This case has illustrated the basics of multiple regression with two continuous predictors. The multiple regression equation that predicts total costs from length of stay and birthweight showed both independent variables to be significant. However, the addition of birthweight showed only very slight improvement in the goodness-of-fit measures. With a RMSE of $1596, the regression model seems insufficiently precise to be useful in practice. Residual analysis suggests that there are other factors that should be included in the regression model.

Regression coefficients should always be assessed for reasonableness in both direction and magnitude. The coefficient for length of stay seems reasonable in the multiple regression, just as it was in the simple regression. The coefficient for birthweight is $179. At first it seems counterintuitive that a larger weight newborn should incur additional costs. Bear in mind, that CVPH is a Level 1 perinatal center and does not have a neonatal intensive care unit and only handles normal and low-risk births. According to Medline, larger birthweight babies are at risk for injury during delivery and problems with blood sugar.

As a next step, incorporating procedures performed and birth complications into a regression model is indicated. All Patient Refined Diagnosis Related Groups (APR-DRGs), APR severity, and APR risk of mortality data elements could be used which classify patients based on their reason for admission, severity of illness, and risk of morality. Using APR-DRGs to perform analysis relies on complete and accurate encoding by health care providers.

Finally, the data used in this analysis was limited in the detail provided so that individuals could not be identified. The full SPARCS data set has additional information that may improve the model. The length of stay of a newborn is often related to the length of stay of the mother. However, this data set does not allow us to link the records of the newborn and mother.

Multiple linear regression is one of a number of possible methods to obtain predictive models. Model building is often an iterative process requiring the analyst to experiment with different combinations of predictor variables. When selecting among several potential predictive models, all things being equal, it is advisable to select the simplest model (i.e., the one with the fewest predictors). This is referred to as the principle of parsimony. The simplest model should be chosen that meets the required precision for its application.

A good understanding of the problem domain can assist the analyst when searching for good predictors and critically evaluating candidate models. Additional insights can be obtained by consulting the literature or subject matter experts.