Say I have the two hypotheses:
- H0: there is no linear relationship between the two variables.
- H1: there is a linear relationship between the two variables.
Now, my significance level is 0.05, and I have used Pearson's correlation coefficient to calculate the p-value for my two variables (shown below).
(-0.19047068210886346, 4.588168807135144e-138)
As you can see, my coefficient is -0.19 and my p-value is 4.6.
Therefore, as my p-value is > 0.05, does this mean I have to accept H0, that there is no linear relationship between the two variables?
Though, my correlation coefficient is -0.19, which indicates a very weak linear relationship, so how do I prove this with my hypothesis test?
What has gone wrong? There clearly is a linear relationship here, but the hypothesis test says otherwise.