Data were collected to discern environmental factors affecting health standards. For 21 small regions we have data on the following variables: 

The data are given in Table 8.27. 

(a) Perform a regression relating DEATHS to the other variables, excluding POP. Compute the variance inflation factors; interpret all results.

(b) Obviously multicollinearity is a problem for these data. What is the cause of this phenomenon? It has been suggested that all variables should be converted to a per capita basis. Why should this solve the multicollinearity problem?

(c) Perform the regression using per capita variables. Compare results with those of part (a). Is it useful to compare R² values? Why or why not?

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POP: population (in thousands), VALUE: value of all residential housing, in millions of dollars; this is the proxy for economic conditions, DOCT: the number of doctors, NURSE: the number of nurses, VN: the number of vocational nurses, and DEATHS: number of deaths due to health-related causes (i.e., not accidents); this is the proxy for health standards.