Question

For the linear regression model, y = β0 + β1x1 + β2x2 + . . . + βkxk + ɛ, which of the following are the competing hypotheses used for a test of joint significance?

Choose both the correct test for the null and alternative hypotheses.
Multiple select question.
A. H0:β1=β2=... =βk=0
B. HA:At least one βi≠0
C. H0: βj =βj0
D. HA: βj ≠βj0

Answer 1

The competing hypotheses are H0: β1 = β2 = ... = βk = 0 and HA: At least one βi ≠ 0.

Step-by-step explanation:

The competing hypotheses used for a test of joint significance in a linear regression model are:

1. H0: β1 = β2 = ... = βk = 0
2. HA: At least one βi ≠ 0

In words, the null hypothesis states that all the coefficients (β) in the linear regression model are equal to zero, meaning there is no significant linear relationship between the independent variables (x1, x2, ..., xk) and the dependent variable (y). The alternative hypothesis states that there is at least one coefficient that is not equal to zero, indicating a significant linear relationship between the independent variables and the dependent variable.