Does exposure to air pollution result in decreased life expectancy? This question was examined in the article "Does Air Pollution Shorten Lives?" (Statistics and Public Policy, Reading, MA, Addison-Wesley, 1977). Data on
y = total mortality rate (deaths per 10,000)
x1 = mean suspended particle reading (µg/m3)
x2 = smallest sulfate reading ([µg/m3] × 10)
x3 = population density (people/mi2)
x4 = (percent nonwhite) × 10
x5 = (percent over 65) × 10
for the year 1960 was recorded for n = 117 randomly selected standard metropolitan statistical areas. The estimated regression equation was
y = 19.607 + .041x1 + .071x2
+ .001x3 + .041x4 + .687x5
a. For this model, R2 = .827. Using a .05 significance level, perform a model utility test.
b. The estimated standard deviation of β^1 was .016. Calculate and interpret a 90% CI for β1.
c. Given that the estimated standard deviation of β^4 is .007, determine whether percent nonwhite is an important variable in the model. Use a .01 significance level.
d. In 1960, the values of x1, x2, x3, x4, and x5 for Pittsburgh were 166, 60, 788, 68, and 95, respectively. Use the given regression equation to predict Pittsburgh's mortality rate. How does your prediction compare with the actual 1960 value of 103 deaths per 10,000?