Lesson 6 of 8 · 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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Intercept tests, indicator variables and p-values · Simple Linear Regression