Problem 3 Consider a binary logit model for car and bus, where the following representative utility functions have been estimated with a sample of 750 individuals belonging to a particular sector of an urban area: Ve 3.5-0.25tc 0.42ec-0.1cc -0.25t 0.42e 0.1cb where t is in-vehicle travel time (min), e is access time (min) and c is travel cost (). Assume the following average data is known: mode Variables Car 25 5 140 Bus 40 8 50 If you are informed that the number of individuals choosing each option in the sector and in the complete area are respectively as follows: Option | No. of individuals choosing option i Sample 283 467 Population 17100 68900 ar 1s Find the following a If the model is estimated with information from a sub-area, or with data from a biased sample, it can be shown that if the model has a complete set of mode-specific constants, an unbiased model may be obtained just by correcting the constants according to the following expressions: K-Kale log() Qi where q is the market share of alternative A in the sample and Q is its market share in the population. All constants must be corrected. Apply the corrections to the model and give its final formulation b Calculate the percent variation in the probability of choosing car if the bus fares go up by 25%. c Find out what would happen if, on the contrary, the car costs increase by 100%