I'm doing some basic enough analysis on predicting transfer fees in football using a linear regression model but ran into a possible issue. I checked the data for linearity as well as normality and everything looks fine. However when looking homoscedasticity (Plot 3) the errors look a lot bigger as transfer fee increases creating this horizontal cone shaped graph.
Plot 1. Transfer fee against market value
Plot 2. Histogram of residuals
Plot 3. Residuals against transfer fee
Is linear regression robust enough to create a good model for this data or do I need to look at something else? Is there anything I have missed or need to consider?
I ran the model anyway to see what came up and unsurprisingly I got a high r^2 but I reckon this is due to the bigger values having more of a much larger pull on the best fit line. More importantly I suppose, I looked at the residual standard error but if the model isn't robust enough to homoscedasticity I can't see how the residual standard error would be in any way meaningful.
I got two values for residual standard error as well which confused me a little depending on whether I typed the transfer fee or market value variable first in the function.
For example: lm(MarketValue ~ TransferFee, or lm(TranferFee ~ MarketValue,
I'm thinking this is something to do with which is the predictor variable but how do I know whether to put that variable first or second in the function?