In: Operations Management
Problem 15-28 (Algorithmic)
South Shore Construction builds permanent docks and seawalls along the southern shore of long island, new york. Although the firm has been in business for only five years, revenue has increased from $320,000 in the first year of operation to $1,188,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars:
Quarter | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
1 | 23 | 38 | 83 | 97 | 202 |
2 | 103 | 137 | 163 | 207 | 308 |
3 | 178 | 246 | 334 | 389 | 471 |
4 | 16 | 27 | 56 | 87 | 207 |
Value | Qtr1 | Qtr2 | Qtr3 |
23 | 1 | 0 | 0 |
103 | 0 | 1 | 0 |
178 | 0 | 0 | 1 |
16 | 0 | 0 | 0 |
38 | 1 | 0 | 0 |
137 | 0 | 1 | 0 |
246 | 0 | 0 | 1 |
27 | 0 | 0 | 0 |
83 | 1 | 0 | 0 |
163 | 0 | 1 | 0 |
334 | 0 | 0 | 1 |
56 | 0 | 0 | 0 |
97 | 1 | 0 | 0 |
207 | 0 | 1 | 0 |
389 | 0 | 0 | 1 |
87 | 0 | 0 | 0 |
202 | 1 | 0 | 0 |
308 | 0 | 1 | 0 |
471 | 0 | 0 | 1 |
207 | 0 | 0 | 0 |
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.783434 | |||||
R Square | 0.613768 | |||||
Adjusted R Square | 0.54135 | |||||
Standard Error | 87.29361 | |||||
Observations | 20 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 3 | 193750 | 64583.33 | 8.475308 | 0.001339 | |
Residual | 16 | 121922.8 | 7620.175 | |||
Total | 19 | 315672.8 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | 78.6 | 39.03889 | 2.013377 | 0.061213 | -4.15875 | 161.3588 |
Qtr1 | 10 | 55.20933 | 0.181129 | 0.858541 | -107.039 | 127.0385 |
Qtr2 | 105 | 55.20933 | 1.901852 | 0.075351 | -12.0385 | 222.0385 |
Qtr3 | 245 | 55.20933 | 4.437656 | 0.000414 | 127.9615 | 362.0385 |
Estimated regression equation:
ŷ = 78.6 + (10)Qtr1 + (105)Qtr2 + (245)Qtr3
c.
Revenue | Period | Qtr1 | Qtr2 | Qtr3 |
23 | 1 | 1 | 0 | 0 |
103 | 2 | 0 | 1 | 0 |
178 | 3 | 0 | 0 | 1 |
16 | 4 | 0 | 0 | 0 |
38 | 5 | 1 | 0 | 0 |
137 | 6 | 0 | 1 | 0 |
246 | 7 | 0 | 0 | 1 |
27 | 8 | 0 | 0 | 0 |
83 | 9 | 1 | 0 | 0 |
163 | 10 | 0 | 1 | 0 |
334 | 11 | 0 | 0 | 1 |
56 | 12 | 0 | 0 | 0 |
97 | 13 | 1 | 0 | 0 |
207 | 14 | 0 | 1 | 0 |
389 | 15 | 0 | 0 | 1 |
87 | 16 | 0 | 0 | 0 |
202 | 17 | 1 | 0 | 0 |
308 | 18 | 0 | 1 | 0 |
471 | 19 | 0 | 0 | 1 |
207 | 20 | 0 | 0 | 0 |
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.9759404 | |||||
R Square | 0.9524596 | |||||
Adjusted R Square | 0.9397822 | |||||
Standard Error | 31.630365 | |||||
Observations | 20 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 4 | 300665.6 | 75166.4 | 75.13034 | 9.745E-10 | |
Residual | 15 | 15007.2 | 1000.48 | |||
Total | 19 | 315672.8 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -76.5 | 20.62048 | -3.7099 | 0.002096 | -120.4515 | -32.5485 |
Period | 12.925 | 1.2503 | 10.33752 | 3.22E-08 | 10.260049 | 15.58995 |
Qtr1 | 48.775 | 20.35341 | 2.396404 | 0.030035 | 5.3927361 | 92.15726 |
Qtr2 | 130.85 | 20.16048 | 6.49042 | 1.02E-05 | 87.878952 | 173.821 |
Qtr3 | 257.925 | 20.04383 | 12.86805 | 1.65E-09 | 215.20258 | 300.6474 |
Estimated regression equation:
ŷ = -76.5 + (48.78)Qtr1 + (130.85)Qtr2 + (257.93)Qtr3 + (12.93)Period
Quarter 1 forecast: x1 = 1, x2 = 0, x3 = 0, t = 21
ŷ = -76.5 + (48.78)*1 + (130.85)*0 + (257.93)*0 + (12.93)*21 = 243.7
Quarter 2 forecast: x1 = 0, x2 = 1, x3 = 0, t = 22
ŷ = -76.5 + (48.78)*0 + (130.85)*1 + (257.93)*0 + (12.93)*22 = 338.7
Quarter 3 forecast: x1 = 0, x2 = 0, x3 = 1, t = 23
ŷ = -76.5 + (48.78)*0 + (130.85)*0 + (257.93)*1 + (12.93)*23 = 478.7
Quarter 4 forecast: x1 = 0, x2 = 0, x3 = 0, t = 24
ŷ = -76.5 + (48.78)*0 + (130.85)*0 + (257.93)*0 + (12.93)*24 = 233.7