More on predicting the total amount of PCB. Run a regression to predict PCB using the variables PCB52, PCB118, and PCB138. Note that this is similar to the analysis that you did in given Exercise except that PCB180 is not included as an explanatory variable.
(a) Summarize the results.
(b) In this analysis, the regression coefficient for PCB118 is not statistically significant. Give the estimate of the coefficient and the associated P-value.
(c) Find the estimate of the coefficient for PCB118 and the associated P-value for the model analyzed in given Exercise.
(d) Using the results in parts (b) and (c), write a short paragraph explaining how the inclusion of other variables in a multiple regression can have an effect on the estimate of a particular coefficient and the results of the associated significance test.
Exercise
Predicting the total amount of PCB. Use the four congeners, PCB52, PCB118, PCB138, and PCB180, in a multiple regression to predict PCB.
(a) Write the statistical model for this analysis. Include all assumptions.
(b) Run the regression and summarize the results.
(c) Examine the residuals. Do they appear to be approximately Normal? When you plot them versus each of the explanatory variables, are any patterns evident?