Question

Can someone please explain a better approach other than to test that the intercept was equal to zero and that the slope was equal to one? Is there any other hypothesis test one can perform for the slope and intercept?

Answer 1

Yes there is a Hypothesis Test for Regression Slope :

The test focuses on the slope of the regression line

Y = Β₀ + Β₁X

where Β₀ is a constant, Β₁ is the slope (also called the regression coefficient), X is the value of the independent variable, and Y is the value of the dependent variable.

If we find that the slope of the regression line is significantly different from zero, we will conclude that there is a significant relationship between the independent and dependent variables.

You can interpret slope value for each predictor as the change in Y when the predictor X increases by 1.

You can interpret intercept value Β₀ as the predicted value when each X is zero.

Hope this will be helpful. Thanks and God Bless You :)