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Forecasting 159

We have labeled the first quarter (winter 1995) as period one, the second quar-

ter (spring 1995) as period two, and so on. We list the complete regression sta-

tistics in Table 4.7. The high F-statistic indicates that the equation has

considerable explanatory power. The time coefficient estimate has a low stan-

dard error (relative to the coefficient), which indicates that we can explain at

least some of the variation in sales by a time trend. Roughly, sales have gone up

an average of 2 million per quarter.

We can use this equation to forecast future sales. For instance, winter 2005

corresponds to t 41. Inserting this value into the equation implies the fore-

cast Q 41 223.08.

SEASONAL VARIATION Now we must account for seasonality. One would

expect most sales to occur in the fall quarter (October to December) prior to

the holidays and the fewest sales in the winter quarter (following the holidays).

Indeed, this is exactly what one observes. Figure 4.5 depicts the seasonal sales

as well as the trend line from the estimated regression equation. Clearly, this

trend line does not account for the seasonal variation in sales. The trend line

consistently underpredicts fall sales and overpredicts winter sales.

One way to correct for seasonality is through the use of dummy variables.

Consider this equation:

QtbtcWdSeUfF.

TABLE 4.7

Time Trend of Toy

Sales

Regression Output

Dependent variable: Q

Sum of squared errors 11,968.8

Standard error of the regression 17.75

R-squared 0.64

Adjusted R-squared 0.63

F-statistic 67.59

Number of observations 40

Degrees of freedom 38

Constant t

Coefficient(s) 141.16 1.998

Standard error of coefficients 5.72 .24

T-statistic 24.68 8.22

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