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I have carried out simple linear regression and I am now checking the models meets the assumption of homogeneity of variance:

• am I correct in concluding that the Levenes tests which gave a p<0.05 indicates a violation of homogeneity of variance?

• some models contain 2 or 3 explanatory variables, but in some models, only 1 explanatory variable gave p<0.05 in the Levenes test. Therefore, should only those explanatory variables which gave p<0.05 be corrected?

• is transformation the best place to start when correcting for violation of homogeneity?

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    $\begingroup$ You may be confusing the assumption of "homogeneity of variances" (explanatory variable has distinct groups as in ANOVA) with the assumption of "homoskedasticity" (explanatory variable is continuous as in regression). Levene's test cannot test the latter assumption. See this answer for details. $\endgroup$ – caracal Aug 1 '12 at 20:02
  • $\begingroup$ Readers may also find this thread of interest: what-does-having-constant-variance-in-a-linear-regression-model-mean. $\endgroup$ – gung Mar 15 '13 at 20:12
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  1. You don't "correct" your covariates; the heterogeneity is in the residuals.
  2. If you're simply running Levene's test as a factorial ANOVA & finding heterogeneity for some of your explanatory variables, you probably have interactions with those variables that you're currently missing & need to add to your model.
  3. Transformations of the response variable are a good place to start once you've accounted for possible omitted variables (such as interactions).
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    $\begingroup$ re #3: Yes, but "transformations" of what? Given that heterogeneity is in the residuals (#1), what could transforming the explanatory variables (as suggested in the question) possibly do about that? $\endgroup$ – whuber Aug 1 '12 at 20:57

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