T-test for slope

Math

Definition

A t-test for slope is a hypothesis test used in linear regression to determine whether there is a statistically significant linear relationship between two variables. It tests whether the true slope of the regression line is different from zero (or another hypothesized value).

How It Works

  1. State the null hypothesis H₀: β = 0 and the alternative hypothesis.
  2. Calculate the estimated slope b from the least-squares regression line.
  3. Compute the standard error of the slope SE(b).
  4. Calculate the test statistic: t = b / SE(b) with df = n − 2.
  5. Find the p-value and compare it to the significance level to make a conclusion.

Examples

  • Testing whether study hours significantly predict exam scores
  • Determining if there is a real linear relationship between advertising spending and sales
  • Checking whether temperature has a significant effect on ice cream sales
Key Fact

t = b / SE(b), with df = n − 2

Related Terms

Least-squares regression Slope inference Confidence interval for slope Correlation

Study This Concept

Practice t-test for slope with free review games in these units:

AP Statistics Unit 9: Inference for Regression