One assumption of OLS regression is Linearity. To check whether the assumption holds, you can plot component + residual plots or partial residual plots. When a linear relationship is apparent, is's fine, if not you have to transform your data.
But what can you do when data transformation fails?
Here is an example of a component + residual plot before transformation:
The dotted line is a linear fit line and the other curve is a lowess curve (just a curve that smoothens the scatter plot). Clearly, the lowess curve is not linear.
I already tried to use a 2nd and 3rd degree polynomial to transform the x-axis, but it did not work. The resulting lowess curve looked similar. Transforming the dependent variable is not sensible in my case because it would affect relationships of other variables in the multiple linear regression.
What to do next?