12.111 A group of activists in Peaceful, Montana, are seeking increased development for this pristine enclave, which has received some national recognition on the television program Four Dirty Old Men. The group claims that increased commercial and industrial development will bring new prosperity and lower taxes to Peaceful. Specifically, it claims that an increased percentage of commercial and industrial development will decrease the property tax rate and increase the market value for owner-occupied residences.

You have been hired to analyze their claims. For this purpose you have obtained the data file Citydatr, which contains data from 45 small cities. The variables are described in the chapter appendix. From these data you will first develop regression models that predict the average value of owner-occupied housing and the property tax rate. Then you will determine if and how the addition of the percent of commercial property and then the percent of industrial property affects the variability in these regression models. The basic model for predicting market value of houses includes the size of house, the tax rate, the per capita income, and the percent of owner-occupied residences as independent variables. The basic model for predicting tax rate includes the tax assessment base, current city expenditures per capita, and the percent of owner-occupied residences as independent variables.

Determine if the percent of commercial and the percent of industrial variables improve the explained variability in each of the two models. Perform a conditional F test for each of these additional variables.

First, estimate the conditional effect of percent commercial property by itself and then the conditional effect of percent industrial property by itself. Carefully explain the results of your analysis. Include in your report an explanation of why it was important to include all the other variables in the regression model instead of just examining the effect of the direct and simple relationship between percent of commercial property and percent of industrial property on the tax rate and market value of housing.