1 Quiz Questions Chapter 4: Linear Regression with One Regressor ...

Quiz Questions Chapter 4: Linear Regression with One Regressor

1. Provide a definition for each of the Key Terms at the end of the chapter. 2. A regression of worker’s average hourly earnings (measured in dollars per hour), AHE, on a binary education variable C = 1 if the person has a college degree, C = 0 if no college degree, yields n = 8.11 + 6.20¥C AHE (0.41) (0.85) a. What does the value 8.11 mean? b. What does the value “6.20” mean? c. Does the regression provide statistically significant evidence that college-educated workers earn more than other workers, on average? Explain. d. Construct a 95% confidence interval for the difference in mean earnings of college and non-college-educated workers. e. Suppose that earnings had been measured in average weekly earnings, AWE, where AWE = 40¥AHE. Fill in the blanks n = ____ + ____¥C AWE (____) ( ____) 3. a. Calculate the p-value for the hypothesis Ho: β1 = 0 versus a two-sided alternative using the estimated regression reported in equation (4.26). b. Construct a 99% confidence interval for β1 in equation (4.26). c. Calculate the p-value for the hypothesis Ho: β1 = 5 versus a two-sided alternative using the estimated regression reported in equation (4.33). 1

d. Construct a 90% confidence interval for β1 in equation (4.33).

4. In a regression using n = 200 observations, TSS = 429 and ESS = 318. a. Compute R2. b. Compute SSR. c. Compute SER.

Multiple Choice 1. In a regression model with β0 = 3.0 and β1 = 2.0, a. the mean of Y is 3.0 + 2.0 = 5.0. b. Y is expected to increase by 2.0 if X increases by 1 unit. c. the least squares assumptions are satisfied. d. the value of β0 does not matter. 2. If R2 = 0.8, then a. SSR/TSS = 0.2. b. var(Y)/var(X) = 0.8. c. β1 > 0. d. β1 > var(X). 3. If the regression errors are homoskedastic, a. the least squares assumptions are not satisfied. b. the ordinary least squares estimator is biased. c. the ordinary least squares estimator is BLUE. d. weighted least squares should be used. 4. If βˆ1 / SE ( βˆ1 ) = 2.0, a. the null hypothesis β1 = 0 can be rejected against a two-sided alternative at the 5% level. b. the null hypothesis β1 = 0 can be rejected against a two-sided alternative at the 1% level. 2

c. the 95% confidence for β1 will include 0. d. R2 > 0.20. 5. The least squares assumption E(ui| Xi ) = 0 means that a. b. c. d.

the regression error and X are independent. E(Yi) = E(ui). E(Yi | Xi ) = β0 + β1Xi. ui has a finite fourth moment.

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