My goal is to get the residual standard error of my model to be as small as possible. I have a linear model lm(y~x). When I plot the standardized residual errors in function of the explanatory variable I get the following plot:
so it seems like I need a quadratic term in my model lm(y~ x + x²) which then gives me the following standardized residual errors in function of x
Now the Breusch-Pagan test gives the following output on my model with a quadratic term
studentized Breusch-Pagan test
data: model_B2_squared BP = 7.5556, df = 2, p-value = 0.02287
meaning that there is still heteroscedasticity? Meaning that the residual standard error in my output summary is not correct?
"Residual standard error: 0.8906 on 75 degrees of freedom"
How can I get a good estimate of my residual standard error that is not completely wrong? I know we can get robust standard errors for my coefficients of my model, but what about the residual standard error? I really need a good estimate for it for my research.