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With Univariate regression it's very easy to see if the correlation is linear or otherwise, but in a multiple regression things can look very complicated, polynomial or other correlations can be hidden by the interaction of of the variables. I understand that you can use power terms in the variables but the relationship to the dependent variable should still be linear. How do I know if multiple regression is appropriate?

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    $\begingroup$ Most common way to check linearity is to scatter-plot residuals (studentized preferably) against the linearly predicted values. Curved or non-horizontally spead cloud on such a plot is diagnostic for non-linearity. To uncover more hidden (partial) non-linearity plot the residuals against each of the predictors. $\endgroup$ – ttnphns Sep 14 '13 at 7:43
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Indeed the most common and easy way would be to use scatter plot of residual versus predicted value; a horizontal band of points indicates a linear relationship.

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