Multiple regression or multivariate regression?

The Breusch-Pagan Test (aka Cook-Weisberg Test) is a good approach. It's included in the "car" package in R:

ncvTest(model)

The test statistic is chi-square distributed. If the p-value is non-significant, the assumption of homoscedasticity is not violated.

Thanks Blaine! that's a very short but great answer! It helps.

Rainer, would having a multiple regression and/or multivariate regression make a difference as to the choice if the test statistic?

Breusch Pagan test is suitable, BUT I would never soley rely on some statistical value to assess homoscedasticity or normality. They have the same power problems as other tests. Small sample size may miss you severe violations, while large sample sizes detect even small violations, which are not harmful. It is important to assess the deviations also by visual inspection.

To your question Hanif Qureshi : in SPSS, as far as I know, multivariate regression is not directly available, only through the MANOVA dialoque and there is no formal test for homoscedasticity available. For multiple regression in SPSS: you could use the General_Linear_Model->Univariate dialogue and request "parameter estimation" to get the typical regression output. Also under options you can get the Breuch-Pagan test, the modified Breusch-Pagan test and the White test, as well as robust estimators HC1 to HC4 for the standard errors in case of heteroscedasticity.

For R you can follow Blaine Tomkins advice.

Rainer, I agree. A combination of visual inspection and a test statistic seems the best way to go. I would not trust my visual instincts, especially when there is a close call. So while a visual inspection is great, the Breusch Pagan test will lend slightly higher credibility to my conclusion.

Am I right?

Hanif Qureshi that is interesting, what is a "close call"? Especially in close calls, I would not rely on a single value. You should also keep in mind, what heteroskedasticity implies and therefore you need to see it by yourself. A funnel may indicate that a predictor or an interaction is missing. Other patterns may indicate other problems. Typically, your parameter estimation is not compromised, but maybe the inferential statistics. To prevent this, why not using robust estimators in the first place?

A test only delivers one single value, which is not very valuable (pun intended) to make decisions.

Hanif -

As I explained in one of my updates to https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, "No need for an hypothesis test," about the 15th update back on that project, an hypothesis test does not tell you much. What you need to know is an estimate of how much heteroscedasticity you have, so you can then see how it impacts results. In most cases, it won't change predictions a great deal, but it generally will have substantial influence on the estimated variance of the prediction error.

Essential heteroscedasticity in finite population sampling is the inherent increase in sigma for estimated residuals associated with larger predictions. The range of heteroscedasticity which should occur because of this has been justified by Ken Brewer, and recognized in another context at least as far back as 1938 (H. Fairfield Smith), and discussed by W.G. Cochran in his Sampling Techniques book, notably in the 3rd ed, Wiley, under the topic of cluster sampling. See

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity.

However, there are model and data issues which may effectively reduce or enhance apparent heteroscedasticity:

https://www.researchgate.net/publication/324706010_Nonessential_Heteroscedasticity

You can estimate the full impact of heteroscedasticity, as shown in examples here:

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

Here is a tool for doing that for your own model and data:

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

By the way, a graphical residual analysis is the start for this, and alone still tells you more than a 'statistical test.' Also, there is no "safe value." Especially please note that a lone p-value, with no other information, is virtually meaningless.

I know that's a lot of material, but it is at its core rather straightforward.

Cheers - Jim

Non-constant Variance Score

R:

ncv.test in package car

An hypothesis test will not help here. There are such 'tests' in existence, but to what end? The effect size is very important, but how would you frame that to know what impact it would have on regression results (predictions, and the estimated variances of the prediction errors)? As I described above, and gave resources to produce, you need to estimate the degree of heteroscedasticity. This is then used to find regression weights and see how they impact your results using weighted least squares (WLS) regression.