Question

Please solve both by hand and using minitab

The dependent variable y was monitored as a function of an independent variable x Conduct a regression analysis by hand and by Minitab and comment the results 2.1947.17 10.45 48.93 10.45 47.1731.2 0.73 3.95 6.8547 1.81 4.4947.94 13.9149.92 13.947.9433.87 54.16 49.0256.03 3.71 11.21 48.19 21.76 50.17 21.76 48.19 38.7254.52 43.55 56.25 6.024 8.4248.77 52.8 40.4655.20 47.43 11.38 49.14 11.38 47.4328.83 52.95 44.2955.39 47.1610.72 49.50 10.7247.16 35.6453.31 36.6855.44 53.8 50.7555.61 47.83 12.35 49.78 12.35 47.8329.35 53.77 37.9955.77 47.44 13.42 49.69 13.42 47.44 34.5 48.20 9.43 50.29 9. 43 48.20 40.08 54.1745.66 56.14 48.5919.92 50.78 19.92 48.59 34.86 54.88 48.00 56.53 19.45 50.41 19.45 48.7738.4754.85 49.00 57.01

Answer 1

By hand

Obs.	Month (x)	Demand (y)	x^2	x*y
1	2.19	47.17	4.80	103.30
2	0.73	47.43	0.53	34.62
3	3.95	47.16	15.60	186.28
4	6.85	47.44	46.92	324.96
5	1.81	47.83	3.28	86.57
6	4.49	47.94	20.16	215.25
7	3.71	48.20	13.76	178.82
8	11.21	48.19	125.66	540.21
9	6.02	48.59	36.24	292.51
10	8.42	48.77	70.90	410.64
11	10.45	48.93	109.20	511.32
12	11.38	49.14	129.50	559.21
13	10.72	49.50	114.92	530.64
14	13.42	49.69	180.10	666.84
15	12.35	49.78	152.52	614.78
16	13.91	49.92	193.49	694.39
17	9.43	50.29	88.92	474.23
18	21.76	50.17	473.50	1091.70
19	19.92	50.78	396.81	1011.54
20	19.45	50.41	378.30	980.47
21	10.45	47.17	109.20	492.93
22	11.38	47.43	129.50	539.75
23	10.72	47.16	114.92	505.56
24	13.42	47.44	180.10	636.64
25	12.35	47.83	152.52	590.70
26	13.91	47.94	193.49	666.85
27	9.43	48.20	88.92	454.53
28	21.76	48.19	473.50	1048.61
29	19.92	48.59	396.81	967.91
30	19.45	48.77	378.30	948.58
31	31.20	52.80	973.44	1647.36
32	28.83	52.95	831.17	1526.55
33	35.64	53.31	1270.21	1899.97
34	34.50	53.80	1190.25	1856.10
35	29.35	53.77	861.42	1578.15
36	33.87	54.16	1147.18	1834.40
37	40.08	54.17	1606.41	2171.13
38	38.72	54.52	1499.24	2111.01
39	34.86	54.88	1215.22	1913.12
40	38.47	54.85	1479.94	2110.08
41	40.46	55.20	1637.01	2233.39
42	44.29	55.39	1961.60	2453.22
43	36.68	55.44	1345.42	2033.54
44	50.75	55.61	2575.56	2822.21
45	37.99	55.77	1443.24	2118.70
46	49.02	56.03	2402.96	2746.59
47	45.66	56.14	2084.84	2563.35
48	43.55	56.25	1896.60	2449.69
49	48.00	56.53	2304.00	2713.44
50	49.00	57.01	2401.00	2793.49
Totals	1125.9	2554.6	36899.1	59935.9
	?x	?y	?x^2	?xy

n =			50
x_hat = ?x/n =			22.518
y_hat = ?y/n =			51.093
? = ?xy - n*x_hat*y_hat =			2411.723
? = ?x^2 - n*x_hat^2 =			11546.980
Slope (b) = ?/? =			0.209
Intercept (a) = y_hat - b*x_hat =			46.390

So, the regression line is: Y = 46.39 + 0.209 * X

Using Minitab

null

Interpretation

The P-values for both the intercept and the slope are less than 0.05. So, the values found are statistically significant at 95% confidence level.

The R-sqr. value is more than 90% which indicates that the model is explained by more than 90% of the data.

The residual analysis shows that there is only one outlier.