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The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. Quarter Year 1 Year

8500 3000+ 2500+ 2000+ Number of Copies Sold 1500+ 1000+ 500+ D- 4 2 3 + 1 2 4 1 2 Year! Year 3 Year 2 Year/Quarter 3500 3000

Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for year 4. (Round your answers

Please help. I'm stuck.

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Answer #1

ANSWER:

a)

For the given data

The time series plot is

3500 3000 2500+ 2000 Number of Coples Sold 1500+ I DOD 500 0 + 2 3 4 Year! 12 3 4 1 2 3 Year 2 Year 3 Year/Quarter

By using excel

A B с D E F G H J K 1 x1 X2 x3 у 1690 Regression ? х 2 1 0 0 3 940 0 1 0 Input Input Y Range: OK 4 2625 0 0 1 $A$1:$A$13 5 Ca

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.989744
R Square 0.979592
Adjusted R Square 0.971939
Standard Error 124.9667
Observations 12
ANOVA
df SS MS F Significance F
Regression 3 5996942 1998981 128.003 4.23E-07
Residual 8 124933.3 15616.67
Total 11 6121875
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0%
Intercept 2492 72.14954 34.53476 5.4E-10 2325.29 2658.044 2325.29
x1 -712 102.0349 -6.97474 0.000116 -946.959 -476.374 -946.959
x2 -1512 102.0349 -14.8152 4.24E-07 -1746.96 -1276.37 -1746.96
x3 327 102.0349 3.20152 0.012584 91.37388 561.9595 91.37388

From the above

Coefficients
Intercept 2492
x1 -712
x2 -1512
x3 327

b)

y = 2492 -712 x1 - 1512 x2 + 327 x3

c)

Quarter 1 forecast y =2492 -712 (1) - 1512 (0)+ 327 (0) 1780
Quarter 2 forecast y =2492 -712 (0) - 1512 (1)+ 327 (0) 980
Quarter 3 forecast y =2492 -712 (0) - 1512 (0)+ 327 (1) 2818
Quarter 4 forecast y =2492 -712 (0) - 1512 (0)+ 327 (0) 2492

d)

y t SUMMARY OUTPUT
1690 1
940 2 Regression Statistics
2625 3 Multiple R 0.301477
2500 4 R Square 0.090889
1800 5 Adjusted R Square -2.3E-05
900 6 Standard Error 746.0205
2900 7 Observations 12
2360 8
1850 9 ANOVA
1100 10 df SS MS F Significance F
2930 11 Regression 1 556408.4 556408.4 0.999752 0.34095
2615 12 Residual 10 5565467 556546.7
Total 11 6121875
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0%
Intercept 1612 459.1439 3.510981 0.005622 589.0091 2635.082 589.0091
t 62 62.38537 0.999876 0.34095 -76.6256 201.3809 -76.6256

y = 1612 + 62 t

Forecast

year 4

Quarter 1 y = 1612 + 62 (13) 2418
Quarter 2 y = 1612 + 62 (14) 2480
Quarter 3 y = 1612 + 62 (15) 2542
Quarter 4 y = 1612 + 62 (16) 2604

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