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There is a simple regression model table I was looking at in a textbook with IQ values grouped into 5 intervals and each group had an N number associated with it. There was also information given about the residuals for each group (mean and variance for the residuals). e.g For the < 75 IQ group, N = 23, Mean of residuals = -0.407 and variance = 71.288

The conclusion from the table was merely stated as "assumptions for regression have been met". I am unable to figure out what method was used to suggest if the homogeneity of variance (homoscedasticity) assumption is reasonable for the model (based on the information in the table). I'd like to know how the book arrived at its conclusion; are there plots of residuals' means/variances that indicate violations clearly? Is it like an ANOVA, where visually, one can make the simplistic estimation that if the ratio of variances exceeds a certain number, the assumption has been violated? Given a table like that, how does one proceed to test the assumptions of a regression model? Thanks!

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3 Answers 3

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Based on your description I would guess that the authors just looked at the variances of the residuals and concluded that they were similar enough. They have given the variances, so you can make up your own mind if you agree with them.

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you can check the plot for residuals against yhat. You can also check the plot residuals against independent variables. Both these plots should be fairly random as opposed to showing a trumpet like pattern. You can also check the Q-Q plot to see the assumption for normality.

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Regression with a categorical independent variable is, indeed, like ANOVA. The same methods for checking homoscedasticity apply, with the same advantages and disadvantages

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