Homework #5 -- Trip Generation Analysis [Due: Wednesday, May 19th]
Problem 1 [20 points]
The data in Table 1 was collected from 10 households (HH31-HH40). Variables
include Household ID Number, HHID), daily trip productions per household (Trips),
HH Income (HHInc, in $1,000s), number of cars in the HH (Cars), persons per HH
(HHSize), and dwelling unit type (DU, 1=Single Family; 2=Multiple Family).
- Hypothesize several alternate model structures [e.g., Trips = f(Inc)] and then
estimate a valid bivariate trip generation model using these 10 data points,
performing the calculations using Excel.
- Hypothesize several alternate multivariate structures [e.g., Trips = f(Inc, Cars)]
and estimate a valid multivariate trip generation model using these 10 data points
(use Excel). Include Excel output.
Table 1. Sample Household Travel and Demographic Data
------------------------------------
HHID Trips Inc Cars HHSize DU
------------------------------------
31 5 50.1 2 2 2
32 6 55.5 2 3 1
33 10 61.2 3 4 1
34 4 45.6 1 2 2
35 8 63.9 2 4 1
36 6 55.5 2 2 2
37 5 49.8 2 3 2
38 8 63.9 2 4 1
39 4 42.9 1 1 2
40 4 45.6 1 2 2
------------------------------------
Problem 2 [10 points]
A base category distribution of households by number of cars per household (1, 2, or 3+)
and type of dwelling unit (1=single family, 2=multiple family) is provided in Table 2.
Each category cell contains the total number of trips and the total number of households,
respectively, but only for the first 40 data points in Table 8. Add the remaining 10
households (HH41-HH50) to this table then build a category trip generation model by
computing trip production rates for each cell (and for row and column totals) of the
matrix. Round to nearest tenth of a trip.
Table 2. Trip Summary (HHs 1-40 only)
+-----+-------------+-----+
| |Dwelling Type| |
|Cars +------+------+ Row |
|/HH | 1=SF | 2=MF | Tot |
+=====+======+======+=====+
| 1 | 12 | 31 | 43 |
| | 2 | 9 | 11 |
+-----+------+------+-----+
| 2 | 69 | 57 | 126 |
| | 10 | 11 | 21 |
+-----+------+------+-----+
| 3+ | 68 | 8 | 76 |
| | 7 | 1 | 8 |
+=====+======+======+=====+
| Col | 149 | 96 | 245 |
| Tot | 19 | 21 | 40 |
+-----+------+------+-----+
Problem 3 [10 points]
Compare your category model with the corresponding regression model (below).
- Evaluate the estimation results statistically.
- Interpret the model coefficients? What do these values imply about trips?
- Compute regression estimates for each cell of the category model. Compare results.
----------------------------------------------------------------------
-------- O R D I N A R Y L E A S T S Q U A R E S ---------
----------------------------------------------------------------------
VARIABLE MEAN S.D. OBS CORREL Cars DU Trips
1. Cars 1.8200 0.7197 50 Cars 1.0000 -0.4425 0.8721
2. DU 1.5800 0.4986 50 DU -0.4425 1.0000 -0.6834
3. Trips 5.6600 2.4042 50 Trips 0.8721 -0.6834 1.0000
MODEL: Cat.Mod.Compar. DEPENDENT VARIABLE => Trips Produced
MULTIPLE R 0.9331 * ANOVA * SUM OF SQR df MEAN SQR F
R-SQUARE 0.8706 MODEL SS 246.58 2 123.29 158.17
ADJ R-SQUARE 0.8651 ERROR SS 36.64 47 0.78
S.E. OF EST. 0.8829 TOTAL SS 283.22 49
VARIABLE NAME B BETA S.E. B T
1. Cars 2.3665 0.7084 0.1954 12.1095
2. DU -1.7840 -0.3700 0.2821 -6.3241
Constant 4.1718
Problem 4 [10 points]
Using the category and the regression production models, forecast the number of
trips per household for the six HH holdout sample (HH54-HH59; see Table 4),
comparing forecast and observed trip rates.
