As an example of the polynomial regression, consider the data on output and total cost of production of a commodity in the short run given in Table 7.4. What type of regression model will fit these data? For this purpose, let us first draw the scattergram, which is shown in Figure 7.2.
From this figure it is clear that the relationship between total cost and output resembles the elongated S curve; notice how the total cost curve first increases gradually and then rapidly, as predicted by the celebrated law of diminishing returns. This S shape of the total cost curve can be captured by the following cubic or third-degree polynomial:
Y, = ¡0 + ¡1 X + ¡2 X2 + ¡3 X3 + u, (7.10.4) where Y = total cost and X = output.
Total cost, $
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