Question

What is the relationship between the price of crude oil and the price you pay at the pump for​ gasoline? The accompanying table shows the prices of crude oil and the price you pay at the pump for 24 consecutive months. Complete parts​ (a) through​ (h) below.

b. Use the​ least-squares method to develop a simple linear regression equation to predict the gasoline prices using the average crude oil cost as the independent variable.

Month	Crude_Oil	Gasoline
1	75	1.986
2	76	1.937
3	76	1.807
4	76	1.537
5	77	1.493
6	77	2.076
7	76	1.918
8	83	2.229
9	75	1.638
10	78	1.372
11	81	1.832
12	78	2.019
13	78	2.354
14	80	2.447
15	81	2.211
16	84	2.331
17	80	2.667
18	78	2.884
19	74	2.775
20	81	2.531
21	83	2.619
22	85	3.415
23	84	3.119
24	84	3.096

Answer 1

b.

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
-4.1667	-0.2762	17.3611	1.1509
-3.1667	-0.3252	10.0278	1.0298
-3.1667	-0.4552	10.0278	1.4415
-3.1667	-0.7252	10.0278	2.2965
-2.1667	-0.7692	4.6944	1.6666
-2.1667	-0.1862	4.6944	0.4035
-3.1667	-0.3442	10.0278	1.09
3.8333	-0.0332	14.6944	-0.1273
-4.1667	-0.6242	17.3611	2.6009
-1.1667	-0.8902	1.3611	1.0386
1.8333	-0.4302	3.3611	-0.7887
-1.1667	-0.2432	1.3611	0.2837
-1.1667	0.0918	1.3611	-0.1071
0.8333	0.1848	0.6944	0.154
1.8333	-0.0512	3.3611	-0.0939
4.8333	0.0688	23.3611	0.3325
0.8333	0.4048	0.6944	0.3373
-1.1667	0.6218	1.3611	-0.7254
-5.1667	0.5128	26.6944	-2.6494
1.8333	0.2688	3.3611	0.4928
3.8333	0.3568	14.6944	1.3677
5.8333	1.1528	34.0278	6.7246
4.8333	0.8568	23.3611	4.1412
4.8333	0.8338	23.3611	4.03
		SS: 261.3333	SP: 26.0902

Sum of X = 1900
Sum of Y = 54.293
Mean X = 79.1667
Mean Y = 2.2622
Sum of squares (SSX) = 261.3333
Sum of products (SP) = 26.0902

Regression Equation = ŷ = bX + a

b = SP/SSX = 26.09/261.33 = 0.0998

a = MY - bMX = 2.26 - (0.1*79.17) = -5.6414

ŷ = 0.0998X - 5.6414