20. The demand for a commodity typically depends on the income of the consumer, the real price of the commodity, and the real price of complementary or competing products. Table P-20 gives the per capita consumption of chicken in the United States (in pounds); the per capita disposable income (in dollars); and the retail prices for chicken, pork, and beef (in cents per pound) for several years.

a. Compute the correlation matrix for all the variables, using both the original units and the log-transformed units. Comment on the implied strength of the linear association between chicken consumed and each of the remaining variables. Can you think of a reason why one must be careful interpreting the magnitudes of correlation coefficients constructed from time series data?

b. Using the original data, run a stepwise regression program with chicken consumption as the dependent variable and the remaining variables as predictor variables. Set alpha to .

TABLE P-20 Year Per Capita Chicken Consumption (lbs.) Disposable Income ($) Chicken Price (c/lb.) Pork Price (c/lb.) Beef Price (c/lb.) 1 28.0 397.5 42.2 50.7 78.3 2 29.9 413.3 38.1 52.0 79.2 3 30.1 439.2 40.3 54.0 79.2 4 30.9 459.7 39.5 55.3 79.2 5 31.4 492.9 37.3 54.7 77.4 6 33.7 528.6 38.1 63.7 80.2 7 35.6 560.3 39.3 69.8 80.4 8 35.6 624.6 37.8 65.9 83.9 9 37.1 666.4 38.4 64.5 85.5 10 38.5 717.8 40.1 70.0 93.7 11 40.3 768.2 38.6 73.2 106.1 12 40.2 843.3 39.8 67.8 104.8 13 41.7 911.6 39.7 79.1 114.0 14 39.9 931.1 52.1 95.4 124.1 15 39.7 1,021.5 48.9 94.2 127.6 16 39.0 1,165.9 58.3 123.5 142.9 17 39.1 1,349.6 57.9 129.9 143.6 18 42.8 1,449.4 56.5 117.6 139.2 19 44.9 1,575.5 63.7 130.9 165.5 20 48.3 1,759.1 61.6 129.8 203.3 21 49.0 1,994.2 58.9 128.0 219.6 22 49.4 2,258.1 66.4 141.0 221.6 23 49.6 2,478.7 70.4 168.2 232.6

c. Run a full regression of chicken consumption on the remaining variables. Be sure to delete variables one at a time that you deem to be not significant until you are satisfied with your final model. Is your result consistent with the result of the stepwise procedure in part b? Is serial correlation likely to be a problem in this regression analysis?