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I am working with a data set of roughly 1,500 obs. The model I built is a double-log GLM model to estimate price elasticities. During testing, I discovered the residuals and the dependent variable are strongly negatively correlated (0.85). Of note, the residuals are not correlated with the independent variables.

I have scoured econometrics and statistics textbooks and the only thing I can surmise is the model is misspecified in the functional form or there's an omitted variable. Do either of these make sense?

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Correlation of residuals with response is not a surprise as the response is modeled as a regression part plus residuals. Given that the model doesn't fully explain the data, the remaining 'explanation' is hidden in the residuals. However, if the correlation is extreme it may be that your model (covariates) is not capturing the data well. I'd check adequacy of the double-log GLM model.

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    $\begingroup$ If it's very high then you may have low explanatory power of a model, it's all noise $\endgroup$
    – Aksakal
    Commented May 3, 2019 at 19:50

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