Lesson 4 of 9 · All lessons in this module
  1. The regression model and least squares
  2. Interpreting coefficients, fitted values and residuals
  3. The four assumptions and residual plotsVideo lesson
  4. Sums of squares, \(R^2\), the ANOVA table and the SEEVideo lesson
  5. Testing the slope: t-test, correlation test and F-testVideo lesson
  6. Intercept tests, indicator variables and p-values
  7. Forecasts and prediction intervals
  8. Functional forms: log-lin, lin-log and log-logVideo lesson
  9. Integrated cases: reading a full regression printout

Lesson 4 of 9 · 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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