This may have a quick response (i.e. don't do it).

Just attended a lecture on multivariable linear regression where the outcome is forced expiratory volume (the amount of air you can push out of your lungs in one go). The explanatory variables are age, height, gender and smoking status. In this example, the lecturer finds that height is skewed and therefore transforms the variable to Height^2.

After performing forward selection he ends up with 5 significant explanatory variables in his model: age, height, gender, smoking status and height^2.

My question is: How can you end up with both height^2 and height in your model. Wouldn't they interact (be highly related)? More broadly, when we transform a variable, should the untransformed variable ever be in the model with the transformed?