Confidence intervals and Significance Tests for Correlation and Regression (3 of 5)

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The slope itself (b) is:



Using the general formula for a confidence interval, the confidence interval on the slope is: b ± t where t is based on N - 2 degrees of freedom. For the example data, there are 4 degrees for freedom. The t for the 95% confidence interval is 2.78 (t table). The 95% confidence interval is:

0.924 ± (2.78)(.272)
0.168 ≤ Population slope ≤ 1.681

Significance Test
The significance test for the slope of the regression line is done using the general formula for testing using the standard error. Specifically,



For the example data with a null hypothesis that the population slope is 0, t = .924/.2725 = 3.39. The degrees of freedom are N - 2 = 4. Notice that this value of t is exactly the same as obtained for the significance test of r.