# Fitting a curve or raw transformation in a logistic regression

For my project, I am fitting a logistic regression to the some 'dummy' bank data. The head of the dataset looks like this

Obs counterparty_id data_period default age LTV
1   1               200712      1       15  120
2   1               200801      1       15  125
... ...             ...         ...     ... ...
100 10              200712      0       5   50
101 10              200801      0       5   50


And in the process, I have been told to fit a curve to age and LTV in order to find the best transformation, so I fit the curve and I get some results which look like this

Cubic transformation:

Score = beta_0 + beta_1*Age + beta_2*Age^2 + beta_3*Age^3
Score = 0.4    + 0.2*Age    + 0.15*Age^2   + 0.7*Age^3


Score = beta_0 + beta_1*Age + beta_2*Age^2
Score = 0.1    + 0.13*Age    + 0.17*Age


I understand the purpose of the curve fit in the logistic regression and I select the best transformation using Somers' D and R_sq_adj

However, now I am at the stage of preparing my variables for multi-factor-analysis, I unsure whether or not I apply just the cubic transformation to my raw data

Cubic_score = age^3


Or, I save the coefficients and then I apply this exact transformation to my variable

Cubic_score = 0.4    + 0.2*Age    + 0.15*Age^2   + 0.7*Age^3


So, my MFA regression would essentially look like this (I've left out LTV until now just to show the example of the process of selecting the best variables)

Option 1: Applying the transformation to the raw data

default = coefficient + age^3 + log(LTV)


Option 2: Applying the curve fit to the raw data

default = coefficient + (0.4 + 0.2*Age + 0.15*Age^2 + 0.7*Age^3) + (0.1 + 0.7* log(LTV))