R2/(k — 1)

(1

— R2)/(n — k)

where use is made of the definition R2 = ESS/TSS. Equation (8.5.11) shows how F and R2 are related. These two vary directly. When R2 = 0, F is zero ipso facto. The larger the R2, the greater the F value. In the limit, when R2 = 1, F is infinite. Thus the F test, which is a measure of the overall significance of the estimated regression, is also a test of significance of R2. In other words, testing the null hypothesis (8.5.9) is equivalent to testing the null hypothesis that (the population) R2 is zero.

Source of variation |
SS df |
MSS* |

Due to regression |
R 2(E y,2) 2 |
R 2(E y,2)/2 |

Due to residuals |
(1 - R 2)(E y,2) n - 3 |
(1 - R 2)(E y,2)/(n - 3) |

Total |
E y,2 n -1 |
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