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INTRODUCTION
The author and the restaurant manager were interested in forecasting weekly sales of a small restaurant near Marquette University in Milwaukee, Wisconsin. The author decided to employ regression and Box-Jenkins analysis. The restaurant compiled the previous week's sales every Monday morning. We began our analysis by obtaining weekly sales data from the week ending January 4, Year 1 through the week ending December 26, Year 2, a total of 104 observations. (At the restaurant manager's request, the author has disguised the years for which the weekly sales data were obtained). The mean weekly sales for these 104 weeks turned out to be $4862.
Figure 1 is a graph of the weekly sales over time. (Figure 1 omitted) The graph indicates that weekly sales are quite volatile, ranging from $1870 to $7548, with very little trend.
At the time this study was begun, the manager was forecasting the current week's sales as equal to the previous week's sales. The manager was dissatisfied with the accuracy of this "naive" forecasting method. Thus he was quite willing to consider more sophisticated forecasting methods.
REGRESSION ANALYSIS
We tested three predictors. The first predictor was time. The second predictor was a dummy variable indicating whether or not Marquette University was in full session that week (0 means not in full session, 1 means in full session). Examination of the sales data revealed that weekly sales always dropped when Marquette was not in full session; namely, during the Christmas break, the Spring break, and the summer. This is not surprising, since the restaurant is located on Marquette's campus and most of its customers are members of the Marquette community. The third predictor we made was sales lagged one week, since examination of the data indicated sales for two adjacent weeks were often similar.
Using Minitab, we then computed the simple correlations between the three potential predictors and the dependent variable weekly sales. The results are shown below, in Table 1. (Table 1 omitted) As expected, there is almost no trend in the weekly sales. However, the dummy variable is strongly correlated with current sales; that is, whether or not Marquette University is in full session is a good predictor of the current week's sales. The previous week's sales are moderately...