# Choosing a significance test, trend appears either linear or quadratic

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?

2. You do not test normality of "the data". To assess the assumptions of the (exact finite sample) linear model, you must assess the normality of the residuals. This is an interesting paradox for some: if the wrong model produces normal errors, but a better trendline creates non-normal errors, which do you choose? Well, the scientific question should guide you. Choose the model that best answers the question and deal with both the trend and the residuals in robust ways. The OLS needs no adjustment if the residuals are nonnormal because of the Lindeberg-Feller CLT. If there is heteroscedasticity, use sandwich errors if $$n > 40$$, or jackknife error estimates.