CEE 123 Transport Systems 3: Planning & Forecasting
Spring 2026: Michael G. Mc Nally (mmcnally-at-uci-dot-edu) [15450]
Homework #5 -- Trip Generation Modeling [Due: Friday 15 May 2026]

Problem 1 [20 points]

The data in Table 1 was collected from 10 households (HH). Variables include Household Identification Number, HHID), daily trips per household (Trips), HH Income (HHInc, in $1,000s), number of cars in the HH (Cars), number of persons in the HH (HHSize), and dwelling unit type (DU, 1=Single Family; 2=Multiple Family). These 10 observations are the first set of 10 households in Table 7 [ xls ].

  1. Hypothesize several alternate model structures (via causal arrow diagrams: X -> Y) and then find a valid bivariate trip generation model performing the calculations by hand.
  2. Hypothesize several alternate model structures (via causal arrow diagrams: X1, X2 -> Y) and then find a valid multivariate trip generation model (use any available software -- Excel, TransCAD, or a statistical package -- but please identify the software and include appropriate model output.

Table 1. Sample Household Travel and Demographic Data

       ------------------------------------
       HHID Trips HHInc  Cars  HHSize  DU
       ------------------------------------
          1    4   45.0     2     3     2
          2    3   40.2     1     2     2
          3    4   46.5     1     1     2
          4    5   50.4     2     3     2
          5    6   57.3     2     2     2
          6    6   49.8     2     3     1
          7    7   52.5     1     2     1
          8    7   55.5     2     3     1
          9    6   55.8     2     3     1
         10    3   42.6     1     2     2
       ------------------------------------

Problem 2 [20 points]

Table 2 provides a category distribution of 40 households by number of persons per household (categorized as 1-2 or 3 plus) and HH income (categorized as 45k and under, 45.1 to 60k, or >60k). Each cell contains the total number of trips and the total number of households for the first 40 of 50 data points in Table 7.

  1. Add the remaining 10 households to this table
  2. 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)

 
       +------+-------------+-----+
       |      |    HHSize   |     |
       | HHInc+------+------+ Row |
       |      | 1-2  |  3+  | Tot |
       +======+======+======+=====+
       | .LE. |  24  |   4  |  28 |
       | 45k  |   7  |   1  |   8 |
       +------+------+------+-----+
       | 45.1 |  53  |  98  | 151 |
       |to 60k|  10  |  15  |  25 |
       +------+------+------+-----+
       | .GT. |   0  |  66  |  66 |
       | 60k  |   0  |   7  |   7 |
       +======+======+======+=====+
       |Column|  77  | 168  | 245 |
       |Total |  17  |  23  |  40 |
       +------+------+------+-----+

Problem 3 [10 points]

Compare your category model from Problem 2 with the corresponding regression model (see output below).

  1. Evaluate the regression estimation results statistically.
  2. Interpret the model coefficients -- what do these values imply?
  3. Compute regression estimates for trips corresponding to each cell of the category model (use appropriate discrete values). Compare results.

Table 3. Regression Results for Trips versus HHInc and HHSize

 
 ----------------------------------------------------------------------
 --------     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   HHInc     HHSize    Trips
 1. HHInc   50.5080  8.7108   50     HHInc   1.0000    0.8033    0.9499
 2. HHSize   2.7400  1.1031   50     HHSize  0.8033    1.0000    0.8356
 3. Trips    5.6600  2.4042   50     Trips   0.9499    0.8356    1.0000

* * * * * *   O R D I N A R Y   L E A S T   S Q U A R E S   * * * * * *

  MODEL: Cat.Mod.Compar.   DEPENDENT VARIABLE => Trips Produced

  MULTIPLE R    0.9577     * ANOVA *  SUM OF SQR  df  MEAN SQR    F
  R-SQUARE      0.9171     REGRESSION     259.74   2    129.87  260.01
  ADJ R-SQUARE  0.9136     RESIDUALS       23.48  47      0.50
  S.E. OF EST.  0.7067     TOTAL SS       283.22  49

  VARIABLE NAME        B         BETA     S.E. B     T
     1. HHInc         0.2168    0.7856    0.0195   11.1411
     2. HHSize        0.4458    0.2045    0.1537    2.9009
        Constant     -6.5124

Problem 4 [10 points]

Using both the category and the regression production models, forecast the number of trips per household for the six household not used in model estimation (households 51-56; 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 
+-------------------------------+-------------------------------+
  51    6   45.0    2    3    2 | 54   10   59.4    3    5    1 
  52    3   40.2    1    2    2 | 55    8   58.5    3    4    1 
  53    4   49.5    1    1    2 | 56    5   43.8    2    2    1 
+-------------------------------+-------------------------------+

