Info

18,891.4

Note: 2001 data are preliminary.

Source: Company annual reports (various years).

Note: 2001 data are preliminary.

Source: Company annual reports (various years).

Note that these sales projections are based on a linear trend line, which implies that sales increase by a constant dollar amount each year. In this example, Microsoft sales are projected to grow by $1,407.3 million per year. However, there are important reasons for believing that the true trend for Microsoft sales is nonlinear and that the forecasts generated by this constant change model will be relatively poor estimates of actual values. To see why a linear trend relation may be inaccurate, consider the relation between actual sales data and the linear trend shown in Figure 6.2. Remember that the least squares regression line minimizes the sum of squared residuals between actual and fitted values over the sample data. As is typical, actual data points lie above and below the fitted regression line. Note, however, that the pattern of differences between actual and fitted values varies dramatically over the sample period. Differences between actual and fitted values are generally positive in both early (1984-1987) and later (1996-2001) periods, whereas they are generally negative in the intervening 1988-1995 period. These differences suggest that the slope of the sales/time relation may not be constant but rather may be generally increasing over the 1984-2001 period. Under these circumstances, it may be more appropriate to assume that sales are changing at a constant annual rate rather than a constant annual amount.

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