Analysis of Variance
The Analysis of Variance table summarizes information
about the sources of variation in the data.
Sum of Squares represents variation present in the data.
These values are calculated by summing squared deviations.
In multiple regression, there are three sources of variation:
Model, Error, and C Total.
C Total is the total sum of squares corrected for the mean,
and it is the sum of Model and Error.
Degrees of Freedom, DF, are associated with each
sum of squares and are related in the same way.
Mean Square is the Sum of Squares divided
by its associated DF (Moore and McCabe 1989).
If the data are normally distributed, the ratio of the
Mean Square for the Model to the Mean Square for
Error is an F statistic.
This F statistic tests the null hypothesis
that none of the explanatory variables has
any effect (that is, that the regression coefficients
, ,and are all zero).
In this case the computed F statistic
(labeled F Stat) is 18.8606.
You can use the p-value (labeled Pr > F)
to determine whether to reject the null hypothesis.
The p-value, also referred to as the probability
value or observed significance level, is the probability
of obtaining, by chance alone, an F statistic greater than
the computed F statistic when the null hypothesis is true.
The smaller the p-value, the stronger
the evidence against the null hypothesis.
In this example, the p-value is so small that you can
clearly reject the null hypothesis and conclude that at least
one of the explanatory variables has an effect on GPA.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.