A simple hypothesis test question. But, while reading the following hypothesis test, I am stuck:
H0: β = 0
Ha: β ≠ 0
The answer shows that the null hypothesis represent there is no linear relationship while alternative hypothesis suggest that there is linear relationship.
How should I understand that and what is the β in statistics?
A quick search in google shows the top result is:
Beta (β) refers to the probability of Type II error in a statistical hypothesis test.
which is confusing to me.
What is the relationship between β and linear relationship?
Any helps given will be appreicated!
P.S. I could provide the full question if necessary
Edit:
The Hypothesis test I am looking at is about about regression line and how to do the judgement of the slope
There is no one single fixed use of $\beta$ in mathematics, and it needs to be interpreted from context. In the case of your given hypothesis test, it looks like $\beta$ is being used as the slope coefficient in the linear regression, i.e. there is an assumed linear relationship of the form $y \sim \beta x + c$, and the hypothesis test is trying to find out whether there is evidence that $\beta \neq 0$, since $\beta = 0$ implies that the linear relationship does not exist. This kind of notation is often used when we have multiple predictors and we use a vector representation such as $y \sim \mathbf{x}^{\intercal} \beta$.
In different contexts, $\beta$ may also be used to represent the probability of Type II error as you have found, but it does not look like that is the case here.