Data values in the following study are taken from Statistical Abstract of the United States, U.S. Department of Commerce, 103rd and 109th Editions (see Table 9-16). All data values represent annual averages as determined by the U.S. Department of Commerce.

1. Construct a regression model with Response variable: x₃ (foreign investments) Explanatory variables: x₅ (GNP), x₆ (U.S. dollar), and x₇ (consumer credit)

TABLE 9-16 Economic Data, 1976–1987 (on the data disk)
Year	x1	x2	x3	x4	x5	x6	x7
1976	10.9	7.61	31	974.9	1718	1.757	234.4
1977	12.0	7.42	35	894.6	1918	1.649	263.8
1978	12.5	8.41	42	820.2	2164	1.532	308.3
1979	17.7	9.44	54	844.4	2418	1.380	347.5
1980	28.1	11.46	83	891.4	2732	1.215	349.4
1981	35.6	13.91	109	932.9	3053	1.098	366.6
1982	31.8	13.00	125	884.4	3166	1.035	381.1
1983	29.0	11.11	137	1190.3	3406	1.000	430.4
1984	28.6	12.44	165	1178.5	3772	0.961	511.8
1985	26.8	10.62	185	1328.2	4015	0.928	592.4
1986	14.6	7.68	209	1792.8	4240	0.913	646.1
1987	17.9	8.38	244	2276.0	4527	0.880	685.5

We will use the following notation:

x₁  = price of a barrel of crude oil, in dollars per barrel

x₂  = percent interest on 10-year U.S. Treasury notes

x₃  = total foreign investments in U.S., in billions of dollars

x₄  = Dow Jones Industrial Average (DJIA)

x₅  = Gross National Product, GNP, in billions of dollars

x₆  = purchasing power of U.S. dollar with base 1983 corresponding to $1.000

x₇  =consumer credit (i.e., consumer debt), in billions of dollars

What is the coefficient of multiple determination?

(a) Use a 1% level of significance and test each coefficient for significance (two-tailed test).

(b) Examine the coefficients of the regression equation. Then explain why you think the following statement is true or false: “If the purchasing power of the U.S. dollar did not change and the GNP did not change, then an increase in consumer credit would likely be accompanied by a reduction in foreign investments.”

(c) Suppose x₅= 3500, x₆= 0.975, and x₇= 450.Predict the level of foreign investment. Find a 90%confidence interval for your prediction.

2. Construct a new regression model with Response variable: x₄ (DJIA) Explanatory variables: x₃ (foreign investments), x₅

(GNP), and x₇ (consumer credit) What is the coefficient of multiple determination?

(a) Use a 5% level of significance and test each coefficient for significance (two-tailed test).

(b) Examine the coefficients of the regression equation; then explain why you think the following statement is true or false: “If the GNP and consumer credit didn’t change but foreign investments increased, the DJIA would likely show a

strong increase.”

(c) Suppose x₃= 210, x₅= 4260, and x₇= 650.Predict the DJIA and find an 85% confidenceinterval for your prediction.

Construct a new regression model with Response variable: x₇ (consumer credit) Explanatory variables: x₃ (foreign investments), x₅ (GNP), and x₆ (U.S. dollar) What is the coefficient of multiple determination?

(a) Use a 1% level of significance and test each coefficient for significance (two-tailed test).

(b) Examine the coefficients of the regression equation; then explain why you think each of the following statements is true or false: “If both GNP and purchasing power of the U.S. dollar didn’t change, then an increase in foreign investments would likely be accompanied by a reduction in consumer credit.” “If both foreign investments and purchasing power of the U.S. dollar remained fixed, then an increase in GNP would likely be accompanied by an increase in consumer credit.”

(c) Suppose x₃= 88, x₅= 2750, and x₆= 1.250.Predict consumer credit and find an 80% confidenceinterval for your prediction.