Lesson 2 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 2 of 9 · 12 min

Interpreting coefficients, fitted values and residuals

The slope tells you how much Y moves per one-unit move in X, the intercept tells you Y when X is zero, and each residual tells you how far an observation sits above or below the line.

In short

  • Slope: the expected change in Y for a one-unit change in X, in Y's units. Positive slope = same direction; negative = opposite.
  • Intercept: the predicted Y when X = 0. It is only meaningful if X = 0 is realistic.
  • Fitted value Y^i=b^0+b^1Xi\hat Y_i = \hat b_0 + \hat b_1X_i; residual ei=Yi−Y^ie_i = Y_i - \hat Y_i. Positive residual = actual above the line.
  • Regression shows association, not causation.
  • Cross-sectional data: many entities at one time (index i). Time-series data: one entity over many periods (index t).

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