12.103 An economist wishes to predict the market value of owner-occupied homes in small midwestern cities. He has collected a set of data from 45 small cities for a 2-year period and wants you to use this as the data source for the analysis. The data are in the file Citydatr the variables are described in the chapter appendix. He wants you to develop a multiple regression prediction equation. The potential predictor variables include the size of the house, tax rate, percent of commercial property, per capita income, and total city government expenditures.

a. Compute the correlation matrix and descriptive statistics for the market value of residences and the potential predictor variables. Note any potential problems of multicollinearity. Define the approximate range for your regression model by the variable means {2 standard deviations.

b. Prepare multiple regression analyses using the predictor variables. Remove any variables that are not conditionally significant. Which variable, size of house or tax rate, has the stronger conditional relationship to the value of houses?

c. A business developer in a midwestern state has stated that local property tax rates in small towns need to be lowered because, if they are not, no one will purchase a house in these towns. Based on your analysis in this problem, evaluate the business developer’s claim.