# Interpretation of coefficients in polynomial regression for predictive modeling

I am building a predictive model (binary target variable) in the financial services industry. One of the (many) potential predictors I am adding to the model is related to the customers checking account balance trend (longitudinal balance).

I'd like to capture if the balance is increasing or decreasing and how much. I have access to end of month balances going back a ways. One of the things I was considering is to, for each customer - fit a polynomial regression and include the coefficients into my predictive model.

In R, an example of a single customer:

balances <- c(657709,620729,713637,619224,558238,572402,536548,0,0,0)
time <- seq(1:10)
mod <- lm(balances~time+I(time*time))
mod$coefficients[2:3] mod$coefficients[2:3]
time          I(time * time)
61239.99      -13317.43


Questions:

1. Thoughts? Of course the fit can be very poor, but as a global process to include into a predictive model does it have merit? Is there a better way?

2. It seems I have seen description of these coefficients in terms of velocity and acceleration, but I cant find it anywhere. Is this a true interpretation of them?

• Your customer seems to have closed her account by time 8. – Henry Sep 20 '11 at 0:14
• Yes, and that can happen. I would include the current month balance, min, max, avg balance etc as other predictors. – B_Miner Sep 20 '11 at 0:40

Explanation at UCLA

Like other polynomial models, your model is likely to be worse an a linear model if you extrapolate outside the time for which you have data as the time * time term is likely to dominate and the sign of its coefficient will determine whether you predict a large positive or large negative balances, when for many people balances are rather more stable.