# Question

The following data on air pollution in 41 U. S. cities are from Biometry (Sokal and Rohlf, 1981). The type of air pollution under study is the annual mean concentration of sulfur dioxide. The values of six explanatory variables were recorded in order to examine the variation in the sulfur dioxide concentrations. They are as follows:

y = annual mean concentration of sulfur dioxide ( micrograms per cubic meter)

x1 = average annual temperature (° F)

x2 = number of manufacturing enterprises employing 20 or more workers

x3 = population size ( 1970) census ( thousands)

x4 = average annual wind speed ( mph)

x5 = average annual precipitation ( inches)

x6 = average number of days with precipitation per year

A model relating y to the six explanatory variables is of interest in order to determine which of the six explanatory variables are related to sulfur dioxide pollution and to be able to predict air pollution for given values of the explanatory variables.

a. Plot y versus each of the explanatory variables. From your plots, determine if higher- order terms are needed in any of the explanatory variables.

b. Is there any evidence of collinearity in the data?

c. Obtain VIF for each of the explanatory variables from fitting a first- order model relating y to x1 through x6. Do there appear to be any collinearity problems based on the VIF values?

y = annual mean concentration of sulfur dioxide ( micrograms per cubic meter)

x1 = average annual temperature (° F)

x2 = number of manufacturing enterprises employing 20 or more workers

x3 = population size ( 1970) census ( thousands)

x4 = average annual wind speed ( mph)

x5 = average annual precipitation ( inches)

x6 = average number of days with precipitation per year

A model relating y to the six explanatory variables is of interest in order to determine which of the six explanatory variables are related to sulfur dioxide pollution and to be able to predict air pollution for given values of the explanatory variables.

a. Plot y versus each of the explanatory variables. From your plots, determine if higher- order terms are needed in any of the explanatory variables.

b. Is there any evidence of collinearity in the data?

c. Obtain VIF for each of the explanatory variables from fitting a first- order model relating y to x1 through x6. Do there appear to be any collinearity problems based on the VIF values?

## Answer to relevant Questions

Refer to Exercise 13.76. a. Use a variable selection program to obtain the best four models of all possible sizes using R2adj as your criterion. Obtain values for R2, MSE, and Cp for each of the models. b. Using the ...In Chapter 3, a data set was presented that related math and reading scores to % minority and % poverty in 22 third-, fourth-, and fifth- grade classes. a. Fit a model that relates math scores to reading scores, % minority, ...Refer to the study described in Exercise 14.11. a. Perform appropriate F tests and draw conclusions from these tests concerning the effects of the percentages of sweetener, air, and milk fat on the sensory ratings. Use α = ...Refer to Exercise 14.1. The researchers decide to use the following model, which relates the response variable y to the four instructional conditions. y = μ + τi + ɛij for i = 1, 2, 3, 4 and j = 1, 2, 3, 4, 5 a. Write an ...Refer to Exercise 14.27. a. Construct an AOV table for the experiment. b. Are the differences in mean temperatures for the nine medications the same for all three severities of the blood pressure disorders? Use α = .05. c. ...Post your question

0