Which of the followings in correct when checking model fit in a MLR? Choose all

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Which of the followings in correct when checking model fit in a MLR? Choose all correct answers. a. In large sampled, the normality assumption is not important because the Central Limit Theorem shows that the sample distribution of the estimators are normal. b. A high R^2 can occur when outliers are present in the data set. c. We cannot formally test for non-zero mean residuals. d. A high r^2 can occur when there exists a multi collinearity in the data set. e. It is possible that timple pairwise correlations are small, and yet a multicollinearity exists in a data set. 37. Which of the followings is correct about multicollinearity in a MLR? Choose all correct answers. a. Correcting multicollinearity is not important if you are using regression only for inference and coefficient estimation. b. Data-based multicollinearity may be caused by creating new ibdependent variable from other predictor variables. c. A structural multicollinearity is always present to some degree. d. We can reduce a data-based multicollinearity by doing what is known as "centering the predictors." e. It is possible that partial linear correlations are small, and yet a multicollinearity exists in a data set. 38. Which of the following is correct when a multicollinearity presents in a MLR? Choose all correct answers. a. The marginal sum of squares SSR(X_1) is very to the extra sum of squares SSR(X_1|X_2). b. When independent variables are correlated, the effect on the response ascribed to an independent variable is similar regardless of the other independent variables in the model. c. The common interpretation of a regression coefficient as measuring the change in the expected value of the response variable when the given predictor variable is increased by one unit while all other predictor variables are held constant is still valid when multicollinearity exists. d. The precision of the estimated regression coefficients increases as more predictor variables are added to the model. Variables in model. e. The individual estimates could be statistically significant, whereas the overall f-test is insignificant. f. The regression coefficient of anyone variable does not depend on which other predictor variables are not included in the model. g. Large changes in the estimated regression coefficients when a predictor variable is added or deleted do no indicate a multicollinearity in a data set. h. When some or all predictor variables are correlated among themselves, in general, it inhibits our ability to obtain a good fit and tends to affect inferences about mean responses or predictions of new observations, provided these inferences are made within the region of observations. i. VIFs measure how much the variances of the estimated regression coefficients are inflated as compared to when the independent variables are not linearly related. j. Multicollinearity needs to be corrected if a regression is used obly for forceasting. 39. Whihc of the followings is incorrect about detection of a multicollinearity in a MLR? Choose all correct answers. a. Nonsignificant results in individual tests on the regression coefficients for important predictor variables. b. Estimated regression coefficients with an algebraic sign that is the opposite of that expected from theoretical considerations or prior expreience. c. VIFs exceeding 10 are signs of serious multicollinearity requiring correction. d. Large simple correlation coefficients between pairs of predictor variables in the correlation matrix. e. Wide confidence intervals for the regression coefficients representing important predictor variables.

Explanation / Answer

answer to question no 36 is (d)

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