Last updated 18 October 1995

Statistics 343
Autumn, 1995

Homework 2
Due Tuesday, 24 October 1995

1. Problem 2.1, page 55 from Weisberg. Data sets are ALR056 and ALR057. Omit part 2.1.5.

2. [This problem is adapted from Problem 2.8, pages 62--63 of Weisberg. Answer the questions here rather than the questions in Weisberg.]

High ozone levels represent one measure of air quality. From 1965 through 1977, the number of days each year in the San Francisco Bay area on which the ozone level exceeded federal standards for at least one hour showed a decline of approximately 5% per year. These levels show some large, unexplained fluctuations, however. One possible factor causing these variations might be the weather from the previous year or two years. For example, winter rainfall might influence ozone levels in the following summer. The data in ALR063 are from a study of Sandberg, Basso, and Okin (1978). The variables occur in the following order.

YEAR = Year of ozone measurement
RAIN = Average winter precipitation (cm) for preceding two winters
SF   = Summer quarter maximum hourly average ozone reading (ppm) at San Francisco
SJ   = Summer quarter maximum hourly average ozone reading (ppm) at San Jose,
       a city at the southern end of the Bay.
Use SF as the response variable. Fit the regression of SF on YEAR.
Plot the residuals of the fit in (a) against the residuals from the regression of RAIN on YEAR. This is called an added-variables plot of RAIN and SF, adjusting for YEAR. Does it suggest that RAIN is a useful predictor? Why or why not?
Repeat part (b), except calculate the added variables plot for YEAR and SF, adjusting for RAIN.
Compute two new variables, SUM=SF+SJ and DIFF=SF-SJ. Study the regression models of SUM on YEAR and RAIN, and of DIFF on YEAR and RAIN.
Interpret the results obtained above. That is, what do the data suggest about predictors of summer ozone levels?

3. This problem should be submitted on a separate piece of paper from the other parts. It will be separated (temporarily) from the rest of your homework set.

For purposes of this exercise, suppose that you were the investigator in the preceding problem. Write a paragraph of no more than 100 words describing your results, for publication in the Science section of the Chicago Tribune.