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

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.

(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 R^2 values? Why or why not?

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Health.txt

POP VALUE DOCT NURSE VN DEATHS

100 141.83 49 76 221 661

110 246.80 103 250 378 1149

130 238.06 76 140 207 1333

142 265.90 95 150 381 1321

202 397.63 162 324 554 2418

213 464.32 194 282 560 2039

246 409.95 130 211 465 2518

280 556.03 205 383 942 3088

304 711.61 222 461 723 1882

316 820.52 304 469 598 2437

328 709.86 267 525 911 2177

330 829.84 245 639 739 2593

337 465.15 221 343 541 2295

379 839.11 330 714 330 2119

434 792.02 420 865 894 4294

434 883.72 384 601 1158 2836

436 939.71 363 530 1219 4637

447 1141.80 511 180 513 3236

1087 2511.53 1193 1792 1922 7768

2305 6774.16 3450 5357 4125 14590

2637 8318.92 3131 4630 4785 19044