I am testing a one-sided hypothesis of association between two variables. I want to know if I increase variable A, then will variable B also increase?
For my experimental design, I increase the variable A in a defined interval and calculate the result (B) at the end of my measurement. By plotting this results B over the variable A, the signal is noisy. A rise upwards is visible but not over the whole range of inputs. I'm not sure if the trendline is a linear or quadratic form. The data are normally distributed. I confirmed that by test with $\chi^2$-test.
Now I want to do a significance test to assess my hypothesis. I have done the R2-Test for the linear model. Can I use the R2 also vor squared distributed data? How can report confidence intervals? I also used the F-Test. xI considered different designs, like a factorial design, but this seems not to be possible.
What is the significance test to assess my hypothesis? What test says, that variable A and variable B are dependent or not? Is there a coefficient of determination?