I am trying to figure out how to test for homoscedasticity. But run into a small issue. I am using this r-bloggers article as a learning resource. According to this article there is no homoscedasticity in a certain model. That is expressed in the image below. According to the article this is due to the red lines (in both left plots) not being straight lines. enter image description here

It then continues on how to perform the Breusch Pagan Test. From what I read this tests whether or not there is homoscedasticity. The result from the test are shown in the following code fragment:

lmtest::bptest(lmMod)  # Breusch-Pagan test
    studentized Breusch-Pagan test

data:  lmMod
BP = 3.2149, df = 1, p-value = 0.07297

What I see is a p-value of 0.07297 which would confirm the presence of homoscedasticity as it is greather than 0.05.

Am I understanding this wrong?

  • $\begingroup$ The usual stance is that homoscedasticity is desirable and heteroscedasticity less desirable, so you are testing for the latter. There is a cultural divide here between those at one extreme who insist that every action in data analysis must hinge on a significance test (some kinds of economists among them) and those at another extreme who muddle through using experience and subject-matter knowledge as a guide (which is not so easy if you don't have much). $\endgroup$
    – Nick Cox
    Commented May 19, 2020 at 7:44
  • $\begingroup$ I don't see much to worry about in these plots, which is not to say that your model can't be improved. I am generally positive about such plots, but as you say nothing about the data or the model you fitted, it is hard to know what to suggest. The situation is like getting negative results on certain specific medical tests, good news in itself, but which is consistent with the possibility that different diet and exercise might be a good idea. Beware of treating 0.05 as having a magic it really doesn't have. Two or three identified data points might deserve some thought. $\endgroup$
    – Nick Cox
    Commented May 19, 2020 at 7:47
  • $\begingroup$ @NickCox from what I get from your reply is that the Breusch-Pagan test, tests for heteroscedasticity. So a score of 0.07 tells us that there is a 7% chance so heteroscedasticity cannot be disproven? $\endgroup$ Commented May 19, 2020 at 9:32
  • $\begingroup$ The null hypothesis here is of homoscedasticity. This is well documented. en.wikipedia.org/wiki/Breusch%E2%80%93Pagan_test $\endgroup$
    – Nick Cox
    Commented May 19, 2020 at 10:20
  • $\begingroup$ @NickCox just for my understanding. Think I got it now. How would you interpret the results from the test in combination with the plotted datat? $\endgroup$ Commented May 19, 2020 at 11:52


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