Which of the following; is correct in diagnosing a multiple linear regression? C

Question

Which of the following; is correct in diagnosing a multiple linear regression? Choose all correct answers. a. Difference in Fits (DFITS) is a measure of the change in the predicted value when observation i is omitted. b. DFFITS > 2 squareroot p/n can be used as a criterion for declaring an influential outlier. c. COOK'S Distance summarizes how much all of the fitted values clings when the ith observation is deleted. d. If the COOK'S Distance is greater than 1. then the ith data point Is worthy of further investigation. e. DFBETAS is a measure of the influence of the ith case on each regression coefficient by the difference between the estimated regression coefficient based on all n cases and the regression coefficient obtained when the ith case is omitted. Which of the followings is correct in diagnosing a multiple linear regression? Choose all correct answers. a. The DFBETA value by its sign indicates whether inclusion of a case leads to an increase or a decrease in the estimated regression coefficient, and its absolute magnitude shows the size of the difference relative to the estimated standard deviation of the regression coefficient. b. The absolute value of DFBETAS p/n merits further investigation. c. Standardized residuals are simply the residuals of a regression, divided by the standard deviation of the residuals. d. If the residuals are normal with mean zero, dividing each residual by its standard deviation makes the standardized residuals distributed as a standard normal. c. To identify an outlier with respect to X, we simply look for standardized residuals which are large in alisolute value. Which of the followings is correct in diagnosing a multiple linear regression? Choose all correct answers. a. Shapiro-Wilk Test and Kolmogorov-Smirnov Test are used to check for outliers. b. Box-Cox Transformations are employed when there are outliers. c.A small p-value in Shapiro-Wilks test concludes that there exists a multicollinearity problem in the data set. d. Examining the normal probability plot of residuals can detect outliers. e. All outliers are influential points. Which of the followings is correct when checking assumpt ions in a multiple linear regression? Choose all correct answers. a. Residual plot can be used to examine the independence assumption. b. Studentized residual can be used to check of possible outliers with respect to independent variaWes in the model c. Residual plot can be used to check for the normality assumption. d. Studentized residual plot can not be used to check for homoscedasticity assumption. e. Studentized residual plot can be used to check for the zero mean assumption of errors.

Explanation / Answer

For diagonising multiple linear regression, all the options (a)-(e) are correct.

For the second set of options of dianonising multiple linear regression, options (c)-(e) are correct.

For the third set of options, only option (d) is correct.

For the final set of options, options (a), (b), (c), and (e) are correct.

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