Question

how to test for non linear relationship

Answer 1

If you are dealing with just two variables then first need to make a histogram of each variable to determine the underline stastical properties. If they are not normal, you may need to transform the data using logarithm or root transform.you may be surprised to find a good linear fit after log transformation. After making the scatter plot and fitting the equation, look at the residual histogram and plot the residual versus independent variable to check for heteroskedasticity. If your data affected by outliers try the spearman rank correlation are the other rank methods that are robust to outliers. After all this, if you can't find a non linear relationshipbut you believe the variables are related you need to figure out why the data is hiding what you believe or you need to check your hypothesis.