Question

The estimated model is

Ahe ​= −13.8666 ​+ 1.0217​Age, R2​= 0.121

(0.368​)

Where the number in parentheses is the homoskedastic standard error for the regression coefficient β1. Using the sample of high school​ graduates, suppose you wanted to test the hypothesis that β1 equals zero at the​ 5% significance level. That​ is,

H0: β1=0 vs. H1: β1≠0

Report the t​-statistic and p​-value for this test. The t​-statistic 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

H0: β1=0 vs. H1: β1≠0

As we can see that B1^ = 0.74879

T statistics =( B1^ - B1)/ SE(B1)

T statistics =( 0.74879 - 0 )/ 0.399

T statistics = 0.74879 / 0.399 = 1.87

Also P value of B1^ is given by 0.06399 as shown in table . So P value is greater than 5 % significance level . So we fail to reject the null hypothesis .