Question

Explain why the slope can be used as a test of the relationship of two variables in simple regression

Answer 1

The simple linear eqaution is

Y = a + b X

Where Y = Dependent Variable , X is independent vatale.

a is intercept and b is slope .

Now if we have to check is there any relationship between the independent varible and dependent variable .So this relationship is totally dependent on slope b .Because for 1 unit of x there is an increment in y slope times that is b times .Therefore to check this relationship we test

Ho: Slope =0 vs H1 : Slope 0

If we fail to reject null hypothesis then we get regression equation as

Y = a . So this is constant model we get ,and there is no relationship between the independent and dependent variable .Therefore we use slope test for checking the relationship between the variables.