Question: In a September 1982 article in Business Economics, C. I. Allmon related \(y=\) Crest toothpaste sales in a given year (in thousands of dollars) to \(x_{1}=\) Crest advertising budget in the year (in thousands of dollars), \(x_{2}=\) ratio of Crest's advertising budget to Colgate's advertising budget in the year, and \(x_{3}=\) U.S. personal disposable income in the year (in billions of dollars). The data analyzed are given in Table 14.15. When we perform a regression analysis of these data using the model

we find that the least squares point estimates of the model parameters and their associated \(p\) -values (given in parentheses) are \(b_{0}=30,626(.156), b_{1}=3.893(.094), b_{2}=-29,607(.245)\), and \(b_{3}=86.52(<.001)\). Suppose it was estimated at the end of 1979 that in 1980 the advertising budget for Crest would be 28,000; the ratio of Crest's advertising budget to Colgate's advertising budget would be 1.56; and the U.S. personal disposable income would be 1,821.7. Using the model, a point prediction of and a 95 percent prediction interval for Crest sales in 1980 are 251,059 and [221,988,280,130]. Show how the point prediction has been calculated.

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