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*Note that in computing the Fvalue there is no need to multiply R2 and (1 - R2) by Ey2 because it drops out, as shown in (8.5.12).

*Note that in computing the Fvalue there is no need to multiply R2 and (1 - R2) by Ey2 because it drops out, as shown in (8.5.12).

For the three-variable case (8.5.11) becomes

R2/2

By virtue of the close connection between F and R2, the ANOVA Table 8.1 can be recast as Table 8.4.

For our illustrative example, using (8.5.12) we obtain:

which is about the same as obtained before, except for the rounding errors.

One advantage of the F test expressed in terms of R2 is its ease of computation: All that one needs to know is the R2 value. Therefore, the overall F test of significance given in (8.5.7) can be recast in terms of R2 as shown in Table 8.4.

Testing the Overall Significance of a Multiple Regression in Terms of R2

Decision Rule. Testing the overall significance of a regression in terms of R2: Alternative but equivalent test to (8.5.7). Given the k-variable regression model:

Yi = 0i + 02 X2i + 03 X3i +■ ■ ■ + 0xXH + Ui To test the hypothesis

versus compute

H\. Not all slope coefficients are simultaneously zero

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