# In a residuals vs fitted plot, how do I interpret a homoscedastic variance that is not randomly distributed above/below the line?

I'm learning linear regression, and I ran a step function for linear regression and checked out the residuals vs fitted plot for the final equation. The residual looks homoscedastic but it's not randomly distributed above and below the line. I'm not sure how to interpret that. The residuals vs leverage plot doesn't indicate I have any points with a high cook's distance. My R-squared value is pretty awful...here's the summary output:

Residual standard error: 2.337 on 58588 degrees of freedom

Multiple R-squared: 0.3692, Adjusted R-squared: 0.3671

F-statistic: 174.1 on 197 and 58588 DF, p-value: < 2.2e-16

But I don't quite understand what this residuals vs fitted plot means. And what my next step in developing a better model would be.

• the residuals are neatly clustered. Do you work with many indicators? However, without seeing the model it is hard to tell anything. I also don't understand what your question is in detail! Heteroscedastic errors do not influence your estimated coefficients. They only influence the estimated standard deviation. You could, e.g. use robust standard errors in this case. Did you run a test on heteroscedasticity? – Peter Mar 14 at 12:36

This suggests that there's a nonlinearity in your data that isn't reflected in your fitted model. You haven't told us anything about your predictor variables, but for example if you've fit a model of the form $$y=ax+b$$, then perhaps you could try adding a quadratic term $$y=ax^{2}+bx+c$$.