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# forecasted sales for Quarter I, Quarter II, Quarter III, and Quarter IV of 2011

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A forecaster used the following regression equation: Qt = a + bt + c1D1 + c2D2 + c3D3 + e. Where, Qt is quarterly sales, D1, D2 and D3 are seasonal dummy variables for quarters I, II, and III, and e is the error term. The model was estimated using quarterly sales data for the period 2002II -2010IV (t = 1 for 2002II, ..., 35) and the following regression results were obtained.
Variable Parameter Estimate Standard Error of Estimate t-Stat
INTERCEPT 21.0 6.2 3.39
t 0.90 0.24 3.75
D1 8.0 2.60 -3.08
D2 6.0 1.80 -3.33
D3 4.0 0.60 -6.67
R2 = t = 35, R2 = 0.92, F-value = 88.54, critical t-value @ 5% significance level & 30 df = 2.042.

a. Is the trend coefficient estimate statistically significant at 5 percent level of significance? If it is significant, what is the estimated trend equation? What is the quarterly trend in sales?
b. Based on the regression results above, what are the forecasted sales for Quarter I, Quarter II, Quarter III, and Quarter IV of 2011?
c. What percent of the variation in sales is explained by this model?

According to some studies, the price elasticity of cigarettes is -0.85, and income elasticity is 1.75. Answer the following questions based on this information.
a. Explain whether the seller should decrease or increase the price of cigarettes in order to increase sales revenue.
b. If consumer income falls by 10%, what would be the percentage change in the quantity of cigarettes sold?

https://brainmass.com/economics/regression/forecasted-sales-quarter-quarter-quarter-quarter-iv-391142

#### Solution Preview

A forecaster used the following regression equation: Qt = a + bt + c1D1 + c2D2 + c3D3 + e. Where, Qt is quarterly sales, D1, D2 and D3 are seasonal dummy variables for quarters I, II, and III, and e is the error term. The model was estimated using quarterly sales data for the period 2002II -2010IV (t = 1 for 2002II, ..., 35) and the following regression results were obtained.
Variable Parameter Estimate Standard Error of Estimate t-Stat
INTERCEPT 21.0 6.2 3.39
t 0.90 0.24 3.75
D1 8.0 2.60 -3.08
D2 6.0 1.80 -3.33
D3 4.0 0.60 -6.67
R2 = t = 35, R2 = 0.92, F-value = 88.54, critical t-value @ 5% ...

#### Solution Summary

Forecasted sales for Quarter I, Quarter II, Quarter III, and Quarter IV of 2011 of this case are illustrated.

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