LO 3.2.1.J

Learning Objective: Describe null and alternative hypotheses.

Review:

• A common hypothesis test on coefficient 𝛽1 involves testing

the null hypothesis

                H0 : There is no relationship between X and Y, that is

                H0 : 𝛽1 = 0

versus the alternative hypothesis

Ha :  There is some relationship between X and Y, that is

                Ha : 𝛽1 ≠ 0

The rationale of the test: if 𝛽1 = 0 then the regression model reduces to

Y = 𝛽0 + 𝜀, and X is not associated with Y.