HW10_SOLN - (Assume a total of 70 students(See Example 8.6...

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Problem 4 1. A data set including real and perceived waiting time is provided ( data.xls on the class website). You are asked to estimate the coefficients ( ) , 1 0 using Data-analysis software provided by Excel (See the procedure in Appendix on the class website). Answer: Therefore, 967 . 0 106 . 0 0 and WT PWT * 967 . 0 106 . 0 (1) 2. Since people are likely to pick options where their perceived travel time is smaller, then we can use Equation (1) above to serve as the deterministic (non-random) component of a disutility function of a timing plan. If we assume that utility is the negative of the disutility, then Equation (2) below will serve as our utility function with error term ε to capture randomness in our model: ) * ( 1 0 WT V (2) Based on the coefficients you estimated in Question (1), You are asked to apply the Logit Model to estimate how many students will choose plan #1 given following two signal timing plans.
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Unformatted text preview: (Assume a total of 70 students). (See Example 8.6 in the textbook). WT Plan #1 3min Plan #2 2.5min Answer: Utility function (non-random): WT U * 967 . 106 . So, for plan #1 795 . 2 3 * 967 . 106 . 1 U For plan #2 312 . 2 5 . 2 * 967 . 106 . 2 U The probability of Plan #1: 382 . ) 1 # Pr( 312 . 2 795 . 2 795 . 2 2 1 1 e e e e e e Plan U U U The probability of Plan #2: 618 . ) 1 # Pr( 1 ) 2 # Pr( 312 . 2 795 . 2 312 . 2 2 1 2 Plan e e e e e e Plan U U U Predicted number of students that choose Plan #1 is=70*0.382 = 27 Predicted number of students that choose Plan #2 is=70*0.618 = 43...
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