Note that the mean of the residuals is approximately 0 (which is consistent with a key assumption of the regression model) and standard deviation 7.69.
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.