Math
T-test for slope.
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 · 5 phases
Step by step.
- State the null hypothesis H₀: β = 0 and the alternative hypothesis.
- Calculate the estimated slope b from the least-squares regression line.
- Compute the standard error of the slope SE(b).
- Calculate the test statistic: t = b / SE(b) with df = n − 2.
- Find the p-value and compare it to the significance level to make a conclusion.
Examples
Real-world.
- 1 Testing whether study hours significantly predict exam scores
- 2 Determining if there is a real linear relationship between advertising spending and sales
- 3 Checking whether temperature has a significant effect on ice cream sales
Key Fact
t = b / SE(b), with df = n − 2