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I ran a multiple regression with 16 predictors and did assumption testings. I am not sure if my graph shows homoscedasticity, I googled and the information that I have gathered suggests that my data is neither funnel-shaped nor randomly scattered. enter image description here

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    $\begingroup$ Your outcome is almost certainly binomial, meaning linear regression is the wrong model to apply. Notions of homoscedasticity are irrelevant at this point, and I would encourage you to try fitting a logistic regression instead. $\endgroup$ Aug 24, 2021 at 4:04
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    $\begingroup$ You have a binary response. Have you considered that 0's and 1's cannot be approximately conditionally normal? That with a binary response with changing mean you don't have constant variance? That the response function won't be linear? (else it would crash through the barriers at 0 and 1) $\endgroup$
    – Glen_b
    Aug 24, 2021 at 4:04

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When we build a linear regression, we try to estimate the accuracy of a chosen model. For this purpose we use LM, RESET and others tests. Also, there is a famous “residual - fitted values” plot we use for testing the correctness of our model.

In a good model (for the first look), covariance between fitted values (of dependent variable) and studentised (or standardised) residuals must be zero (except one case known for me). So, you could see that you have the wrong functional form of your model, this exactly we could see on your graph. You should try to build another type of regression model and do not look at the other assumptions of Classical linear model in this regression with the wrong functional form.

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  • $\begingroup$ Could you tell us why you think the covariance between the residuals and fitted values in this graph is nonzero? $\endgroup$
    – whuber
    Aug 25, 2021 at 18:12
  • $\begingroup$ more precisely: you could see 4 tails of these 2 lines (lower and upper). Left tail of the lower line has a trend, correlation is about -1, i.e. covariance is not zero (for -2.5 < fitted value < -1.5). This pattern we could see where the fitted values are from ~1 to ~2.3. This means that either incorrect model specification or there is something variable that is missing (we could mathematically describe this). $\endgroup$ Aug 25, 2021 at 19:05
  • $\begingroup$ Thank you. I think you miscalculate the correlation, though, because you do not weight the points appropriately. $\endgroup$
    – whuber
    Aug 25, 2021 at 21:17

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