Lesson 6 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 6 of 9 · 13 min

Intercept tests, indicator variables and p-values

The intercept is tested just like the slope; a 0/1 indicator variable turns the regression into a test of a difference in means; and the p-value tells you the smallest significance level at which you would reject.

In short

  • Intercept test: t=(b^0−B0)/sb^0t = (\hat b_0 - B_0)/s_{\hat b_0}, df = n − 2, with sb^0=se1/n+Xˉ2/∑(Xi−Xˉ)2s_{\hat b_0} = s_e\sqrt{1/n + \bar X^2/\sum (X_i-\bar X)^2}.
  • Indicator (dummy) variable: X = 0 or 1. Intercept = mean of Y when X = 0; slope = difference in means between the two groups.
  • A t-test on a dummy's slope is a test of whether the two group means differ.
  • p-value: the smallest significance level at which H0H_0 can be rejected. Reject if p-value < α\alpha.
  • Lowering α\alpha cuts the chance of a Type I error but raises the chance of a Type II error.

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