# 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?

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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

I think the general answer is : not that easily. There are ways to interpret the derivative, talk about which way the curve opens, etc. But nothing simple and clear like in the linear model. My hunch is that you shouldn't be modeling this as a quadratic, tho.

I would also chuck out the zeros and call your model 'Balances of accounts which have not been closed'.

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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.