I was going through the assumptions of linear regression and of course one of them was linearity between the dependent and the independent variables - to be precise I should say that the assumption is the conditional mean of $Y_i$ given $X_i$ is linear in the parameters.
I looked in many textbooks and resources online and all of them suggested to check that assumption through a scatter plot of the residuals versus the fitted values. Although I can see that this is a valid and helpful way, I can't help but notice that it can be a bit arbitrary and subjective in some cases.
My question is if there is a statistical test to examine that assumption as well. For example when testing heteroscedasticity we can see the residual plot but we also have Levene's test.
I can see in that in How can I use the value of $R^2$ to test the linearity assumption in multiple regression analysis? ,which is very helpful, it stated the R squared is not that statistic but doesn't mention anything as a viable alternative.
Thanks in advance