Multiple-choice Questions (4 points each in total, where choose the best answer, 2 points, and briefly explain your reasoning, 2 points.)

1. Which of the following models is a linear regression model?

a)   Y = α+ log(X +  β)+ u

b)   Y = α+ Xβ + u

c)   Y = + u

d)   Y = α+  β+ u

2. To estimate a simple linear regression wage = α+  βage + u , which of the following will cause R2 by OLS to be higher?

a)   Measuring age in years instead of months.

b)  Measuring wage in thousands of dollars instead of dollars.

c)   Regressing wage on α only.

d)  None of the above.

3. Which of the following will cause OLS estimators for a regression Income = α+  βAlcohol + u to be biased?

a)   Income varies a little in the sample.

b)  Omitting the intercept in estimation when the true valueα =0.

c)   Education is correlated with both Alcohol (i.e., alcohol consumption) and Income (i.e., individuals yearly income), which is omitted in the model.

d)  Both b) and c)

4. In which of the following cases OLS estimation of the SLR collegeGPA = α+  βSAT + u will be biased?

a)   Only include students who is college GPA is greater than 2.0 (not on academic probation).

b)  College GPA has some missing values, but those whose GPA are missing are a random sample.

c)   College GPA has some random typing errors.

d)  College GPA varies a lot even for the same SAT score.

5.  Changing the units of measurement for dependent variable, e.g. measuring tests cores in 100s in a regression testscore = α+  βstudytime + u , will do all of the            following EXCEPT for changing the

a)   residuals

b)  numerical value of the slope estimate

c)   interpretation of the effect that a change in X has on the change in Y

d)  numerical value of the intercept estimate

6. Assume that the sample means of X and Y are both 0.3 in a simple linear                   regression Y = α+  βX + u . You have estimated αˆ = 0 . What is your predict of Y given that X = 0.5 ?

a) 0.3

b)  0.5

c)   1

d)  Cannot be determined

For questions 7 and 8: Suppose a researcher is interested in estimating the habit formation for alcohol drinking and estimating following model using a random

sample:

log(alcohol1 ) = α+  βlog(alcohol0 ) + u

where alcohol1 and alcohol0 are the average number of alcoholic drinks consumed  per week this year and last year, respectively; the unobservable u is an individual’s generic disposition for drinking.

7. Then the OLS estimator of the slope   βˆfor the above model will tend to

a)  be biased.

b)  be unbiased but inefficient.

c)   be efficient.

d)  be negative.

8. Which of the following is true regarding the OLS estimator  βˆ?

a) Using weekly rather than daily number of alcoholic drinks consumed will make   βˆ larger.

b) Using weekly rather than daily number of alcoholic drinks consumed will make   βˆ smaller.

c) Using weekly rather than daily number of alcoholic drinks consumed will make   βˆunchanged.

d) Using weekly rather than daily number of alcoholic drinks consumed will change  βˆ , but could be either larger or smaller.

9. Demeaning data means subtracting the sample mean from each observation so that they are mean zero. Given a simple linear regression Y = α+  βX + u, OLS

estimation yields

 = .12  + .34X.

(.05)    (.029)

If you demean X and Y first and then regress demeaned Y on demeaned X. For notational convenience, denote the demeaned X and Y as X~ and , that is,      X~ = X − X and  = Y − Y and you estimate  = α + βX~ + u. (6 points each)

(1) What would be the OLS estimate of αˆ ?

(2) What would be the OLS estimate of   βˆ?

10. A simple linear regression that describes the relationship between individuals’

income and savings is given by

avings = −0.25 + 0.18 income,

n = 1000, R2  = .314,

where savings and income are measured in thousands of dollars. (6 points each)

1)  How would you interpret the estimated coefficient on income in the above?

2)    How would you interpret R2   in the above?

3)    What would be the estimated coefficient on income change if both income and savings are measured in dollars? How would you interpret the              estimated slope in this case?

4)  What would be the estimated coefficient on income change if income is          measured in dollars while savings is measured in thousands of dollars? How would you interpret the estimated slope in this case?