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 Yi corresponding to the lowest Xi observation with the Yi corresponding to
the highest Xi 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) R2 = .
B) 0 < R2 < 1.
C) R2 = 0.
D) R2 > (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
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5. The OLS residuals, i, are defined as follows:
A) i - 0 - 1Xi
B) Yi - β0 - β1Xi
C) Yi - i
D) (Yi - )2
6. In the simple linear regression model Yi = β0 + β1Xi + ui:
A) the intercept is typically small and unimportant.
B) β0 + β1Xi represents the population regression function.
C) the absolute value of the slope is typically between 0 and 1.
D) β0 + β1Xi 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 Ci = β0+β1Yi+ ui where C is consumption and Y is disposable income. The estimate of
β1 will tell you:
A)
B) The amount you need to consume to survive
C)
D)
2
9. A low regression R2 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.
D) the SSR is low relative to the total variation in Y.
10. R2 is the ratio of the explained variation compared to the total variation.
a. True
b. False
11. There are n-1 degrees of freedom in Ordinary Least Square residuals.
a. True
b. False
12. In a simple linear regression model, wage = + male + u, where male is a binary variable
(1 if a person is male, and 0 otherwise), is the difference in the average wage between males
and non-males.
a. True
b. False
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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 Yi corresponding to the lowest Xi observation with the Yi corresponding to
the highest Xi 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) R2 = .
B) 0 < R2 < 1.
C) R2 = 0.
D) R2 > (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
4
5. The OLS residuals, i, are defined as follows:
A) i - 0 - 1Xi
B) Yi - β0 - β1Xi
C) Yi - i
D) (Yi - )2
Answer: C
6. In the simple linear regression model Yi = β0 + β1Xi + ui:
A) the intercept is typically small and unimportant.
B) β0 + β1Xi represents the population regression function.
C) the absolute value of the slope is typically between 0 and 1.
D) β0 + β1Xi 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 Ci = β0+β1Yi+ ui where C is consumption and Y is disposable income. The estimate of
β1 will tell you:
A)
B) The amount you need to consume to survive
C)
D)
Answer: D
9. A low regression R2 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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D) the SSR is low relative to the total variation in Y.
Answer: C
10. R2 is the ratio of the explained variation compared to the total variation.
a. True
b. False
ANSWER: True
11. There are n-1 degrees of freedom in Ordinary Least Square residuals.
a. True
b. False
ANSWER: False
12. In a simple linear regression model, wage = + male + u, where male is a binary variable
(1 if a person is male, and 0 otherwise), is the difference in the average wage between males
and non-males.
a. True
b. False
ANSWER: True
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