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6See K. A. Brownlee, Statistical Theory and Methodology in Science and Engineering, John Wiley & Sons, New York, 1960, pp. 278-280.

7Ibid.

256 PART ONE: SINGLE-EQUATION REGRESSION MODELS

relatively larger than the RSS, taking due account of their respective df. Therefore, the F value of (8.5.3) provides a test of the null hypothesis that the true slope coefficients are simultaneously zero. If the F value computed from (8.5.3) exceeds the critical F value from the F table at the a percent level of significance, we reject H0; otherwise we do not reject it. Alternatively, if the p value of the observed F is sufficiently low, we can reject H0.

Table 8.2 summarizes the F test. Turning to our illustrative example, we obtain the ANOVA table, as shown in Table 8.3.

128,681.2 1742.88

The p value of obtaining an F value of as much as 73.8325 or greater is almost zero, leading to the rejection of the hypothesis that together PGNP and FLR have no effect on child mortality. If you were to use the conventional 5 percent level-of-significance value, the critical F value for 2 df in the numerator and 60 df in the denominator (the actual df, however, are 61) is about 3.15 or about 4.98 if you were to use the 1 percent level of significance. Obviously, the observed F of about 74 far exceeds any of these critical F values.

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