Use the “CO2Concentration” dataset, which contains the average carbon dioxide concentration (labeled CO2) for 161 months. The two columns labeled CO2lag1 and CO2lag2 contain lag 1 carbon dioxide concentration and lag 2 carbon dioxide concentration. Lag 1 corresponds to values from the previous month and lag 2 corresponds to values from two months ago. (a) Determine partial autocorrelations for the carbon dioxide concentration series. What do the results indicate about an auto-regression model for a time series that describes carbon dioxide concentration? That is, what are the “large” partial autocorrelations? (b) Do a multiple regression with CO2 as the y-variable and CO2lag1 and CO2lag2 values as x-variables. Store the residuals. i. Write the estimated regression equation. ii. Use the regression equation to find the fitted value for the carbon dioxide concentration for the 162nd month. [For this question you don’t need to use the method at the bottom of Section 14.3.] (c) Plot the residuals versus order for the regression that you did in part (b). What is indicated about the validity of the independent errors assumption for the regression model? (d) Obtain a PACF plot of the residuals for the regression that you did in part (b). What is indicated about the validity of independent errors assumption for the regression model? (e) Are the conclusions in parts (c) and (d) in agreement? Suggest any remedial measures to remove the correlated nature of errors.

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