Linear Regression makes impossible predictions I have created a multiple linear regression model to predict prices and about 17% of the predicted prices have come out to be negative.  Is there a way to correct for this error, or does it mean that the independent variables are not good predictors?  The R^2 coefficient is 0.865.
 A: One option would be to fit a generalized linear model with a different reference distribution that is bounded at zero (and probably more appropriate than the normal distribution, depending on what kind of prices you're modeling). For example, the negative binomial distribution suits discrete distributions of counts; this could work if your data are whole numbers representing counts of currency units. The gamma distribution is a continuous alternative (with an otherwise similar shape) that may be more suitable, as it's much more commonly used for financial data (see "Real-life examples of common distributions").
Negative predictions do not reflect badly on the utility of your predictors.
A: It's not the predictors (IVs) that are the problem, but the analysis.
Indeed, the mere existence of an impossible part of the range of the response (you can't have negative prices) would be a hint to consider something other than multiple regression (at least on the untransformed variable) - since it clearly can have negative predictions.
There are a number of ways of dealing with non-negative variables, but two fairly simple approaches might be worth considering:


*

*modelling log-price; this is a common strategy with price-like variables in economics

*using generalized linear models (GLMs). A gamma-model with a log-link would be quite similar to modelling log-price, but the model would be for the expected price rather than expected log-price. This may have some advantages. If you need the relationship with the predictors to be linear in actual price, this can be done (identity link), but a log link for this sort of data would be more common.
As Bill mentions in comments, there's an issue with log-price when you transform back to original units - you no longer have a model for the expectation, but for the median. That said, if you assume normality on the log-scale you can easily compute an ML or MOM estimate of the mean on the original scale.  
(And if you can't assume normality on the log-scale you can still approximate the expectation on the original scale via a Taylor expansion.)
Prediction intervals for a new observation, however, transform just fine.
