My study is related to the visual attractiveness of route-plans in a logistics context. In practice, route-plans are rejected based on the fact that they "do not look nice". I have conducted an experiment where I showed participants of one group a route-plan with certain characteristics, while other groups were shown route-plans with different characteristics, however they both had the same quality ( in terms of total distance). Three main concepts I studied were: beauty 1=ugly - 10=beautiful), perceived quality (0 - 100% of shortest route-plan possible), and choice to accept a route-plan or not (yes/no).
I wanted to analyze the relationship between beauty (independent) and perceived quality (dependent), however the data for perceived quality is strongly skewed to the left. I tried several transformations, but I wasn't able to normalize the data for perceived quality. To be clear, multiple linear regression does not require the variables to be normally distributed, however the residuals should be. The residuals look normally distributed, but just not in the middle of the distribution.
Is there anything I can do or is it just not possible to test the relationship between those variables reliably? Perhaps non-parametric tests? If so, which ones?