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Unformatted text preview: STA 3024 Exam 3 Sample Questions 1. In multiple linear regression, which of the following would probably happen if we decided to include an additional explanatory variable? (A) The ˆ Y i s would tend to get farther from ¯ Y . (B) The ˆ Y i s would tend to get closer to ¯ Y . (C) The Y i s would tend to get farther from ¯ Y . (D) The Y i s would tend to get closer to ¯ Y . 2. A multiple regression with two explanatory variables and 47 observations yields the following regression equation ˆ Y ( X 1 ,X 2 ) = 3 . 673 . 0992 X 1 + 3 . 746 X 2 . The data for a few observations is shown below. Observation X 1 X 2 Y . . . . . . . . . . . . 33 38.7 31.2 373.3 34 102.7 36.7208.8 35 49.7 39.6 165.8 . . . . . . . . . Calculate the quantity that we call ˆ Y 34 . (A) 131.0 (B) 134.4 (C) 141.4 (D) 144.0 (E) 151.3 3. In multiple regression, which of the following would probably change if we redid our calculations using a different random sample with the same number of observations? (A) the values of b 1 ,...,b p (B) the value of MS Res (C) both (A) and (B) (D) neither (A) nor (B) 4. Which of the following would be the most useful for checking the normality assumption in multiple regression? (A) scatterplots of the standardized residuals (B) a histogram of the standardized residuals (C) the residual mean square ( MS Res ) (D) the residual sum of squares ( SS Res ) (E) the residual degrees of freedom ( df Res ) 5. In multiple regression, generally speaking, if we want to use more explanatory variables, then (A) we need to have fewer observations. (B) we need to have more observations. 6. In multiple linear regression with five explanatory variables, a researcher is using the Bonferroni method to construct simultaneous confidence intervals for the five parameters β 1 ,...,β 5 . Suppose he wants an overall simultaneous confidence level of 95%, and he (correctly) uses a tscore of 2.678. How many observations must his data set have included? (A) 56 (B) 58 (C) 62 (D) 78 (E) 87 7. A scatterplot of the standardized residuals versus the response variable Y is shown below for a multiple linear regression with two explanatory variables. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Y Standardized Residual What can we conclude from this scatterplot? (A) We can conclude that the linearity assumption appears to be satisfied....
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 Spring '08
 TA
 Linear Regression, Regression Analysis, Errors and residuals in statistics, explanatory variables, SS Res

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