These data describe 506 census tracts in the Boston area. These data were assembled in the 1970s and used to build a famous model in economics, known as a hedonic pricing model.13 The column Median Value is the median value of owner-occupied homes in the tract (in thousands of dollars back in the 1970s, so the amounts will seem quite small), and the column Crime Rate gives the number of crimes per 100,000 population in that tract.
(a) Make a scatterplot of the median value on the crime rate. Do any features of this plot strike you as peculiar?
(b) Find the correlation using all of the data as shown in the prior scatterplot.
(c) Tracts in 1970 with median home values larger than $50,000 were truncated so that the largest value reported for this column was 50. The column Larger Value replaces the value 50 for these tracts with a randomly chosen value above 50. Use this variable for the response, make the scatterplot, and find the correlation with Crime Rate. Does the correlation change?
(d) What can we conclude about the effects of crime on housing values in Boston in the 1970s?