ECON 122B

Sample Midterm 1
DATA FOR QUESTIONS 1 AND 2.
Dependent Variable: EARN
Method: Least Squares
Date: 03/30/16 Time: 10:29
Sample: 1 1744
Included observations:1744
White heteroskedasticity-consistent standard errors &amp; covariance
Variable

Coefficient

Std. Error

C
AGE

239.1600
5.200000

20.2400
0.57000

R-squared
S.E. of regression
F-statistic
Prob(F-statistic)

0.058497
0.058365
287.2100
140.1750
0.000000

t-Statistic

Prob.

Mean dependent var
S.D. dependent var
Akaike info criterion
Durbin-Watson stat

Dependent Variable: EARN
Method: Least Squares
Date: 03/30/16 Time: 10:31
Sample: 1 1744
Included observations: 1744
White heteroskedasticity-consistent standard errors &amp; covariance
Variable

Coefficient

C
FEMALE
AGE

323.7095
-169.7876
5.150033

R-squared
F-statistic
Prob(F-statistic)

0.132538
0.132278
125.0624
0.000000

Std. Error

t-Statistic

Prob.

Mean dependent var
S.D. dependent var
Durbin-Watson stat

Wald Test:
Equation: Untitled
Test Statistic
F-statistic
Chi-square

Value

df

Probability

125.0624
250.1247

(2, 1741)
2

0.0000
0.0000

Value

Std. Err.

Null Hypothesis: C(2)=0, C(3)=0
Null Hypothesis Summary:
Normalized Restriction (= 0)
C(2)
C(3)

-169.7876
5.150033

0.246620
0.042927

1

ECON 122B
1. You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and
are interested in the relationship between weekly earnings and age. Earn and Age are measured in
dollars and years respectively.
a) Write down the regression equation

b) Write down the estimated equation

c) Interpret the coefficients.

d) Interpret the measures of fit.

e) The average age in this sample is 37.5 years. What is the average annual income in this sample?

f)

Is the relationship between Age and Earn statistically significant?
State the null and the alternative hypotheses

Calculate the value of the test statistic

2

ECON 122B
g) Construct a 95% confidence interval for the slope coefficient.

2. You decide to control for gender in addition to age in your regression results.
a. Write down the new regression equation

b. Write down the new estimated equation

c.

Interpret the coefficients.

d. How much, on average, does a 40-year-old female make per year in your sample?

e. How much, on average, does a 20-year-old male make per year in your sample?

f.

Interpret the change in the adjusted R-squared between the first and the second
regression.

3

ECON 122B
g. Your friend thinks that age and gender do not affect earnings. Does your data support his
claim?
State the null and the alternative hypotheses

Calculate the value of the test statistic

4

ECON 122B
3. You have collected 14,925 observations from the Current Population Survey. There are 6,285
females in the sample, and 8,640 males. The females report a mean of average hourly earnings of
\$16.50 with a standard deviation of \$9.06. The males have an average of \$20.09 and a standard
deviation of \$10.85. The overall mean average hourly earnings is \$18.58.
a) You decide to run two regressions: first, you simply regress average hourly earnings on an
intercept only. Next, you repeat this regression, but only for the 6,285 females in the sample.
What will the regression coefficients be in each of the two regressions?

b) Finally you run a regression over the entire sample of average hourly earnings on an intercept
and a binary variable DFemme, where this variable takes on a value of 1 if the individual is a
female, and is 0 otherwise. What will be the value of the intercept? What will be the value of the
coefficient of the binary variable?

c) You have read in the news that women make 70 cents to the \$1 that men earn. Do your
regression results support this claim?
i.

Specify your null and alternative hypothesis.

ii.

Calculate the standard error of the slope coefficient.

iii.

Perform the test.

5