# How to do data imputation and normalization when using polynomial regression?

The question is about the practical use of polynomial regression. Let's say there is a dataset with columns A, B, T where T is a dependent variable, A and B are independent variables. A and B contain missing values. I want to fill in the gaps with the mean, then normalize values by the formula:

(x - u) / s,

where u is the mean and s is the standard deviation. Everything is clear when I use linear regression. What about polynomial? A^2, B^2 and AB columns are added for a quadratic polynomial case. How to fill AB, if the values ​​of A and B are missing? By the product of averages? When calculating AB, should I multiply the normalized values ​​or should I normalize the result after?

• You shuld do imputation only with the observed variables, and ten compute the generated variables (interactions ond polynomials) afterwards. Mar 11, 2022 at 16:59

Third, for derived variables like $$A^2$$, $$B^2$$ and $$AB$$, van Buuren says in section 6.4.1:
So your best choice is to do multiple imputation of the missing data on $$A$$ and $$B$$ and then just let standard design-matrix calculations produce the polynomial terms from the $$A$$ and $$B$$ values in each imputed data set.