The analysis of variance (ANOVA) equation for simple linear regression expresses the total variation in the responses as the sum of two sources: the linear relationship of with and the residual variation in responses for the same . The equation is expressed in terms of sums of squares.
Each sum of squares has a degrees of freedom. A sum of squares divided by its degrees of freedom is a mean square. The residual mean square is the square of the regression standard error.
The ANOVA table gives the degrees of freedom, sums of squares, and mean squares for total, regression, and residual variation. The ANOVA statistic is the ratio . In simple linear regression, is the square of the statistic for the hypothesis that regression on does not help explain .
The square of the samplecorrelation can be expressed as
and is interpreted as the proportion of the variability in the response variable that is explained by the explanatory variable in the linear regression.