Question

In this​ exercise, you will investigate the relationship between a​ worker's age and earnings.​ (Generally, older workers have more job​ experience, leading to higher productivity and​ earnings.) The following table contains data for​ full-time, full-years​ workers, age​ 25-34, with a high school diploma or​ B.A./B.S. as their highest degree. Download the data from the table by clicking the download table icon A detailed description of the variables used in the data set is available here Use a statistical package of your choice to answer the following questions. Suppose you are interested in estimating the following model

Ahe​ = β0 ​+ β1Age ​+ u

Run a regression of average hourly earnings (AHE​) on age ​(Age​).

Run a regression of average hourly earnings ​(AHE​) on age ​(Age​) using the sample for which the indicator variable college​ = 0.

What is the estimated intercept β0​ & β1?

The estimated intercept β0 is ________

The estimated intercept β1 is ________

College Distance
Ahe	Age	College
12.6102	34	1
17.2572	25	1
4.0307	32	1
26.146	33	1
33.352	27	1
8.9155	27	1
64.6712	26	1
9.3487	26	1
44.0298	30	1
8.1751	31	1
24.4249	26	1
16.0365	31	1
31.7643	26	1
32.8926	33	1
25.9257	29	1
26.8499	30	1
22.6707	30	1
14.4586	27	1
15.6864	27	1
55.2604	32	1
27.1889	29	1
38.0335	31	1
28.1463	26	1
14.3612	31	1
15.8709	30	1
29.2048	28	1
45.106	34	1
23.4888	27	1
18.44	33	1
27.2437	25	1
39.4441	27	1
14.2008	30	1
22.896	33	1
31.9338	27	1
17.7686	28	1
25.2584	27	1
36.9844	33	1
17.4559	32	1
24.827	31	1
25.9448	34	1
9.3946	31	1
24.5044	34	1
36.0618	29	0
13.5713	28	0
8.0061	26	0
20.0158	29	0
45.4987	33	0
7.2858	27	0
11.9818	33	0
18.1214	25	0
7.6007	32	0
12.5471	29	0
16.9855	28	0
15.1409	29	0
6.7083	27	0
22.2952	33	0
12.148	30	0
8.2473	28	0
15.0424	27	0
6.7796	25	0
16.8188	25	0
14.8258	30	0
15.7019	25	0
2.6229	30	0
23.8469	31	0
12.2451	31	0
21.8335	33	0
15.4616	26	0
32.2909	29	0
10.7363	28	0
11.2132	34	0
14.9038	28	0
24.3312	29	0
12.9998	30	0
17.0164	26	0
9.7228	25	0
10.2584	28	0
18.4956	29	0
11.1666	33	0
18.4905	29	0
15.8924	34	0
17.4147	29	0
17.99	29	0
12.807	25	0
9.8222	29	0
4.0649	25	0
7.177	25	0
9.2321	31	0
19.2232	30	0
12.0358	25	0
22.8428	29	0
20.2687	26	0
14.0444	30	0
8.7165	25	0
31.0064	33	0
7.6344	26	0
16.8722	31	0
12.7747	28	0
23.2383	30	0
16.8357	30	0

Answer 1

Ahe^​ = β0 ​+ β1Age ​

The regression output of average hourly earnings (AHE​) on age ​(Age​) is:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.185942625
R Square	0.03457466
Adjusted R Square	0.024723381
Standard Error	10.93882456
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	1	419.9587292	419.9587292	3.50966204	0.063991825
Residual	98	11726.47252	119.6578828
Total	99	12146.43125
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-2.278743498	11.68247745	-0.195056529	0.845752519	-25.46223979	20.9047528	-25.46223979	20.9047528
Age	0.748794072	0.399695951	1.873409203	0.063991825	-0.044389534	1.541977678	-0.044389534	1.541977678

Ahe^​ = -2.2787 ​+ 0.7488*Age ​

The estimated intercept β0 is -2.2787

The estimated intercept β1 is 0.7488

The regression output of average hourly earnings ​(AHE​) on age ​(Age​) using the sample for which the indicator variable college​ = 0 is:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.348240043
R Square	0.121271127
Adjusted R Square	0.10557954
Standard Error	7.342102804
Observations	58
ANOVA
	df	SS	MS	F	Significance F
Regression	1	416.6117057	416.6117	7.728417	0.00738867
Residual	56	3018.762521	53.90647
Total	57	3435.374227
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-13.86590425	10.60662849	-1.30729	0.196458	-35.11353433	7.38172582
Age	1.021676993	0.367509306	2.780003	0.007389	0.285467386	1.7578866

Ahe^​ = -13.8659 ​+ 1.0217*Age ​

The estimated intercept β0 is -13.8659

The estimated intercept β1 is 1.0217