Lesson 9 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 9 of 9 · 16 min

Integrated cases: reading a full regression printout

A regression printout holds every number you need for fit, significance, forecasting and risk; the case is to find the right cell, convert between them, and avoid the labels that look alike.

In short

  • From R² and the sign of the slope get the correlation: r=±R2r = \pm\sqrt{R^2}, with the sign of the slope. 'Multiple R' on a printout is ∣r∣|r|, not R2R^2.
  • Two 'standard errors' sit on a printout: the SEE (MSE\sqrt{\text{MSE}}, in Y units) in the regression statistics, and the standard error of each coefficient in the coefficient table.
  • With one predictor, F=t2F = t^2 for the slope, and 'Significance F' equals the slope's p-value. Check that SSR + SSE = SST and the mean squares are SS ÷ df.
  • Test the slope against any hypothesised value with t=(b^1−B1)/sb1t = (\hat b_1 - B_1)/s_{b_1}; the printout's t-statistic tests against zero only.
  • In log-lin and log-log forms, convert slopes exactly: %ΔY=eb1 ΔX−1\%\Delta Y = e^{b_1\,\Delta X} - 1 in a log-lin model; the approximation b1ΔXb_1\Delta X is good only when it is small.

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