1- Airlines regularly try to predict accurately the revenue passenger-miles (RPM) for future periods; this gives the airline a picture of what equipment needs might be and is helpful in keeping costs at a minimum.

The revenue passenger-miles for international flights on major international airlines is shown in the sheet "Problem 1" in accompanying Excel file for the period Jan-1979 to Feb-1984. Also shown is personal income during the same period, in billions of dollars.

a. Build a multiple-regression model for the data to predict RPM for the next month.

b. Use the same data to compute a time-series decomposition model.

c. Judging from the root-mean-squared error, which of the models in parts (a) and (b) proved to be the best forecasting model? Now combine the two models, using a weighting scheme. Choose various weights until you believe you have come close to the optimum weighting scheme. Does this combined model perform better (according to RMSE) than either of the two original models?

2- Estimating the volume of loans that will be made at a credit union is crucial to effective cash management in those institutions. In the sheet "Problem 2" are quarterly data for a real credit union located in a midwestern city. Credit unions are financial institution similar to banks, but credit unions are not-for-profit firms whose members are the actual owners (remember their slogan, "It's where you belong"). The members may be both depositors in and borrowers from the credit union.

a. Estimate a multiple regression model to estimate loan demand and calculate its root-mean-squared error.

b. Estimate a time-series decomposition model to estimate loan demand with the same data and calculate its root-mean-squared error.

c. Combine the models in parts (a) and (b) and determine whether the combined model performs better than either or both of the original models.

3- a. Calculate the first 5 autocorrelations for the data in the sheet "Problem 3"; consider the series to be a quarterly time series. How many of the autocorrelations fall outside the 95 percent confidence interval (positive or negative)?

b. Calculate and display the first 5 partial auto correlations for the 100 time-series observations. How many of the partial autocorrelation coefficients fall outside the 95 percent confidence interval?

c. Estimate the appropriate model as determined from your inspections carried out in parts a and b. Calculate the RMSE for the model.