Please solve both by hand and using minitab
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
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.
Please solve both by hand and using minitab The dependent variable y was monitored as a...