Modern housing areas often seek to obtain, or at least convey, low rates of crimes. Homeowners and families like to live in safe areas and presumably are willing to pay a premium for the opportunity to have a safe home.
These data from Philadelphia Magazine summarize crime rates and housing prices in communities near and including Philadelphia. The housing prices for each community are the median selling prices for homes sold in the prior year. The crime rate variable measures the number of reported crimes per 100,000 people living in the community.
Exclude the data for Center City, Philadelphia from this analysis. It’s a predominantly commercial area that includes clusters of residential housing. The amount of commercial activity produces a very large crime rate relative to the number of residents.
Motivation
(a) How could local political and business leaders use an equation that relates crime rates to housing values to advocate higher expenditures for police?
(b) Would an equation from these data produce a causal statement relating crime rates to housing prices? Explain.
Method
(c) For modeling the association between crime rates and housing prices, explain why a community leader should consider crime rates the explanatory variable.
(d) Do you anticipate differences in the level of crime to be linearly related to differences in the housing prices? Explain in the context of your answer the underlying implication of a linear relationship.
Mechanics
(e) Create a scatterplot for the housing prices on crime rates. Describe the association. Is it strong? What is the direction?
(f) Fit the linear equation of housing prices on crime rates. Interpret the slope, intercept, and summary statistics (r2 and se).
(g) As an alternative to the linear model, ft an equation that uses housing prices as the response with the reciprocal 11 / x2 of the crime rate as the explanatory variable. What is the natural interpretation of the reciprocal of the crime rate?
Message
(h) Which model do you think offers the better summary of the association between crime rates and housing prices? Use residual plots, summary statistics, and substantive interpretation to make your case.
(i) Interpret the equation that you think best summarizes the relationship between crime rates and housing prices.
(j) Does an increment in the crime rate from 1 to 2 per 100,000 have the same impact (on average) on housing prices as the change from 11 to 12 per 100,000?