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

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.