26. The quarterly sales data (number of copies sold) for a college textbook over

Question

26. The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. Year 2 Year 3 Year 1 Quarter 1690 1800 1850 1100 940 900 2625 2900 2930 2615 2500 2360 a. Construct a time series plot. What type of pattern exists in the data? b. Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr 1- 1 if Quarter 1,0 otherwise, Qtr2 1 if Quarter 2, 0 otherwise; Qtr3 1 if Quarter 3, 0 otherwise c. Compute the quarterly forecasts for next year. d. Lett 1 to refer to the observation in quarter 1 of year 1; t 2 to refer to the obser- vation in quarter 2 of year 1 and t 12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.

Explanation / Answer

a.

The Cyclical Pattern is exist in the data because the time series plot shows an alternating sequence of points
below and above the trend line lasting more than one year.

b. The regression model, is

Y=b0+b1 Qtr1+b2 Qtr2+b3 Qtr3+b4 S

561.9595

c.

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% Intercept 2491.667 72.14954 34.53476 5.4E-10 2325.29 2658.044 Qtr1 -711.667 102.0349 -6.97474 0.000116 -946.959 -476.374 Qtr2 -1511.67 102.0349 -14.8152 4.24E-07 -1746.96 -1276.37 Qtr3 326.6667 102.0349 3.20152 0.012584 91.37388

561.9595

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