## 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.