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    $\begingroup$ Hello Dimitri. Thanks for the quick response. So if I understand it correctly unlike the other assumptions of heteroscedasticity and multicollinearity, which affect the accuracy (for lack of a better word) of the OLS estimators, linearity is an assumptions that refers to the relationship between the dependent and the independent variables. We can still use OLS if it is violated but we should not have a straight line model but rather one with splines and the way to test that would be through ANOVA. Is that a correct conclusion? Also instead of ANOVA could we use the R squared? $\endgroup$ Commented Oct 6, 2018 at 21:30