In a study analyzing the determinants of demand for gasoline in the United States, the results shown below were obtained. The dependent variable is miles traveled per car per year (K) and the explanatory variables are C, number of cars (millions); M, miles per gallon; Pg, retail gasoline price index deflated by consumer price index (1953=100); PT, price of public transport (1967=100); Pop, population (millions); L, labour force; Y, per capita disposable income in 1958 prices. a. Do the coefficients have the expected signs? Explain b. Is there a multicollinearity problem? Use at least four diagnosis procedures to answer this question. If there is multicollinearity, what might be causing it? c. If there is multicollinearity problem discuss two remedial measures to remedy the situation. Regression Results Source Model Residual Total K Pop L Y cons K C M Pg PT C M Pg PT Pop L Y 213184.062 281959.59 SS 495143.652 Correlation Matrix Coef. K df -131.7813 68.54994 191.1472 289.2573 -27.19638 18.77995 3294.096 2526.43 18.11863 35.17724 141.1102 74.43945 47927 5390.611 9070 -2200.973 C 7 30454.8661 15 18797.306 Std. Err. 22 22506.5296 MS M t -0.41 Number of obs F(7, 15) Prob> F R-squared Adj R-squared = Root MSE -1.92 0.074 0.66 0.519 -1.45 0.168 1.30 0.212 0.52 0.614 1.90 0.077 217 0.689 Pg P> |t| PT -277.8921 -425.3902 -67.22491 -2090.862 -56.85988 -17.55373 -13690.79 = Pop = = = [95% Conf. Interval] 23 1.62 0.2045 0.4305 0.1648 137.1 14.32943 807.6846 12.83214 8679.055 93.09715 299.7741 L 9288.842 1.0000 0.0689 1.0000 0.0892 -0.8878 1.0000 -0.2522 -0.8014 0.6937 1.0000 -0.0293 0.9485 -0.8565 -0.6614 1.0000 0.0823 0.9932 -0.8602 -0.7969 0.9645 1.0000 0.1244 0.9929 -0.8664 -0.8099 0.9142 0.9825 1.0000 0.1062 0.9783 -0.8778 -0.8160 0.8709 Y 0.9518 0.9849 1.0000 Variance inflation Factor (VIF) Variable C Pop L Y PT Pg M Mean VIF Variable. M Pg PT Pop L Y Partial correlations Partial and semipartial correlations of C with Variable. C Pg PT VIF Pop 1622.49 0.000616 500.39 0.001998 252.27 0.003964 229.31 0.004361 159.72 0.006261 8.83 0.113226 8.66 0.115513 397.38 Variable: -0.2449 0.3559 -0.3285 0.5664 L -0.0943 Y 0.0635 C Pg PT 1/VIF Partial Semipartial Corr. Corr. -0.2449 -0.2627 0.6293 0.5023 0.4655 0.8739 Partial and semipartial correlations of M with -0.0063 -0.0068 0.0201 0.0144 0.0131 0.0446 Partial Semipartial Corr. Corr. 0.8739 0.1697 -0.5597 Pop -0.5063 L -0.1179 M 0.0635 -0.0858 0.1294 -0.1182 0.2336 -0.0322 0.0216 Partial Semipartial Corr. Corr. Partial Semipartial Corr.^2 Corr.^2 0.0600 0.0690 0.3961 0.1187 0.0114 -0.0446 -0.0388 -0.0078 0.0042 0.2523 0.2167 0.7637 Partial and semipartial correlations of Y with 0.0600 0.1267 0.1079 0.3208 0.0089 0.0040 0.0000 0.0000 0.0004 0.0002 0.0002 0.0020 Partial Semipartial Significance Corr.^2 Corr.^2 0.7637 0.0288 0.3133 2 0.2563 0.0139 0.0040 0.0074 0.0168 0.0140 0.0546 0.0010 0.0005 Significance Value 0.0141 0.0001 0.0020 0.0015 0.0001 0.0000 0.3274 0.2923 0.0051 0.0337 0.0516 0.0000 Partial Semipartial Significance. Corr.^2 Corr.^2 Value 0.3274 0.1472 0.1832 0.0143 0.7098 0.8024 Value 0.0000 0.5009 0.0157 0.0320 0.6412 0.8024 Partial and semipartial correlations of Pg with Variable C M PT Pop L Y Variable C M Pg Pop Partial Semipartial Corr. Corr. -0.2627 0.3559 0.7577 -0.5140 0.5677 0.1697 Partial and semipartial correlations of PT with Variable 0.6293 -0.3285 0.7577 0.3173 L -0.7086 Y -0.5597 C M Partial Corr. -0.0916 0.1282 0.3907 -0.2016 0.2320 0.0579 0.5023 0.5664 PT 0.3173 Pg -0.5140 L 0.3766 Y -0.5063 Semipartial Corr. 0.0641 -0.0275 0.0919 0.0265 -0.0795 -0.0534 Partial Semipartial Corr. Corr. Partial Semipartial Significance Corr.^2 Corr.^2 0.0690 0.1267 0.5742 0.2642 0.3223 0.0288 Partial and semipartial correlations of Pop with 0.0260 0.0307 0.0150 -0.0268 0.0182 -0.0262 0.3961 0.1079 0.5742 0.1007 0.5021 0.3133 Partial Semipartial Significance Corr.^2 Corr.^2 0.0084 0.0164 0.1527 0.0407 0.0538 0.0034 0.2523 0.3208 0.1007 0.2642 0.1418 0.2563 0.0041 0.0008 0.0084 0.0007 0.0063 0.0029 3 Partial Semipartial Corr.^2 Corr.^2 Value 0.0007 0.0009 0.0002 0.0007 0.0003 0.0007 0.2923 0.1472 0.0003 0.0291 0.0140 0.5009 Value 0.0051 0.1832 0.0003 0.1995 0.0010 0.0157 Significance Value 0.0337 0.0143 0.1995 0.0291 0.1235 0.0320