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45-734 Probability and Statistics II (4th Mini AY 1997-98 Flex-Mode and Flex-Time)

Assignment #1: Due 19 March 1998

This assignment consists of 3 parts. In the first part you will be analyzing some data concerning economic growth and military mobilization using EVIEWS. The data file is:

Military Mobilization Data

The "Using EVIEWS" handout explains how to use EVIEWS. In the second part you will work problem 3.10 in MS by hand--that is, using a calculator. In the third part you will enter the data for problem 3.10 into EVIEWS and analyze it again.

Be prepared to turn in printouts of the regressions and the graph requested below. Please include graphs and regressions as an appendix to your written answers. Please give concise legible answers and follow the instructions in "Guidelines For Written Assignments For Statistics II".

Part 1

During the 20th century the United States has been involved in five major wars. These wars were: World War I, 1917-1918 (dates are for U.S. involvement only); World War II, 1941-1945; Korea, 1949-1953; Vietnam, 1965-1974; and the Gulf War of 1991. A popular belief about wars is that they stimulate the economy. For example, World War II is credited with pulling the United States out of the Great Depression (1930-1941, the Great Depression was world wide and not just in the United States). The purpose of this problem is to check this popular belief using data for the 1915-1988 period.

Let G be the percentage change in real GNP from year t-1 to year t and let M be the net change in the fraction of the population in the military -- a measure of military mobilization; technically:

                    No. of military       No. of military
                    personnel on      -   personnel on
                    June 30 year t        June 30 year t-1
              Mt  = --------------------------------------
                       Population of U.S. in Year t

The model we wish to test is

Gt = b0 + b1Mt + et

  1. Run this regression and study the graph of the residuals (see the "Using EVIEWS" handout). The residual graph has two parts to it. In the top portion the actual (G ) is graphed with the predicted (G ) and in the lower portion the residuals are graphed. What are the largest residuals associated with and why does the model work so poorly at that time?

  2. Note how closely the actual and predicted values track from 1943 to 1946. What do you suppose happened in 1946 that would explain the tremendous down "spike" in the lines?

  3. Use the sample command (SMPL, see the "Using EVIEWS" handout) and run separate regressions on the time periods 1915-1945 and 1947-1988. Compare the results with the regression for 1915-1988. Why do they differ?

Part 2

Work problem 11.2 in MWS with a calculator and show your work.

Part 3

Enter the data from problem 11.2 in MWS into EVIEWS and use EVIEWS to run the regression (see "Using EVIEWS" handout).