Observation: We can also test whether the slopes of the regression lines arising from two independent populations are significantly different. Note that the 95% confidence interval for the population slope isī ± t crit

0028 2.16 = t crit) we reject the null hypothesis, and so we can’t conclude that the population slope is zero. the slope of the population regression line is zero):Įxample 1: Test whether the slope of the regression line in Example 1 of Method of Least Squares is zero.įigure 1 shows the worksheet for testing the null hypothesis that the slope of the regression line is 0.įigure 1 – t- test of the slope of the regression line Thus Theorem 1 of One Sample Hypothesis Testing for Correlation can be transformed into the following test of the hypothesis H 0: β = 0 (i.e. It follows that ρ = 0 if and only if β = 0. Since by the population version of Property 1 of Method of Least Squares Putting these elements together we get that Observation: By Theorem 1 of One Sample Hypothesis Testing for Correlation, under certain conditions, the test statistic t has the propertyīut by Property 1 of Method of Least SquaresĪnd by Definition 3 of Regression Analysis and Property 4 of Regression Analysis We now show how to test the value of the slope of the regression line.

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