The demand for cable. The following table 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, % 

You are to consider the following model:

Y_i = β₁ + β₂X_2t + β₃X_3t + β₄X_4t + β₅X_5t + β₆X_6t + u_t

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 statistically 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 necessary calculations. 

X4, , Housing Xs, Y, Annual X2, GNP Unemployment, Prime Rate Customer Line Sales (MPF) Year Starts Lag, 6 mos. Gains, % 1503.6 5.9 1968 1051.8 3.6 5.8 6.7 5873 4.5 1969 1078.8 1486.7 3.5 7852 1434.8 1970 1075.3 5.0 8.4 4.2 8189 1107.5 1971 2035.6 6.0 6.2 4.2 7497 2360.8 1972 1171.1 5.6 5.4 4.9 8534 5.0 1973 1235.0 2043.9 4.9 5.9 8688 1217.8 1331.9 1974 5.6 9.4 4.1 7270 5020 6035 1975 1202.3 1160.0 8.5 9.4 3.4 1271.0 1976 1535.0 7.7 7.2 4.2 1332.7 1977 1961.8 7.0 6.6 4.5 7425 2009.3 1978 1399.2 6.0 7.6 3.9 9400 1721.9 1979 1431.6 6.0 10.6 4.4 9350 1980 7.2 3.9 3.1 6540 1480.7 1298.0 14.9 1981 1510.3 1100.0 7.6 16.6 7675 1982 1039.0 1492.2 9.2 17.5 0.6 7419 1983 1535.4 1200.0 8.8 16.0 1.5 7923