As the title says, what test can I use to test the relationship between Y and X variable when the data is not normally distributed and the variance is not constant. Initially, I wanted to do linear regression. So, what test can I do to at the end say like 'When x does this, Y does this'?
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1$\begingroup$ Do you expect (or hope for) a linear relationship? You might start by plotting the data in a scatter plot. $\endgroup$– Joel W.Commented Jul 2, 2018 at 13:21
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$\begingroup$ @JoelW. Yes but even if it is linear it's not normal and the variance is not constant. Can I still use linear regression? $\endgroup$– korasCommented Jul 2, 2018 at 15:04
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You don't need your variables to be linear to do a linear regression. The assumptions of linear regression are based on the distribution of the residuals. To estimate the linear slope using ordinary least squares, you don't need to make any assumptions about normality or homoscedasticity. To perform significance testing on the slopes, you can make those assumptions or use methods that don't require those assumptions, such as using a sandwich standard error or a bootstrap confidence interval.
