Question

We performed a linear regression analysis between number of times on phone per drive and number of near accidents. The equation is Y= 0.320 + 0.943X, where Y is the number of times on phone per drive and X is the number of near accidents. calculate the p-value and give a conclusion.

number of times on phone per dr	near accidents
0	0
0	1
1	1
2	1
3	1
1	2
2	2
3	2
4	2
2	3
3	3
4	3
2	4
3	4
4	4
5	4
6	4
3	5
4	5
5	5
6	5
4	6
5	6
7	6
8	7
9	7

Answer 1

Let's calculate the F-statistic first whose formula is:

n = 26

The calculations are given below:

	y	x	yp (Predicted) = 0.320 + 0.943*x	(y-u)*(y-u)	(yp-u)*(yp-u)	(y - yp)*(y-yp)
	0	0	0.32	13.633	11.372	0.102
	0	1	1.263	13.633	5.902	1.595
	1	1	1.263	7.249	5.902	0.069
	2	1	1.263	2.864	5.902	0.543
	3	1	1.263	0.479	5.902	3.017
	1	2	2.206	7.249	2.209	1.454
	2	2	2.206	2.864	2.209	0.042
	3	2	2.206	0.479	2.209	0.630
	4	2	2.206	0.095	2.209	3.218
	2	3	3.149	2.864	0.295	1.320
	3	3	3.149	0.479	0.295	0.022
	4	3	3.149	0.095	0.295	0.724
	2	4	4.092	2.864	0.160	4.376
	3	4	4.092	0.479	0.160	1.192
	4	4	4.092	0.095	0.160	0.008
	5	4	4.092	1.710	0.160	0.824
	6	4	4.092	5.325	0.160	3.640
	3	5	5.035	0.479	1.803	4.141
	4	5	5.035	0.095	1.803	1.071
	5	5	5.035	1.710	1.803	0.001
	6	5	5.035	5.325	1.803	0.931
	4	6	5.978	0.095	5.224	3.912
	5	6	5.978	1.710	5.224	0.956
	7	6	5.978	10.941	5.224	1.044
	8	7	6.921	18.556	10.424	1.164
	9	7	6.921	28.172	10.424	4.322
Average, u	3.692308		Total	129.538	89.233	40.327

SSR = 89.233

SSE = 40.327

F = (89.233/1) / (40.327/24) = 53.09368

p-value = 1.58E-07 (at df = 1, 24)

As the p-value < 0.05, we can conclude that the regression is significant at 0.01 level of significance.

SSE =