Table 4. Households for Validation Test
+-------------------------------+-------------------------------+
ID Trips Income Cars HHS DU | ID Trips Income Cars HHS DU
+-------------------------------+-------------------------------+
54 10 59.4 3 5 1 | 57 3 37.5 1 1 2
55 8 58.5 3 4 1 | 58 5 41.4 1 2 1
56 5 43.8 2 2 1 | 59 8 51.5 2 4 1
+-------------------------------+-------------------------------+
Problem 5 [10 points]
The 50 households in question were sampled from a study area divided into
3 zones (TAZs). The associate population-level distributions for these 3 zones
are provided in Table 5. Compute the total number of trips produced per
zone using your final category model from Problem 2.
Table 5. Population Distribution of Households
TAZ 1 TAZ 2 TAZ 3
+----+-----+-----+-----+ +----+-----+-----+-----+ +----+-----+-----+-----+
|D.U.| 1 | 2 | Row | |D.U.| 1 | 2 | Row | |D.U.| 1 | 2 | Row |
|Cars| SF |Other| Tot | |Cars| SF |Other| Tot | |Cars| SF |Other| Tot |
+====+=====+=====+=====+ +====+=====+=====+=====+ +====+=====+=====+=====+
| 1 | 0 | 0 | 0 | | 1 | 50 | 50 | 100 | | 1 | 20 | 80 | 100 |
+----+-----+-----+-----+ +----+-----+-----+-----+ +----+-----+-----+-----+
| 2 | 50 | 0 | 50 | | 2 | 100 | 30 | 130 | | 2 | 20 | 70 | 90 |
+----+-----+-----+-----+ +----+-----+-----+-----+ +----+-----+-----+-----+
| 3+ | 50 | 0 | 50 | | 3+ | 50 | 20 | 70 | | 3+ | 10 | 0 | 10 |
+====+=====+=====+=====+ +====+=====+=====+=====+ +====+=====+=====+=====+
| Col| 100 | 0 | 100 | | Col| 200 | 100 | 300 | | Col| 50 | 150 | 200 |
+----+-----+-----+-----+ +----+-----+-----+-----+ +----+-----+-----+-----+
Problem 6 [10 points]
The other side of the trip generation stage is estimating trip attractions.
The following regression-based total trip attraction model was estimated for the
region:
Aj = 1.5 POPj + 2.9 EMPj
Table 6 provides regional demographic information. Compute total
attractions and compare these results with the estimates for total productions
from Problem 5. Since every trip has a production and an attraction, normalize
the attractions so that the total equals total productions.
Table 6. Demographic Data Summary
+-----+------+------+------+
| TAZ | HH | POP | EMP |
+=====+======+======+======+
| 1 | 100 | 300 | 0 | HH = total households
+-----+------+------+------+
| 2 | 300 | 1100 | 400 | POP = total population
+-----+------+------+------+
| 3 | 200 | 600 | 100 | EMP = total employment
+=====+======+======+======+
| Tot | 600 | 2000 | 500 |
+-----+------+------+------+
Problem 7 [10 points Extra Credit]
Concisely analyze each of the following bivariate (Table 7A) and multivariate
(Table 7B) regression total trip production models which were estimated using a
subset of the household travel diary data set (see Table 8 below). Discuss
which models are better and why.
