8.25. The demand for cable. Table 8.10 gives data used by a telephone cable manufacturer to predict sales to a major customer for the period 1968–1983.†
The variables in the table are defined as follows:
Y = annual sales in MPF, million paired feet X2 = gross national product (GNP), $, billions X3 = housing starts, thousands of units
X4 = unemployment rate, %
X5 = prime rate lagged 6 months
X6 = Customer line gains, %
TABLE 8.10 REGRESSION VARIABLES
| Year | X2, GNP | X3, housing starts | X4, unemployment, % | X5, prime rate lag, 6 mos. | X6, customer line gains, % | Y, total plastic purchases (MPF) |
| 1968 | 1051.8 | 1503.6 | 3.6 | 5.8 | 5.9 | 5873 |
| 1969 | 1078.8 | 1486.7 | 3.5 | 6.7 | 4.5 | 7852 |
| 1970 | 1075.3 | 1434.8 | 5.0 | 8.4 | 4.2 | 8189 |
| 1971 | 1107.5 | 2035.6 | 6.0 | 6.2 | 4.2 | 7497 |
| 1972 | 1171.1 | 2360.8 | 5.6 | 5.4 | 4.9 | 8534 |
| 1973 | 1235.0 | 2043.9 | 4.9 | 5.9 | 5.0 | 8688 |
| 1974 | 1217.8 | 1331.9 | 5.6 | 9.4 | 4.1 | 7270 |
| 1975 | 1202.3 | 1160.0 | 8.5 | 9.4 | 3.4 | 5020 |
| 1976 | 1271.0 | 1535.0 | 7.7 | 7.2 | 4.2 | 6035 |
| 1977 | 1332.7 | 1961.8 | 7.0 | 6.6 | 4.5 | 7425 |
| 1978 | 1399.2 | 2009.3 | 6.0 | 7.6 | 3.9 | 9400 |
| 1979 | 1431.6 | 1721.9 | 6.0 | 10.6 | 4.4 | 9350 |
| 1980 | 1480.7 | 1298.0 | 7.2 | 14.9 | 3.9 | 6540 |
| 1981 | 1510.3 | 1100.0 | 7.6 | 16.6 | 3.1 | 7675 |
| 1982 | 1492.2 | 1039.0 | 9.2 | 17.5 | 0.6 | 7419 |
| 1983 | 1535.4 | 1200.0 | 8.8 | 16.0 | 1.5 | 7923 |
You are to consider the following model:
Yi = β1 + β2 X2t + β3 X3t + β4 X4t + β5 X5t + β6 X6t + ut
a. Estimate the preceding regression.
b. What are the expected signs of the coefficients of this model?
c. Are the empirical results in accordance with prior expectations?
d. Are the estimated partial regression coefficients individually statisti- cally significant at the 5 percent level of significance?
e. Suppose you first regress Y on X2, X3, and X4 only and then decide to add the variables X5 and X6. How would you find out if it is worth adding the variables X5 and X6? Which test do you use? Show the nec- essary calculations.