Regression analysis is a highly flexible tool that can aid decision-making in many areas. It has been used by La Quinta Motor Inns, a moderately priced hotel chain oriented toward serving the business traveler, to help make site location decisions.

Location is one of the most critical decisions for a lodging firm. All hotel chains search for ideal places and often compete against each other for the same sites. A hotel chain that can select good sites more accurately and quickly than its competition has a distinct competitive advantage.

Kimes and Fitzsimmons (academics hired by La Quinta to model its site location decision process) used regression analysis. They collected data on 57 mature inns belonging to La Quinta during a three-year business cycle. The data included profitability for each inn (defined as operating margin percentage - profit plus depreciation and interest expenses divided by total revenue), as well as several potential explanatory variables that could be used to predict profitability.

These explanatory variables fell into 5 categories: competitive characteristics (such as the number of hotel rooms in the vicinity and average room rates); demand generators (such as hospitals and office buildings within a 4-mile radius that might attract customers to the area); demographic characteristics (such as local population, unemployment rate, and median family income); market awareness (such as years the inn has been open and state population per inn); and physical characteristics (such as accessibility, distance to downtown, and sign visibility).

The analysts then determined which of these potential explanatory variables were most highly correlated (positively or negatively) with profitability and entered these variables into a regression equation for profitability.

The estimated regression equation was:

Predicted Profitability = 39.05 - 5.41 StatePop + 5.81 Price - 3.09 Square Root of MedIncome + 1.75 ColStudents

Where StatePop is the state population (in 1000s) per inn, Price is the room rate for the inn, MedIncome is the median income (in 1000s) of the area, ColStudents is the number of college students (in 1000s) within four miles. (All variables in the equation above were standardized to have a mean of 0 and a standard deviation of 1).

The equation predicts that profitability will increase when the room rate and the number of college students increase and when the state population and median income decrease.

Please create (and explain) a regression equation that contains a minimum of two explanatory variables. Note: I am not concerned with the numbers you use for your explanatory variables (the + and - signs do matter) instead your support and justification for the equation you create. A good practice is to keep it simple, but if you want to get fancy and incorporate an interaction variable, that's fine too (make sure you explain it).