., where is the least squares estimate of E[%), at a new individual with Xi=1 and X;"I ? (a) 3 (b) 2 (c)1 (d) 11 (e)6 () None of these choices

Explanation / Answer

A7) The following dtatement about coefficient if determination is Not true:

R2 near to zero implies that the response variable and explanatory variable are unrelated.

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