where ESSnew = ESS under the new model (i.e., after adding the new re-gressors = Q3), ESSold = ESS under the old model (= Qi) and RSSnew = RSS under the new model (i.e., after taking into account all the regressors = Q4). For our illustrative example the results are as shown in Table 8.7. Now applying (8.5.16), we obtain:
Under the usual assumptions, this F value follows the F distribution with 1 and 62 df. The reader should check that this F value is highly significant, suggesting that addition of FLR to the model significantly increases ESS and hence the R2 value. Therefore, FLR should be added to the model. Again, note that if you square the value of the FLR coefficient in the multiple regression (8.2.1), which is (—10.6293)2, you will obtain the F value of (8.5.17), save for the rounding errors.
Incidentally, the F ratio of (8.5.16) can be recast by using the R2 values only, as we did in (8.5.13). As exercise 8.2 shows, the F ratio of (8.5.16) is equivalent to the following F ratio:9
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