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Source: Quarterly Financial Report for Manufacturing Corporations, Federal Trade Commission and the Securities and Exchange Commission, U.S. government, various issues (computed).

Source: Quarterly Financial Report for Manufacturing Corporations, Federal Trade Commission and the Securities and Exchange Commission, U.S. government, various issues (computed).

432 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL

d. If there is a statistically significant relationship between the two, how would you transform the data so that there is no heteroscedasticity? 11.13. Bartlett's homogeneity-of-variance test." Suppose there are k independent sample variances sj2, s|,..., si with f1( f2,..., fk df, each from populations which are normally distributed with mean ¡i and variance o2. Suppose further that we want to test the null hypothesis io: of = o22 = • • • = ol of the same population variance o2. If the null hypothesis is true, then k

H0: a1f = a22 = ■ ■ ■ = ak = a2; that is, each sample variance is an estimate s2 = 1=1

Efs2

Hfi f provides an estimate of the common (pooled) estimate of the population variance o2, where f = (n — 1), n being the number of observations in the ith group and where f = Yki=1 f.

Bartlett has shown that the null hypothesis can be tested by the ratio A/B, which is approximately distributed as the x2 distribution with k — 1 df, where

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