Can the regression model be used to predict the mean ozone concentration for specified values of the X variables?
Install the faraway package in R as described in Example 15.8 of Section 15.6.3. Type library(faraway) and then airquality in separate lines to access the New York ozone data sample. The data sample consists of ambient air ozone concentrations in parts per billion as the response or Y variable, versus solar radiation in Langleys, wind speed in miles per hour, air temperature in degrees Fahrenheit, month of the year, and day of the month, as the predictor or X variables. The data sample contains 153 observations but 42 of those observations are missing one or more of these six variables. For consistency, delete all observations with a missing variable, to end up with 111 observations. (A) Construct a basic scatterplot matrix of the data using the pairs function in R as described in Example 5.13 of Section 5.4.2 (or using the scatterplotMatrix function described in Section 15.4 if preferred), and examine the plot for potential bivariate relationships between ozone and each of the five X variables. (B) Based on the nonconstant variance or spread of the ozone versus solar radiation plot and the curvature in the ozone versus wind and temperature plots, try log-transformation of the ozone data using natural logarithms (although common log can also be used). Replot the scatterplot matrix to assess improvements in linearity and constancy of variance. (C) Compute a multiple linear regression of ln ozone (i.e., natural log of ozone) versus the five X variables, interpret and evaluate the regression results including compliance with regression assumptions and regression diagnostics. Note that HC or HAC standard errors can be used to verify the significance of the coefficients if necessary, as described in Sections 15.5.3 and 15.5.4. Also note that in addition to the graphical diagnostics, quantitative tests such as the Breusch–Pagan, Durbin–Watson, and Breusch–Godfrey tests can also be used. Can the regression model be used to predict the mean ozone concentration for specified values of the X variables?
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