Alluring Tackle, Inc.. a manufacturer of fishing equipment, makes the Bass Grabber, a type of fishing lure.

Question:

Alluring Tackle, Inc.. a manufacturer of fishing equipment, makes the Bass Grabber, a type of fishing lure. The company would like to develop a prediction model that can be used to obtain point forecasts and prediction interval forecasts of the sales of the Bass Grabber. The sales (in tens of thousands of lures) of the Bass Grabber in sales period t, where each sales period is defined to last four weeks, are denoted by the symbol yt and are believed to be partially determined by one or more of the independent variables x1 = the price in period t of the Bass Grabber as offered by Alluring Tackle (in dollars); x2 = the average industry price in period t of competitors' similar lures (in dollars); and x3 = the advertising expenditure in period t of Alluring Tackle to promote the Bass Grabber (in tens of thousands of dollars). The data in Table 16.20 have been observed over the past 30 sales periods, and a plot of these data indicates

TABLE 16.20

Sales of the Bass Grabber in Tens of Thousands of Lures)

Alluring Tackle, Inc.. a manufacturer of fishing equipment, makes the

that sales of the Bass Grabber have been increasing in a linear fashion over time and have been seasonal, with sales of the lure being largest in the spring and summer, when most recreational tishing takes place. Alluring Tackle believes that this pattern will continue in the future. Hence, remembering that each year consists of 13, four-week seasons, a possible regression model for predicting yt would relate yt to x1, x2, x3, t, and the seasonal dummy variables S2, S3, . . . . . S13,.
Here, for example, S2 equals 1 if sales period t is the second four-week season, and 0 otherwise. As another example, S13 equals 1 if sales period t is the 13th four-week season, and 0 otherwise. If we calculate the least squares point estimates of the parameters of the model, we obtain the following prediction equation (the t statistic for the importance of each independent variable is given in parentheses under the independent variable):

For sales period 31, which is the fifth season of the year, x1 will be 3.80, x2, will be 3.90, and x3 will be 6.80. Using these values, it can be shown that a point prediction and a 95 percent prediction interval for sales of the Bass Grabber are, respectively, 10.578 and [9.683, 11.473]. Using the given prediction equation, verify that the point prediction is 10.578.