Problem

Wheat Exports. The relationship between exchange rates, prices, and agricultural exports i...

Wheat Exports. The relationship between exchange rates, prices, and agricultural exports is of interest to agricultural economists. One such export of interest is wheat. The file named WHEAT4 on the CD contains data on the following variables:

y, U.S. wheat export shipments (SHIPMENT)
x1, the real index of weighted-average exchange rates of the U.S. dollar (EXCHRATE)
x2, the per-bushel real price of no. 1 red winter wheat (PRICE)

The dependent variable is U.S. wheat export shipments. The explanatory variables are exchange rate and price. The data are observed monthly from January 1974 through March 1985. The regression results are shown in Figure 4.23. Use the output to help answer the following questions:

a. What is the estimated regression equation relating SHIPMENT to EXCHRATE and PRICE?
b. Test the overall fit of the regression. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance. What conclusion can be drawn from the result of the test?
c. After taking account of the effect of PRICE, are SHIPMENT and EXCHRATE related? Conduct a hypothesis test to answer this question and use a 5% level of significance. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?
d. What percentage of the variation in the dependent variable has been explained by the regression?
e. Construct a 95% confidence interval estimate for the population regression coefficient of PRICE.
f. What is the value of the R2 adjusted for degrees of freedom? What, if any, is the advantage of this number over the coefficient of determination? (Source: Data are from D. A. Bessler and R. A. Babubla, “Forecasting Wheat Exports: Do Exchange Rates Really Maller?” Journal of Business and Economic Statistics, 5, 1987, pp. 397–406. Copyright 1987 by the American Statistical Association. Used with permission. All rights reserved.)