I have a variable that can range from -100 to +100. When the number is -100, the output from this transformation should be something like 10. For +100 it should be around -10, and for 0 it should be 0. However, the points in between may be skewed so that the value for 1 is not necessarily .1, it may be 2 or .05.
What formula or transform should I use when putting this variable into a linear model for R? I feel like there's a sqrt or log involved but negative values are no good. There are many options, what's the best?
I'm looking for something like: $$y = B_1(x_1) + B_2(x_2) + B_3(transform(x_3))\\$$
I'd like the B3 to be able to tell me the skewness of the variable.