978-0134731889 Exercise 7 - 10

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Exercise 7-10: Dishwashers

Deseasonalized Analysis (to estimate initial values)

Year Quarter Period Sales

Deseasonalized

Level

Level from

Regression

Seasonal

Factor

Seasonal

Factor

Estimate

Regression – Deseasonalized Level vs. Period

1I 11,934 0.94

II 21,276 0.45 Regression Statistics

III 33,991 3,574.3 3,610.0 1.11 1.17 Multiple R 0.99686734

IV 45,632 3,993.0 4,151.4 1.36 1.46 R Square 0.9937445

2I 54,862 4,434.9 4,692.8 1.04 Adjusted R Square 0.99311895

II 61,698 5,362.4 5,234.3 0.32 Standard Error 162.44426

III 77,104 6,059.1 5,775.7 1.23 Observations 12

IV 89,939 6,420.0 6,317.1 1.57

3I 96,129 6,892.0 6,858.6 0.89 ANOVA

II 10 3,318 7,471.4 7,400.0 0.45 df SS MS F

Significance F

X Variable 1 541.43 13.58 39.86 0.00 511.16 571.70 511.16 571.70

Winter’s Model

01,985.7 541.43

1I 11,934 2,480.8 536.79 0.94 2,369 435 435 435 188,816 435 22.5 22.5 1.00

II 21,276 3,000.7 535.11 0.45 1,351 75 75 510 97,245 255 5.9 14.2 2.00

IV 45,632 4,036.9 531.82 1.46 5,944 312 312 958 77,529 239 5.5 9.3 4.00

2I 54,862 4,639.4 538.90 0.92 4,210 (652) 652 305 147,056 322 13.4 10.1 0.95

II 61,698 5,041.6 525.22 0.45 2,307 609 609 915 184,415 370 35.9 14.4 2.47

III 77,104 5,620.6 530.60 1.16 6,478 (626) 626 289 214,019 406 8.8 13.6 0.71

IV 89,939 6,217.9 537.27 1.46 8,966 (973) 973 (684) 305,495 477 9.8 13.1 -1.43

3I 96,129 6,735.8 535.33 0.93 6,310 181 181 (502) 275,200 444 3.0 12.0 -1.13

II 10 3,318 7,307.3 538.95 0.43 3,161 (157) 157 (660) 250,156 416 4.7 11.3 -1.59

III 11 9,260 7,850.6 539.38 1.17 9,209 (51) 51 (710) 227,647 382 0.5 10.3 -1.86

IV 12 12,418 8,394.7 539.86 1.47 12,348 (70) 70 (780) 209,085 356 0.6 9.5 -2.19

4I 13 7,960 8,895.4 535.95 0.93 8,324 364 364 (416) 203,217 357 4.6 9.1 -1.17

II 14 5,459 9,738.5 566.66 0.44 4,118 (1,341) 1,341 (1,757) 317,156 427 24.6 10.2 -4.11

III 15 10,990 10,210.5 557.19 1.17 12,102 1,112 1,112 (645) 378,382 473 10.1 10.2 -1.36

IV 16 13,483 10,606.6 541.08 1.47 15,856 2,373 2,373 1,727 706,550 592 17.6 10.7 2.92

5I 17 10,386 Estimate of SD of forecast error: 739.52

Exercise 7-10: Dishwashers

Deseasonalized Analysis (to estimate initial values)

Year Quarter Period Sales

Deseasonalized

Level

Level from

Regression

Seasonal

Factor

Seasonal

Factor

Estimate

Regression – Deseasonalized Level vs. Period

1I 11,934 0.94

II 21,276 0.45 Regression Statistics

III 33,991 3,574.3 3,610.0 1.11 1.17 Multiple R 0.9968673

IV 45,632 3,993.0 4,151.4 1.36 1.46 R Square 0.9937445

2I 54,862 4,434.9 4,692.8 1.04 Adjusted R Square 0.993119

II 61,698 5,362.4 5,234.3 0.32 Standard Error 162.44426

III 77,104 6,059.1 5,775.7 1.23 Observations 12

IV 89,939 6,420.0 6,317.1 1.57

3I 96,129 6,892.0 6,858.6 0.89 ANOVA

II 10 3,318 7,471.4 7,400.0 0.45 df SS MS F

Significance F

III 11 9,260 8,010.1 7,941.4 1.17 Regression 1 4.2E+07 41920020.13 1588.59 2.363E-12

