Lesson 2 of 8 · 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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Interpreting coefficients, fitted values and residuals · Simple Linear Regression