# Question: The following data on air pollution in 41 U S

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?

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