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Inference for the Slope of a Regression Line

Test H₀: β = 0. t = b / SE_b where SE_b = s/√Σ(x−x̄)². Reject H₀ if |t| > t* → evidence of linear association.

StatisticsCommon Core DAT-2.AREGVerified correct ✓

Worked examples

A regression analysis of hours studied (x) on exam score (y) gives slope b = -4.0 with SE_b = 0.8. Using t* = 2.306, compute the upper endpoint of the 95% confidence interval for the slope β. Round to four decimal places.
Answer: -2.1552
A regression analysis of hours studied (x) on exam score (y) with n = 32 observations yielded slope b = 0.8 with standard error SE_b = 0.25. Compute the t-statistic for testing H₀: β = 0. Round to four decimal places.
Answer: 3.2

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Least-Squares Regression Line — ŷ = a + bxHypothesis Test for a Mean — One-Sample t-Test

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