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 y with x and the residual variation in responses for the same x. 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 Fstatistic is the ratio F=Regression MS/Residual MS. In simple linear regression, F is the square of the t statistic for the hypothesis that regression on x does not help explain y.
The square of the samplecorrelation can be expressed as
r2=Regression SSTotal SS
and is interpreted as the proportion of the variability in the response variabley that is explained by the explanatory variablex in the linear regression.