IV 12 12,418 8,506.6 8,482.9 1.46 Residual 10 263881 26388.13758

4I 13 7,960 8,990.5 9,024.3 0.88 Total 11 4.2E+07

II 14 5,459 9,339.9 9,565.7 0.57

III 15 10,990 Coefficients

Standard Error

t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0%

IV 16 13,483 Intercept 1,985.68 124.63 15.93 0.00 1,708.00 2,263.37 1,708.00 2,263.37

X Variable 1 541.43 13.58 39.86 0.00 511.16 571.70 511.16 571.70

Winter’s Model

Year Quarter Period Sales Level Trend

Seasonal

factor

Forecast

EtAtBias MSE MAD

Percent

Error

MAPE TS

II 61,698 5,230.8 540.26 0.45 2,343 645 645 1,378 179,861 385 38 15 3.58

III 77,104 5,771.3 540.44 1.17 6,736 (368) 368 1,010 173,517 383 514 2.64

IV 89,939 6,312.0 540.70 1.46 9,244 (695) 695 316 212,148 422 713 0.75

IV 12 12,418 8,474.1 540.54 1.46 12,411 (7) 7 596 148,627 307 0 9 1.94

IV 16 13,483 10,637.9 540.54 1.46 15,582 2,099 2,099 2,799 528,432 515 16 10 5.43

5I 17 10,477 Estimate of SD of forecast error: 644.14

II 18 5,006

III 19 13,047

IV 20 16,372

α0.00061

β0.9

γ0

Exercise 7-10: Dishwashers

Deseasonalized Analysis (to estimate initial values)

Year Quarter Period Sales

Deseasonalized

Level

Level from

Regression

Seasonal

Factor

Seasonal

Factor

Estimate

Regression – Deseasonalized Level vs. Period

1I 11,934 0.94

II 21,276 0.45 Regression Statistics

III 33,991 3,574.3 3,610.0 1.11 1.17 Multiple R 0.9968673

IV 45,632 3,993.0 4,151.4 1.36 1.46 R Square 0.9937445

2I 54,862 4,434.9 4,692.8 1.04 Adjusted R Square 0.993119

II 61,698 5,362.4 5,234.3 0.32 Standard Error 162.44426

III 77,104 6,059.1 5,775.7 1.23 Observations 12

IV 89,939 6,420.0 6,317.1 1.57

3I 96,129 6,892.0 6,858.6 0.89 ANOVA

II 10 3,318 7,471.4 7,400.0 0.45 df SS MS F

Significance F

X Variable 1 541.43 13.58 39.86 0.00 511.16 571.70 511.16 571.70

Winter’s Model

01,985.7 541.43

1I 11,934 2,522.2 537.02 0.94 2,369 435 435 435 188,816 435 22 22 1.00

II 21,276 3,057.0 535.02 0.45 1,370 94 94 529 98,825 264 715 2.00

IV 45,632 4,120.7 530.74 1.46 6,040 408 408 1,138 101,095 284 711 4.00

2I 54,862 4,657.1 535.83 0.94 4,360 (502) 502 635 131,376 328 10 10 1.94

II 61,698 5,178.1 522.51 0.45 2,325 627 627 1,263 175,104 378 37 15 3.34

III 77,104 5,704.7 526.18 1.17 6,654 (450) 450 812 179,060 388 614 2.09

IV 89,939 6,236.7 531.46 1.46 9,126 (813) 813 (1) 239,324 441 813 0.00

3I 96,129 6,765.8 529.28 0.94 6,343 214 214 214 217,842 416 312 0.51

II 10 3,318 7,296.2 530.37 0.45 3,267 (51) 51 163 196,319 380 211 0.43

III 11 9,260 7,827.7 531.38 1.17 9,135 (125) 125 38 179,890 357 110 0.11

IV 12 12,418 8,360.4 532.52 1.46 12,243 (175) 175 (137) 167,451 341 1 9 -0.40

4I 13 7,960 8,888.7 528.72 0.94 8,335 375 375 238 165,378 344 5 9 0.69

II 14 5,459 9,446.7 555.09 0.45 4,217 (1,242) 1,242 (1,004) 263,693 408 23 10 -2.46

III 15 10,990 9,995.6 549.52 1.17 11,674 684 684 (320) 277,302 426 610 -0.75