Table 7A. Bivariate Regression Summary (variables defined in Table 8)
-----------------------------------------------------------------
Model A B C D
-----------------------------------------------------------------
INC 0.79
(t) (21.05)
CARS 2.91
(t) (12.35)
HHS 1.79
(t) (10.68)
DU -3.30
(t) (-6.49)
Cnst -7.58 0.36 0.79 10.87
-----------------------------------------------------------------
R 0.95 0.87 0.84 -0.68
R-Sq 0.90 0.76 0.70 0.47
S.E. 0.76 1.19 1.32 1.77
F 443.10 152.52 114.06 43.12
-----------------------------------------------------------------
Table 7B. Multiple Regression Summary
-----------------------------------------------------------------
Model E F G H I J K
-----------------------------------------------------------------
INC 0.65 0.62 0.49 0.50 0.58 0.65
(t) (8.99) (8.61 (7.17) (7.25) (10.49) (11.04)
CARS 0.66 0.27 0.68 0.87 2.08
(t) (2.27) (0.79 (2.17) (3.52) (5.87)
HHS 0.36 0.16 0.39 0.23 0.45
(t) (1.95) 0.97 (2.82) (0.96) (2.95)
DU -0.95 -1.02 -0.79 -1.68
(t) (-4.11) (-4.59) (-3.46) (-5.57)
Cnst -6.40 -6.17 -2.80 -2.66 -3.98 3.90 -6.45
-----------------------------------------------------------------
R 0.95 0.96 0.97 0.97 0.97 0.93 0.96
R-Sq 0.91 0.92 0.94 0.94 0.93 0.87 0.92
S.E. 0.73 0.71 0.61 0.61 0.63 0.88 0.70
F 243.32 173.16 178.90 238.53 219.11 105.58 261.55
-----------------------------------------------------------------
Table 8. Household Travel Survey Data used in Problems 1-7
+-------------------------------+-------------------------------+
| ID Trips Income Cars HHS DU | ID Trips Income Cars HHS DU |
+-------------------------------+-------------------------------+
| 1 4 45.0 2 3 2 | 26 10 59.4 3 5 1 |
| 2 3 40.2 1 2 2 | 27 8 58.5 3 4 1 |
| 3 4 46.5 1 1 2 | 28 5 40.8 1 2 1 |
| 4 5 50.4 2 3 2 | 29 8 54.3 2 4 1 |
| 5 6 57.3 2 2 2 | 30 9 61.5 3 4 1 |
| 6 6 49.8 2 3 1 | 31 5 50.1 2 2 2 |
| 7 7 52.5 1 2 1 | 32 6 55.5 2 3 1 |
| 8 7 55.5 2 3 1 | 33 10 61.2 3 4 1 |
| 9 6 37.2 2 3 1 | 34 4 45.6 1 2 2 |
| 10 3 42.6 1 2 2 | 35 8 63.9 2 4 1 |
| 11 5 46.8 2 2 2 | 36 6 55.5 2 2 2 |
| 12 7 50.4 2 3 1 | 37 5 49.8 2 3 2 |
| 13 6 52.8 2 2 1 | 38 8 63.9 2 4 1 |
| 14 4 43.2 1 1 2 | 39 4 42.9 1 1 2 |
| 15 5 49.2 2 3 2 | 40 4 45.6 1 2 2 |
| 16 5 49.2 2 3 2 | 41 8 60.6 3 4 2 |
| 17 8 60.0 3 5 2 | 42 7 55.5 2 3 1 |
| 18 3 39.0 1 1 2 | 43 5 48.6 2 3 2 |
| 19 6 51.9 2 2 2 | 44 3 40.5 1 2 2 |
| 20 9 63.0 3 4 1 | 45 2 37.5 1 2 2 |
| 21 11 67.8 3 5 1 | 46 3 40.8 1 1 2 |
| 22 5 49.5 2 3 2 | 47 2 37.5 1 2 2 |
| 23 11 67.5 3 5 1 | 48 3 41.4 1 2 2 |
| 24 2 35.4 1 2 2 | 49 2 35.1 1 2 2 |
| 25 7 57.3 2 3 1 | 50 3 40.8 1 2 1 |
+-------------------------------+-------------------------------+
Key:
- HH ID = household number
- Trips = number of daily trip productions per household
- HHInc = mean Household income (in $1000s)
- Cars = number of cars per HH
- HHS = Household size (persons per HH)
- D.U. = Dwelling Unit Type (1=single family; 2=multiple family)
Review Questions: (do not need to be submitted with HW#6)
- In terms of relationships between variables, how is a HBW production category
model with two explanatory variables comparable to a HBW production regression>/I>
model with the same two explanatory variables?
- What is required to complete a future forecast using the regression-based trip
generation model for HBW productions from the previous review question?
What is required to complete a future forecast using the category model trip
generation model for HBW productions?
- Why is the category approach used for most trip production models while
regression is used for attraction models?
Last Updated: 25 Apr 2022
|