Analysis of variance is a statistical procedure for dividing the variability of a variable into components that can be attributed to different sources. We use ANOVA to determine the usefulness of the independent variable or variables in explaining variation in the dependent variable.
|Source of variation||Degrees of freedom||Sum of squares||Mean sum of squares|
|n – 2||SSE||MSE=SSE/(n-k-1)|
|Total variation||n – 1||SST|
n represents the number of observations and k represents the number of independent variables. With one independent variable, k = 1. Hence, MSR = RSS and MSE = SSE / (n – 2).
Information from the ANOVA table can be used to compute:
The F-statistic tests whether all the slope coefficients in a linear regression are equal to 0. In a regression with one independent variable, this is a test of the null hypothesis against the alternative hypothesis . It measures how well the regression equation explains the variation in the dependent variable.