Logit model and utility calculation. a) Calculate the utility of driving for eac
ID: 3259528 • Letter: L
Question
Logit model and utility calculation. a) Calculate the utility of driving for each person; b) calculate the utility of riding the bus; c) calculate the difference as U = Ucar- Ubus; d) calculate the probability of each individual riding in a car using the logit model. P(x) = 1/(1+e-x)
Person Number
Cost to Drive
Cost to park
Time to Drive (minutes)
Bus Fare
Bus Wait (minutes)
Time to Ride (minutes)
1
9
3.00
9
1.5
5
26
2
12
3.75
24
4.5
45
41
3
6
3.25
6
3
44
34
4
11
4.50
5.5
4.5
28
40
5
6
5.00
7.5
3
44
24
6
9
2.25
13.5
4.5
16
47
7
14
4.50
14
1.5
43
32
8
9
5.00
4.5
4.5
60
47
9
10
4.75
15
4.5
46
24
10
8
4.75
14
3
33
24
11
5
2.00
10
4.5
19
19
12
12
4.50
21
4.5
32
49
13
12
3.50
6
1.5
50
37
14
7
5.00
7
1.5
29
22
15
15
3.00
7.5
3
51
36
Time Value of Money: $12.00 per hour
Person Number
Cost to Drive
Cost to park
Time to Drive (minutes)
Bus Fare
Bus Wait (minutes)
Time to Ride (minutes)
1
9
3.00
9
1.5
5
26
2
12
3.75
24
4.5
45
41
3
6
3.25
6
3
44
34
4
11
4.50
5.5
4.5
28
40
5
6
5.00
7.5
3
44
24
6
9
2.25
13.5
4.5
16
47
7
14
4.50
14
1.5
43
32
8
9
5.00
4.5
4.5
60
47
9
10
4.75
15
4.5
46
24
10
8
4.75
14
3
33
24
11
5
2.00
10
4.5
19
19
12
12
4.50
21
4.5
32
49
13
12
3.50
6
1.5
50
37
14
7
5.00
7
1.5
29
22
15
15
3.00
7.5
3
51
36
Time Value of Money: $12.00 per hour
Explanation / Answer
time value of money = 12/hr. = 12/60 = .2/mnt.
(a)
U_car = CD + CP + .2*TD ; CD: cost to drive;CP:cost to park; TD:time to drive
U_car
13.80
20.55
10.45
16.60
12.50
13.95
21.30
14.90
17.75
15.55
9.00
20.70
16.70
13.40
19.50
(b)U_bus = Bf + .2*Bw + .2*Tr ; Bf:Bus fare;Bw:Bus waiting;Tr:time to ride
U_bus
7.7
21.7
18.6
18.1
16.6
17.1
16.5
25.9
18.5
14.4
12.1
20.7
18.9
11.7
20.4
(c)U_diff = u_car - U_bus
U_dif
6.10
-1.15
-8.15
-1.50
-4.10
-3.15
4.80
-11.00
-0.75
1.15
-3.10
0.00
-2.20
1.70
-0.90
(d)Prob of riding a car = exp(U_car)/(exp(Ucar) + exp(U_bus))
[just like logit(p) = b0 + b1*U_car + b2*U_bus ; p=prob of riding car]
so prob. for each individual is given below
prob.
0.997762
0.240489
0.000289
0.182426
0.016302
0.041091
0.991837
0.000017
0.320821
0.759511
0.043107
0.500000
0.099750
0.845535
0.289050
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