Sample questions Quiz 1

1 Sample Questions Quiz 1 Quiz 1 will contain a set of multiple-choice and true/false questions based on the material of Lectures 1 and 2 and relevant readings from the textbook. Examples for review (solutions in p.4, answer before looking at the solutions) 1. In the simple linear regression model, the regression slope: A) indicates by how many percent Y increases, given a one percent increase in X . B) when multiplied with the explanatory variable will give you the predicted Y . C) indicates by how many units Y increases, given a one unit increase in X . D) represents the elasticity of Y on X . 2. The OLS estimator is derived by: A) connecting the Y i corresponding to the lowest X i observation with the Y i corresponding to the highest X i observation. B) making sure that the standard error of the regression equals the standard error of the slope estimator. C) minimizing the sum of absolute residuals. D) minimizing the sum of squared residuals. 3. When the estimated slope coefficient in the simple regression model, 1 , is zero, then: A) R 2 = . B) 0 < R 2 < 1. C) R 2 = 0. D) R 2 > ( SSR / TSS ). 4. Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student-teacher ratio by 2 will: A) reduce test scores by 2.28 on average B) result in a test score of 698.9 C) reduce test scores by 2.56 on average D) increase test scores by 4.56 on average

2 5. The OLS residuals, i , are defined as follows: A) i - 0 - 1 X i B) Y i - β 0 - β 1 X i C) Y i - i D) ( Y i - ) 2 6. In the simple linear regression model Y i = β 0 + β 1 X i + u i : A) the intercept is typically small and unimportant. B) β 0 + β 1 X i represents the population regression function. C) the absolute value of the slope is typically between 0 and 1. D) β 0 + β 1 X i represents the sample regression function. 7. To obtain the slope estimator using the least squares principle, you divide the: A) sample variance of X by the sample variance of Y . B) sample covariance of X and Y by the sample variance of Y . C) sample covariance of X and Y by the sample variance of X . D) sample variance of X by the sample covariance of X and Y . 8. Assume that you have collected a sample of observations from over 100 households and their consumption and income patterns. Using these observations, you estimate the following regression C i = β 0 +β 1 Y i + u i where C is consumption and Y is disposable income. The estimate of β 1 will tell you: A) B) The amount you need to consume to survive C) D)

4 SOLUTIONS: Examples for review 1. In the simple linear regression model, the regression slope: A) indicates by how many percent Y increases, given a one percent increase in X . B) when multiplied with the explanatory variable will give you the predicted Y . C) indicates by how many units Y increases, given a one unit increase in X . D) represents the elasticity of Y on X . Answer: C 2. The OLS estimator is derived by: A) connecting the Y i corresponding to the lowest X i observation with the Y i corresponding to the highest X i observation. B) making sure that the standard error of the regression equals the standard error of the slope estimator. C) minimizing the sum of absolute residuals. D) minimizing the sum of squared residuals. Answer: D 3. When the estimated slope coefficient in the simple regression model, 1 , is zero, then: A) R 2 = . B) 0 < R 2 < 1. C) R 2 = 0. D) R 2 > ( SSR / TSS ). Answer: C 4. Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student-teacher ratio by 2 will: A) reduce test scores by 2.28 on average B) result in a test score of 698.9 C) reduce test scores by 2.56 on average D) increase test scores by 4.56 on average Answer: D

5 5. The OLS residuals, i , are defined as follows: A) i - 0 - 1 X i B) Y i - β 0 - β 1 X i C) Y i - i D) ( Y i - ) 2 Answer: C 6. In the simple linear regression model Y i = β 0 + β 1 X i + u i : A) the intercept is typically small and unimportant. B) β 0 + β 1 X i represents the population regression function. C) the absolute value of the slope is typically between 0 and 1. D) β 0 + β 1 X i represents the sample regression function. Answer: B 7. To obtain the slope estimator using the least squares principle, you divide the: A) sample variance of X by the sample variance of Y . B) sample covariance of X and Y by the sample variance of Y . C) sample covariance of X and Y by the sample variance of X . D) sample variance of X by the sample covariance of X and Y . Answer: C 8 Assume that you have collected a sample of observations from over 100 households and their consumption and income patterns. Using these observations, you estimate the following regression C i = β 0 +β 1 Y i + u i where C is consumption and Y is disposable income. The estimate of β 1 will tell you: A) B) The amount you need to consume to survive C) D) Answer: D 9. A low regression R 2 means that: A) the regression is bad. B) tells you what the other factors influencing the left hand variable are. C) there are other important factors that influence the left hand variable.

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