In this exercise, you will use these data to investigate the relationship between the number of completed years of education for young adults and the distance from each student's high school to the nearest four-year college. (Proximity lowers the cost of education, so that students who live closer to a four-year college should, on average, complete more years of higher education.)The following table contains data from a random sample of high school seniors interviewed in 1980 and re-interviewed in 1986. Download the data from the table by clicking the download table icon

.

A detailed description of the variables used in the dataset is available here

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Use a statistical package of your choice to answer the following questions.Suppose you are interested in estimating the following modelED =

0

+

1Dist

+ uRun a regression of years completed of education

(ED)

on distance to the nearest college

(Dist).

What is the estimated intercept

0?

The estimated intercept

0

is

enter your response here.

(Round

your response to three decimal

places)

What is the estimated slope

1?

The estimated slope

1

is

enter your response here.

(Round

your response to three decimal

places)

The estimated model is

ED = 13.532 + 0.009Dist, R2= 0.000
(0.069)

Where the number in parentheses is the homoskedastic standard error for the regression coefficient

1.

Suppose you wanted to test the hypothesis that

1

equals zero at the 1%, 5% and 10% level. That is,H0:1=0vs.H1:10Report the

t-statistic

and

p-value

for this test.The

t-statistic

is

enter your response here.

(Round

your response to two decimal

places)

The

p-value

is

enter your response here.

(Round

your response to three decimal

places)

Can you reject the null hypothesis at the 5% significance level?

A.

Yes.

B.

No.

Construct a 95% confidence interval for the slope coefficient

1.

The 95% confidence interval for the slope coefficient

1

is

[enter your response here,

enter your response here]

(Round

your response to three decimal

places)

Now, suppose you are interested in estimating the following model for the subpopulation of females

(female

= 1)ED =

0

+

1Dist

+ uRun a regression of years completed of education

(ED)

on distance to the nearest college

(Dist)

using the sample for which the indicator variable female = 1.What is the estimated intercept

0?

The estimated intercept

0

is

enter your response here.

(Round

your response to three decimal

places)

What is the estimated slope

1?

The estimated slope

1

is

enter your response here.

(Round

your response to three decimal

places)

The estimated model is

ED = 13.8530.079Dist, R2= 0.008
(0.125)

Where the number in parentheses is the homoskedastic standard error for the regression coefficient

1.

Suppose you wanted to test the hypothesis that

1

equals zero at the 1%, 5% and 10% level. That is,H0:1=0vs.H1:10Report the

t-statistic

and

p-value

for this test.The

t-statistic

is

enter your response here.

(Round

your response to two decimal

places)

The

p-value

is

enter your response here.

(Round

your response to three decimal

places)

Can you reject the null hypothesis at the 5% significance level?

A.

Yes.

B.

No.

Now, suppose you are interested in estimating the following model for the subpopulation of males

(female

= 0)ED =

0

+

1Dist

+ uRun a regression of years completed of education

(ED)

on distance to the nearest college

(Dist)

using the sample for which the indicator variable female = 0.What is the estimated intercept

0?

The estimated intercept

0

is

enter your response here.

(Round

your response to three decimal

places)

What is the estimated slope

1?

The estimated slope

1

is

enter your response here.

(Round

your response to three decimal

places)

The estimated model is

ED = 13.264 + 0.034Dist, R2= 0.004
(0.080)

Where the number in parentheses is the homoskedastic standard error for the regression coefficient

1.

Suppose you wanted to test the hypothesis that

1

equals zero at the 1%, 5% and 10% level. That is,H0:1=0vs.H1:10Report the

t-statistic

and

p-value

for this test.The

t-statistic

is

enter your response here.

(Round

your response to two decimal

places)

The

p-value

is

enter your response here.

(Round

your response to three decimal

places)

Can you reject the null hypothesis at the 5% significance level?

A.

Yes.

B.

No.

data

College Distance
Education	Distance	Female
12	5.256	0
12	0.558	0
16	11.671	0
12	1.186	0
12	0.746	0
17	2.359	0
12	1.304	0
15	0.825	0
13	0.379	0
13	1.007	0
12	0.828	0
13	1.92	0
15	0.868	0
13	1.197	0
12	1.256	0
13	5.25	0
15	2.013	0
14	0.612	0
12	7.275	0
13	1.641	0
13	1.483	0
16	0.416	0
16	4.801	0
17	0.619	0
16	1.678	0
15	1.47	0
13	1.656	0
12	1.602	0
12	2.977	0
14	15.929	0
15	1.699	0
12	1.547	0
16	1.932	0
12	0.383	0
12	0.928	0
12	0.644	0
12	4.195	0
12	4.691	0
15	0.209	0
12	0.38	0
16	2.271	0
12	1.266	0
12	5.237	0
12	8.361	0
12	4.054	0
12	1.571	0
16	4.781	0
12	2.017	0
12	1.053	0
13	1.275	0
12	4.027	0
12	0.383	1
12	4.575	1
17	2.24	1
12	1.07	1
15	0.964	1
12	1.444	1
15	2.468	1
12	1.064	1
12	0.597	1
16	5.549	1
12	0.998	1
12	0.881	1
16	0.408	1
16	1.09	1
14	1.784	1
14	1.693	1
17	0.479	1
12	1.115	1
15	4.915	1
12	1.93	1
12	1.518	1
16	0.816	1
12	1.651	1
12	1.315	1
14	0.459	1
16	2.377	1
12	3.1	1
12	0.542	1
16	2.571	1
12	1.148	1
14	2.121	1
12	10.893	1
12	5.111	1
14	0.933	1
16	1.295	1
12	4.061	1
15	2.003	1
12	0.961	1
12	6.521	1
18	0.578	1
12	6.964	1
12	0.04	1
17	1.598	1
12	0.598	1
14	1.583	1
15	1.653	1
16	7.542	1
14	1.566	1
12	4.242	1