Efficient test for nonlinearity [closed]

Fitting and testing the assumptions of a linear regression model (in my case 80 observations on 9 variables) I´ve come across diagnostics to assess linearity/non-linearity of my model. While testing for outliers, heteroscedasticity, normality of residuals etc. I always found there to be graphical solutions as well as some parametric tests like shapiro-wilk test for normality etc. However I can´t find such tests for the assumption of linearity and the problem with graphical solutions is always the interpretation and subjectiveness of if. Is there a more formal way to test for nonlinear relations between dependent and independent variables? Ideally also giving an indication on the form of the non-linearity that you know about and that can be implemented in R without much work? I´d appreaciate any hints.