TABLE 22 Refer to table 22 which gives data on Gas, HDI, and PIX for Iraq. Consi
ID: 1187881 • Letter: T
Question
TABLE 22
Refer to table 22 which gives data on Gas, HDI, and PIX for Iraq. Consider the following log-log model:
lnImports = B1 + B2 lnGDP + B3 lnCPI + u
***********************please use "SAS format" ************************* (where/if possible)
1) Estimate the parameters using the data given in the table 22.
2) Do you suspect that there is multicollinearity in the data? Why or why not?
3) Regress:
(a) ln GAS = A1 + A2 ln(HDI)
(b) ln GAS = B1 + B2 ln(PIX)
(c) ln HDI = C1+ C2 ln(PIX)
On the basis of these regressions, what could you say about the nature of multicollinearity in the data?
4) Suppose there is multicollinearity in the data but B2 and B3 are individually significant at the 5% level and the overall F test is also significant. In this case should we worry about the collinearity problem?
Year PIX HDI Gas 1 53.8 1,638.3 98185 2 56.9 1,825.3 124228 3 60.6 2,030.9 151907 4 65.2 2,294.7 176002 5 72.6 2,563.3 212007 6 82.4 2,789.5 249750 7 90.9 3,128.4 265067 8 96.5 3,255.0 247642 9 99.6 3,536.7 268901 10 103.9 3,933.2 332418 11 107.6 4,220.3 338088 12 109.6 4,462.8 368425 13 113.6 4,739.5 409765 14 118.3 5,103.8 447189 15 124.0 5,484.4 477665 16 130.7 5,803.1 498438 17 136.2 5,995.9 491020 18 140.3 6,337.7 536528 19 144.5 6,657.4 589394 20 148.2 7,072.2 668690 21 152.4 7,397.7 749374 22 156.9 7,816.9 803113 23 160.5 8,304.3 876470 24 163.0 8,747.0 917103 25 166.6 9,268.4 1029980 26 172.2 9,817.0 1224408 27 177.1 10,128.0 1145900 28 179.9 10,469.6 1164720 29 184.0 10,960.8 1260717 30 188.9 11,712.5 1472926 31 195.3 12,455.8 1677371
Explanation / Answer
Multicollinearity in regression is a condition that occurs when some predictor variables in the model are correlated with other predictor variables. If multicollinearity exists, the predicted values and residuals are still computed with great accuracy. However, the standard deviation of each coefficient will be large, and the estimated coefficients may be unstable. Therefore: Coefficients may appear to be nonsignificant even when a significant relationship exists between the predictor and the response. Coefficients for highly correlated predictors will vary widely from sample to sample. Removing any highly correlated terms from the model will greatly affect the estimated coefficients of the other highly correlated terms. Coefficients of the highly correlated terms may even have the wrong sign. If the correlation is moderately high, Minitab warns you in a message and continues with computations. If the correlation of a predictor with other predictors is very high, Minitab eliminates that predictor from the equation and displays a message. For details on how Minitab determines if predictors are very highly correlated with other predictors and should be removed from the regression equation, see Knowledgebase ID 469 by clicking the link below. To quantify multicollinearity you could look at the VIFs (variance inflation factors) and the ratio of the largest and smallest eigenvalues calculated from the predictor matrix. Note: Multicollinearity does not effect the goodness of fit and the goodness of prediction.
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