Lesson 4 of 8 · 14 min

Sums of squares, \(R^2\), the ANOVA table and the SEE

Total variation in Y splits into the part the line explains (SSR) and the part it misses (SSE). The ANOVA table organises that split and gives R2R^2, the F-statistic and the standard error of the estimate.

In short

  • SST (total) = SSR (explained, regression) + SSE (unexplained, error).
  • Coefficient of determination R2R^2 = SSR ÷ SST: the share of Y's variation explained by X. In simple regression R2=r2R^2 = r^2.
  • Degrees of freedom: regression 1, error n − 2, total n − 1. MSR = SSR ÷ 1, MSE = SSE ÷ (n − 2).
  • Standard error of the estimate (SEE, ses_e) = MSE\sqrt{MSE}: the typical size of a residual, in Y units. Smaller = better fit.
  • R2R^2 and F are relative measures of fit; the SEE is an absolute one.

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Sums of squares, \(R^2\), the ANOVA table and the SEE · Simple Linear Regression