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As asked in the title, I would like to know if tests for the assumptions of linear regression models like the Dubin-Watson test are necessary if I can achieve good predictions on my test set.

For example, if I have a data set for house prices, a numeric variable for the area of the house called "area" and a variable with the size of the house with data for 4000 houses and my training set contains 3500 houses and my test set contains 500 houses and the mse is $200, do I really still need to check assumptions of regression models?

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  • $\begingroup$ Assessing assumptions via a statistical test is not a good idea. If your goal is inference, you can evaluate the assumptions graphically by looking at qq plots. If your goal is prediction, model fit not really that important since we care mostly about out of sample performance. $\endgroup$ Apr 15, 2021 at 16:19
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    $\begingroup$ Durbin Watson tests for auto-correlation (and is not the ideal way to do that, there are many better test now). Unless you have time series this is not a major issue usually. It will not bias the results regardless, it will just impact the standard errors. If all you care about are predictive accuracy I don't think it matters. For the most part the regression assumptions are important for test of a null hypothesis for the population from your sample. Are you even doing that? I would just compare how accurate your predictions actually are. $\endgroup$
    – user54285
    Apr 15, 2021 at 16:29

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