confusion about Ho/Ha hypothesis for simple/multiple regression

The one thing I do not understand (and my book doesn't explain) is how do you determine if it's Ha > 0, Ha < 0 or Ha =/= 0? Anyone can shed some light on this problem?

And if you determine that Ha =/= 0, it becomes a two-tailed test, so you have to divide the alpha by 2 when finding the rejection zone, or also multiply the P-value by two, right?

I'll give an example from some questions that I have to answer for a homework:

1) Given the following statistics of a multiple regression model, can we conclude at the 1% significance level that X1 and y are linearly related?

2) Test at the 5% significance level to determine whether annual household income and annual family clothes expenditure are positively linearly related.

3) Test at the 1% significance level to determine whether the number of family members and annual family clothes expenditure are linearly related.

Thank you very much!
Could anyone confirm if this is true?

If the question says positive linear, it's >

If the question says negative linear, it's <

If nothing is mentioned, it's =/=


TS Contributor
Hi Parad0x,

When you run a regression model, you get parameter estimates, that help you understand the relationship between the regressors and the expected value of a dependent variable. Using those coefficients and the hypothesis testing related to them, you can answer the problem.