Regression Problem 3

Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Total 3.) R Square Standard Error Significance F

Utility Cost $2,527 2,515 2,654 2,593 2,455 2,509 2,557 2,588 2,540 2,707 2,731 2,697 31,073

Labor Hours Machine Hours 4,150 2,500 4,000 2,375 4,360 2,600 4,200 2,450 4,050 2,525 4,100 2,410 4,275 2,720 4,250 2,525 4,050 2,350 4,500 2,610 4,600 2,700 4,375 2,675 50,910 30,440

Multiple Regression Labor Hours Machine Hours 0.91 0.87 0.42 29.96 33.32 71.21 0 0 0.02

4.) The best cost driver would have to be the set between labor and machine hours. The multiple regression has the highest R square and the residuals show no sign of being part of a pattern, which tells me that the data is good. Standard Error for the multiple regression is also the lowest of the three, showing that it has the smallest distance between points. Despite the fact that the significance f is not the lowest on the multiple regression it is still very low and shows that the multiple regression between labor and machine hours would be the best choice for the data to explain what the real cost driver is.

SUMMARY OUTPUT Regression Statistics Multiple R 0.95 R Square 0.91 Adjusted R Square 0.89 Standard Error 29.96 Observations 12 ANOVA df Regression Residual Total

Intercept Labor Hours Machine Hours

SS MS 2 79014.93 39507.46 9 8077.99 897.55 11 87092.92

F Significance F 44.02 0

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 770.4 205.72 3.74 0 305.03 1235.76 305.03 1235.76 0.56 0.08 6.89 0 0.38 0.75 0.38 0.75 -0.22 0.12 -1.84 0.1 -0.5 0.05 -0.5 0.05

Residual Plot RESIDUAL OUTPUT ObservationPredicted Utility Cost Residuals 1 2545.58 -18.58 2 2489.17 25.83 3 2641.35 12.65 4 2584.91 8.09 5 2483.72 -28.72 6 2537.6 -28.6 7 2566.66 -9.66 8 2596.25 -8.25 9 2522.9 17.1 10 2717.87 -10.87 11 2753.99 -22.99 12 2632.99 64.01

70 60 50 40 30 20 10 0 -10 -20 -30 2450

2500

2550

2600

2650

2700

2750

2800

SUMMARY OUTPUT Regression Statistics Multiple R 0.93 R Square 0.87 Adjusted R Square 0.86 Standard Error 33.32 Observations 12 ANOVA df Regression Residual Total

SS MS 1 75987.79 75987.79 10 11105.13 1110.51 11 87092.92

F Significance F 68.43 0

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% Intercept 717.17 226.54 3.17 0.01 212.4 1221.93 212.4 1221.93 Labor Hours 0.44 0.05 8.27 0 0.32 0.56 0.32 0.56

RESIDUAL OUTPUT Observation Predicted Utility Cost Residuals 1 2548.6 -21.6 2 2482.4 32.6 3 2641.27 12.73 4 2570.66 22.34 5 2504.46 -49.46 6 2526.53 -17.53 7 2603.76 -46.76 8 2592.73 -4.73 9 2504.46 35.54 10 2703.05 3.95 11 2747.18 -16.18 12 2647.89 49.11

Upper 95.0%

SUMMARY OUTPUT Regression Statistics Multiple R 0.65 R Square 0.42 Adjusted R Square 0.36 Standard Error 71.21 Observations 12 ANOVA df Regression Residual Total

SS MS 1 36379.01 36379.01 10 50713.91 5071.39 11 87092.92

F

Significance F 7.17 0.02

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% Intercept 1432.74 432.36 3.31 0.01 469.39 2396.09 469.39 2396.09 Machine Hours 0.46 0.17 2.68 0.02 0.08 0.84 0.08 0.84

RESIDUAL OUTPUT Observation Predicted Utility Cost Residuals 1 2572.7 -45.7 2 2515.7 -0.7 3 2618.3 35.7 4 2549.9 43.1 5 2584.1 -129.1 6 2531.66 -22.66 7 2673.01 -116.01 8 2584.1 3.9 9 2504.3 35.7 10 2622.86 84.14 11 2663.89 67.11 12 2652.49 44.51