Problem 5 [10 points]

The 50 households were sampled from a study area divided into three zones (TAZs). The associated population-level distributions for these 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 (HHInc by HHSize)

 
         TAZ 1                       TAZ 2                       TAZ 3
+-----+-----+-----+-----+   +-----+-----+-----+-----+   +-----+-----+-----+-----+
|HHSiz| 1-2 | 3-5 | Row |   |HHSiz| 1-2 | 3-5 | Row |   |HHSiz| 1-2 | 3-5 | Row |
|HInc |     |     | Tot |   |HInc |     |     | Tot |   |HInc |     |     | Tot |
+=====+=====+=====+=====+   +=====+=====+=====+=====+   +=====+=====+=====+=====+ 
|LE 45|   0 |   0 |   0 |   |LE 45|  40 |  40 |  80 |   |LE 45|  30 |  70 | 100 |
+-----+-----+-----+-----+   +-----+-----+-----+-----+   +-----+-----+-----+-----+
|45-60|   0 |  60 |  60 |   |45-60|  40 |  80 | 120 |   |45-60|  70 |  20 |  90 |
+-----+-----+-----+-----+   +-----+-----+-----+-----+   +-----+-----+-----+-----+
|GT 60|   0 |  40 |  40 |   |GT 60|  20 |  80 | 100 |   |GT 60|   0 |  10 |  10 |
+=====+=====+=====+=====+   +=====+=====+=====+=====+   +=====+=====+=====+=====+
| Col |   0 | 100 | 100 |   | Col | 100 | 200 | 300 |   | Col | 100 | 100 | 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 + 3.0 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 for 223 (Optional 10 points Extra Credit for CEE123)]
The following regression results summarize an attempt to build a home-to-work trip production model. Fill in the blanks, interpret the parameters, and discuss the results, and select a significant model (if any).

 

           VARIABLE         NAME          MEAN        S.D.     OBS
        1. Population        POP       4090.90     3624.10      29
        2. Labor Force      LABF       1630.93     1424.85      29
        3. HH Income         INC       6068.55     1337.82      29
        4. Employment       EMPL        735.14      853.31      29
        5. Work Origins     TRIP       1324.93     1207.45      29

           Correlation Matrix:
        1. POP      1.0000    0.9971    0.0061    0.4894    0.9652
        2. LABF     0.9971    1.0000   -0.0002    0.5069    0.9693
        3. INC      0.0061   -0.0002    1.0000   -0.2717    0.0271
        4. EMPL     0.4894    0.5069   -0.2717    1.0000    0.4778
        5. TRIP     0.9652    0.9693    0.0271    0.4778    1.0000
        Variables:    POP       LABF      INC       EMPL      TRIP

(a) ====  OLS MODEL #1 : DEPENDENT VARIABLE => TRIP  ==================

    MULTIPLE R    ______   * ANOVA *   df   SUM OF SQR    MEAN SQR    F
    R-SQUARE      ______   REGRESSION  ___  38354310.0    ________  _____
    ADJ R-SQUARE  0.9372   RESIDUALS   ___   2470519.0    ________
    S.E. OF EST.  ______   TOTAL SS    ___  __________

            VARIABLE NAME       B         BETA     S.E. B     T
              1. LABF          0.8214    0.9693    0.0401   _____
                 Constant    ________

    Model #1 Comments:

(b) ====  OLS MODEL #2 : DEPENDENT VARIABLE => TRIP  ==================

    MULTIPLE R    0.9694   * ANOVA *   df   SUM OF SQR    MEAN SQR    F
    R-SQUARE      ______   REGRESSION  ___  38363630.0    ________  _____
    ADJ R-SQUARE  0.9351   RESIDUALS   ___  __________    ________
    S.E. OF EST.  ______   TOTAL SS    ___  __________

            VARIABLE NAME       B         BETA     S.E. B     T
              1. POP          -0.0672   -0.2016    0.2094   ____
              2. LABF          0.9917    1.1702    0.5326   ____
                 Constant    _______

    Model #2 Comments: 

(c) Which, if any, is the better model? Why? Would POP by itself make a good model?

Table 7. Household Travel Survey Data 

+-------------------------------+-------------------------------+
| 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   55.8    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 |
  1. HH ID = household number
  2. Trips = number of daily trips per household
  3. HHInc = mean Household income (in $1000s)
  4. Cars = number of cars per HH
  5. HHSiz = Household size (persons per HH)
  6. DUTyp = Dwelling Unit Type (1=single family; 2=multiple family)
Last Updated: 29 April 2026