Chapter 9 Multiple Regression 359
There are many different parts to an ANOVA table. At this point, you
should just concentrate on the F ratio and its p value, which tell you whether
the regression is signifi cant. This ratio is large when the predictor variables
explain much of the variability of the response variable, and hence it has a
small p value as measured by the F distribution. A small value for this ratio
indicates that much of the variability in y is due to random error (as esti-
mated by the residuals of the model) and is not due to the regression. The
next chapter, on analysis of variance, contains a more detailed description
of the ANOVA table.
The F ratio, 7.197, is located in cell E12. Under the null hypothesis, you
assume that there is no relationship between the six predictors and the cal-
culus score. If the null hypothesis is true, the F ratio in the ANOVA table
follows the F distribution, with 6 numerator degrees of freedom and 73 de-
nominator degrees of freedom. You can test the null hypothesis by seeing
whether this observed F ratio is much larger than you would expect in the
F distribution. If you want to get a visual picture of this hypothesis test, use
the F distribution worksheet from the Distributions workbook and display
the F(6, 73) distribution.
The Signifi cance F column gives a p value of 4.69 31026 (cell F12), re-
presenting the probability that an F ratio with 6 degrees of freedom in the
numerator and 73 in the denominator has a value 7.197 or more. This is
much less than .05, so the regression is signifi cant at the 5% level. You
could also say that you reject the null hypothesis at the 5% level and ac-
cept the alternative that at least one of the coeffi cients in the regression is
not zero. If the F ratio were not signifi cant, there would not be much inter-
est in looking at the rest of the output.
Multiple Correlation
The regression statistics appear in the range A3:B8, shown in Figure 9-4
(formatted to show column labels and the values to three decimal places).
Figure 9-3
Multiple
regression
ANOVA table
