Question 4: What assumptions about the sample and distributions are needed for this analysis and what could we do to check them?
As for simple or unifactorial regression, in multiple or multifactorial regression we must assume that the observations are independent of one another and that the residuals follow an approximately Normal distribution with uniform variance. As for simple regression, we can find a histogram and a Normal plot for the residuals:
We usually plot the residuals against the value predicted by the regression equation:
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