9.6. Inferences About The Slope
After using residual analysis to show that the assumptions of a least-squares regression model have not been seriously violated and that the straight-line model is appropriate, you can make inferences about the linear relationship between the dependent and independent variables in a population based on your sample results.
t Test for the Slope
You can determine the existence of a significant relationship between the X and Y variables by testing whether β1 (the population slope) is equal to 0. If you reject this hypothesis, you conclude that there is evidence of a linear relationship between Y and X. The null and alternative hypotheses are as follows:
H0: β1 = 0 (There is no linear relationship.)
H1: β1 ≠ 0 (There ...
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