Problem 4.2 Consider the following trip attraction models estimated using a stan
ID: 3303297 • Letter: P
Question
Problem 4.2 Consider the following trip attraction models estimated using a standard statistical software (t-values are shown in parentheses) Y 123.2 (5.2) + 0.89 X1 (7.3) Y = 40. l (64) + 0. 14 X2 ( 1.9) + 0.6 1X3 (24) + 0.25X4 (1.8) Y =-1.7 (-0.6) + 2.57XI (9.9)-1.78x4 (-9.3) R" = 0.90 R2 0.925 R-0996 Where Y are work trips attracted to the zone. XI is total employment, X2 is industrial employment, X3 is commercial employment, and X4 is service employment. Choose the most appropriate model, explaining clearly whyExplanation / Answer
1.
Good explanatory power of base year travel behavior should be achieved by the equation, i.e. the explanatory variables must be highly correlated with the dependent variable. Actually, the R2 of all the three equations are more than 0.9 with a good explanatory power (goodness of fit)
2.
The parameters of the trip generation equation should be stable over time, and the explanatory variables should be reliably predicted for the horizon year. In general, employment is certainly a good measure, while the more the employment in a zone, the more the work trips attracted to the zone, and the relationship (coefficients) is expected to remain constant.
3.
The independent variables should not be highly correlated between themselves. As a result, equation 3 should be simply rejected in spite of its highest explanatory power. Because X1 already contains X2 (they are highly correlated to each other). This also explains why t-value associated with the coefficient X4 becomes negative, which is not realistic.
4.
Equation1 use only one explanatory variable with good explanatory power and also being statistically significant (pass t-test), so it is acceptable. But the value of the intercept (constant, i.e. 123.2) is too large compared with the coefficient, i.e. 0.89. Imagine that if some zone only have less than 100 employments, how many work trips will attracted to that zone according to equation 1? Is that realistic?
5.
Equation 2 also has good explanatory power and being statistically significant. It use three independent variables instead of one. This is desirable, since typically some zones in a region are characterized by different categories of employment which may have quite different rates of work trips attraction. Indeed, as shown in equation 2, the coefficients associated with X1 X2 and X3 are quite different. So it is has better explanatory power, . Besides the constant (40.1) is relatively acceptable.
Model 2