Which test to evaluate the assumption of homegeneity of variances of residuals (apart from residual vs predicted plot) ?

[#1]

Hi community,

In the residuals analysis, I evaluate normality and constant variance with the default graphs given in the regression analysis. However, I was wondering in which way I could test constant variance with a test that allow me to have sort of a p-value that make the situation more precise than looking at the graphs.

I am able to do it for normality, but not yet for the constance variance.

For example for the normality, I get the plot:

I can give some conclusions visually, but I also like to have a more precise description of the situation and therefore, I save the residuals and using the distribution platform (fit normal) I can get:

 The shapiro-wilk test allow me to evaluate (in addition to the visual evaluation) the normality of my residuals.

I am now looking to do something similar (doing a test) for the constance variance of the residuals in addition to the residual vs predicted plot (that I add here below)

I know that in the case of conducting an Anova in the "fit y by x" platform, there is the possibility of evaluating constance variance with "Lavene's test", but have not been able to do it in my case after plotting in this platform my saved  residuals and saved predicted values.

Do you know if there is a way in addition to the plot to test constance variance for my residuals ?

Thanks for any help,

Julian

[#2 · Accepted solution]

I think I found a nice tutorial from Professor Parris to do this:

Regression Diagnostics using JMP - Equality of Error Variance (youtube.com)

[#3]

Aside from the requested test, your residual plot suggests lack of fit. Could there be a non-linear effect in the residuals?

[#4]

Thank you @Mark_Bailey  for your comment.

Did you notice this in the residual by predicted plot or in the residual normal quantile plot ?

[#5 · Accepted solution]

Did you notice this in the residual by predicted plot or in the residual normal quantile plot ?

Your residual by predicted plot shows a curvature pattern. This is a strong evidence that one of the assumption behind the use of linear regression is not respected (errors should be normally distributed with random pattern, see Regression Model Assumptions | Introduction to Statistics), and that you might be missing some effects in your model : quadratic effect(s) (or higher order terms), and/or any terms introducing curvature in the relationship between your response and the factors, like interaction terms.

See more in the related posts :

Interpretation related to response model (RSM)

How I can I know if linear model or non-linear regression model fit to my variables?  

[#6]

Thank you @Victor_G  for your reply,

I actually did the verification of residuals and performed a box cox transformation which improved the situation. I cannot really add more terms since we had a rather simple case with not too many degrees of freedom. 

However, your message allowed me to see the point in @Mark_Bailey comment. I was forgetting that interactions and quadratic terms bring that non-linearity to the model if added after verification of residuals. A silly oversight from my part   : S