The following table gives data on new passenger cars sold in the United States as a function of several variables.

a. Develop a suitable linear or log€“linear model to estimate a demand function for automobiles in the United States.

b. If you decide to include all the regressors given in the table as explanatory variables, do you expect to face the multicollinearity problem? Why?

c. If you do expect to face the multicollinearity problem, how will you go about resolving the problem? State your assumptions clearly and show all the calculations explicitly.

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Year X2 Хз X4 X5 X6 10,227 10,872 11,350 8,775 8,539 9,994 11,046 11,164 10,559 8,979 8,535 7,980 9,179 10,394 11,039 11,450 4.89 1971 112.0 121.3 776.8 79,367 82,153 85,064 86,794 85,846 88,752 92,017 96,048 98,824 99,303 100,397 99,526 100,834 105,005 107,150 109,597 1972 111.0 125.3 839.6 4.55 1973 111.1 133.1 949.8 7.38 117.5 147.7 8.61 1974 1,038.4 1,142.8 1,252.6 1,379.3 1,551.2 1,729.3 1,918.0 2,127.6 2,261.4 2,428.1 2,670.6 2,841.1 3,022.1 1975 127.6 161.2 6.16 1976 1977 135.7 170.5 5.22 5.50 142.9 181.5 1978 153.8 195.3 7.78 1979 166.0 217.7 10.25 1980 179.3 247.0 11.28 1981 190.2 272.3 13.73 197.6 1982 286.6 11.20 1983 202.6 297.4 8.69 9.65 1984 208.5 307.6 1985 215.2 318.5 7.75 6.31 1986 224.4 323.4