All this theoretical discussion might seem a bit tedious. But this knowledge is extremely useful when we examine the empirical results, for if the empirical results do not agree with prior expectations, then, assuming we have not committed a specification error (i.e., chosen the
wrong model), we will have to modify our theory or look for a new theory and start the empirical enquiry all over again. But as noted in the Introduction, this is the nature of any empirical investigation.
When the third-degree polynomial regression was fitted to the data of Table 7.4, we obtained the following results:
Y = 141.7667 + 63.4776X — 12.9615*2 + 0.9396 X73 (6.3753) (4.7786) (0.9857) (0.0591)
19See Alpha C. Chiang, Fundamental Methods of Mathematical Economics, 3d ed., McGraw-Hill, New York, 1984, pp. 250-252.
CHAPTER SEVEN: MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF ESTIMATION 229
EXAMPLE 7.4 (Continued)
(Note: The figures in parentheses are the estimated standard errors.) Although we will examine the statistical significance of these results in the next chapter, the reader can verify that they are in conformity with the theoretical expectations listed in (7.10.5). We leave it as an exercise for the reader to interpret the regression (7.10.6).
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