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Unformatted text preview: STA 3024 Exam 3 Practice Questions 1. A simple linear regression yields the regression equation ˆ Y ( X ) = 26 . 3 . 47 X, where the X values of our data vary from about 12 to about 28. Find the predicted value of Y for a new observation with an X value of 20.8. (A) 16.5 (B) 36.1 (C) 46.6 (D) We should not predict the value of Y for this new observation, because 20.8 is between 12 and 28. 2. For n = 42 observations, we record the values of X and Y . Summary statistics for the two samples are as follows: ¯ X = 1 . 75 S X = 0 . 25 ¯ Y = 0 . 69 S Y = 0 . 16 Calculate the regression equation, ˆ Y ( X ) = a + bX . (A) ˆ Y ( X ) = . 43 + 0 . 64 X (B) ˆ Y ( X ) = 0 . 05 + 0 . 64 X (C) ˆ Y ( X ) = 1 . 81 + 0 . 64 X (D) We do not have enough information to calculate the regression equation. 3. In simple linear regression, we talk about two equations: μ Y ( X ) = α + βX and ˆ Y ( X ) = a + bX . Which one of the following statements is true? (A) β is a parameter; we know its value. (B) β is a statistic; we do not know its value. (C) b is a parameter; we do not know its value. (D) None of these statements are true. 4. In simple linear regression, the sample correlation between the two variables is r , and the slope of the regression line is b . Which one of the following statements is true? (A) It is possible to have a negative r and a positive b (in the same regression). (B) r depends on the units used to measure the variables, but b does not. (C) b depends on the units used to measure the variables, but r does not. (D) Both r and b depend on the units used to measure the variables. 5. Suppose we do a simple linear regression, and we use the results to do a t test for whether the X variable affects the response ( α = 0 . 05). We get a pvalue of 0.011. Which one of the following statements is true? (A) We see evidence that β = 0, which means we see evidence that the explanatory variable affects the response. (B) We see evidence that β = 0, which means we see evidence that the explanatory variable does not affect the response. (C) We see evidence that β 6 = 0, which means we see evidence that the explanatory variable affects the response. (D) None of these statements are true. 6. We’re constructing the ANOVA table for a simple linear regression with 78 observations. What are df Regr and df Res ? (A) df Regr = 1 , df Res = 76 (B) df Regr = 1 , df Res = 77 (C) df Regr = 2 , df Res = 76 (D) df Regr = 2 , df Res = 77 7. In simple linear regression, which of the following would not give us enough information to calculate the total sum of squares, SS Tot ? (A) the values of SS Regr and SS Res (B) the values of a and b in the regression equation (C) the Y values of all the observations (D) the Y values of all the observations and the value of ¯ Y 8. The ANOVA table for a simple linear regression is shown below (some items are missing), along with the F test statistic value and pvalue from the regression F test....
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This note was uploaded on 12/15/2011 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.
 Spring '08
 TA
 Statistics, Linear Regression

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