I am trying to perform a linear regression analysis but I fear that my data has heteroscedasticity, thus violating the assumption of homoscedasticity which is required for linear regression. I would like to confirm it and also to know how I can reduce it. My data is attached. DBH is the independent variable and Density is the dependent variable.
Evans -
There are examples of considering heteroscedasticity in regression in here:
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity
This is a tool for using it on your data:
https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx
You can see that this is accomplished by first considering a graphical residual analysis.
If you are interested in why there should be heteroscedasticity, please see this:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
For more information, which includes a section on why a hypothesis test here is not helpful, please see the following:
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression
Cheers - Jim
Evans -
I'm just looking at my phone here, and I see you just have one regressor. When doing a graphical residual analysis with predicted y on the x-axis and estimated residuals on the y-axis, if your predicted y is bx, then you can use x on the x-axis because the constant multiplier won't matter. If you are using an intercept term however, you can't ignore that. By the way, an intercept term is often, I think, used when it is just noise. I suggest you not use one unless you have good reason, such as a scatterplot which indicates it contains information, perhaps from missing variables, and is not zero.
It would be nice if you would include a scatterplot for us all to see. They usually tell us a great deal, but sometimes have to be looked at carefully, and might even be misleading. Still, the first thing to do is to make a scatterplot, which is generally very useful.
For an interesting example, please see the scatterplot in the following question, and also please consider my July 2 response to this:
https://www.researchgate.net/post/Hello_Do_you_think_that_this_is_pattern_of_heteroscedasticity_How_can_i_statistically_test_for_homoscedasticity
Cheers - Jim
Look at the residual plot. Usually, periodic shapes indicate heteroscedasticity. See the following link:
https://statisticsbyjim.com/regression/heteroscedasticity-regression/#:~:text=Specifically%2C%20heteroscedasticity%20is%20a%20systematic,a%20constant%20variance%20(homoscedasticity).
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