16-Civ-A6 Highway Design, Construction, and Maintenance · December 2014
Question 3 of 7: Trip Generation — Cross-Classification and Regression
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Examination — 98-Civ-A6 Transportation Planning & Engineering, December 2014. Closed book (one two-sided aid sheet), 3 hours. Seven questions of equal value (20 marks); any five constitute a complete paper. All seven are solved here as a study resource.
Given. Category (cross-classification) trip rates and household counts by the 4 sizes × 3 income levels, and a calibrated regression trip-rate equation.
Given data — trip rate (trips/household) | number of households
Size \ Income
Low
Medium
High
1
0.11 | 42
0.95 | 27
1.20 | 32
2
0.60 | 170
1.38 | 220
2.16 | 132
3
0.93 | 83
1.46 | 104
2.44 | 93
4 or more
1.03 | 50
1.69 | 154
2.60 | 117
Find. Forecast total trips by category rates (a) and by the regression rate (b), and compare the two approaches (c).
Approach. For each cell multiply the trip rate by the number of households and sum; in (b) first evaluate the regression rate for each size/income cell, then multiply and sum.
(a) Cross-classification trips = rate × households, per cell. Applying $t_{ij}=r_{ij}\,H_{ij}$ cell by cell and summing each income column gives Low $=235.31$, Medium $=741.35$, High $=854.64$ trips (see results table). For example the Medium column: $0.95(27)+1.38(220)+1.46(104)+1.69(154)=25.65+303.6+151.84+260.26=741.35$.
$$\text{Total}_{(a)}=235.31+741.35+854.64=\boxed{1831.3\ \text{trips}}.$$
(b) Evaluate the regression rate for each cell. With $r=-0.16+0.33\,\text{HSIZE}+0.72\,\text{INC}$ the rate depends only on size and income level, e.g. size 3, High: $r=-0.16+0.33(3)+0.72(2)=-0.16+0.99+1.44=2.27$. The 12 rates run from $0.17$ (size 1, Low) to $2.60$ (size 4, High).
(b) Regression trips = rate × households, per cell. Multiplying and summing each income column gives Low $=219.03$, Medium $=743.15$, High $=822.91$.
$$\text{Total}_{(b)}=219.03+743.15+822.91=\boxed{1785.1\ \text{trips}}.$$
(c) Compare. The category method makes no functional assumption — each size/income cell carries its own empirically observed rate — so it reproduces non-linear and interaction effects (note the High-income rates climb much faster than a linear fit) but needs a well-populated sample in every cell and cannot extrapolate to categories not surveyed. The regression method assumes the rate is a linear, additive function of size and income; it is compact, smooths sampling noise, and can fill empty or sparse cells, but it imposes constant marginal effects (here $+0.33$ trip per person, $+0.72$ per income step) and so misses the accelerating High-income behaviour, giving a slightly lower total (1785 vs 1831).
Question 3 — forecast trips per cell: (a) category rate × households | (b) regression rate (in brackets) × households
Size \ Income
Low
Medium
High
1
4.62 | 7.14 (0.17)
25.65 | 24.03 (0.89)
38.40 | 51.52 (1.61)
2
102.00 | 85.00 (0.50)
303.60 | 268.40 (1.22)
285.12 | 256.08 (1.94)
3
77.19 | 68.89 (0.83)
151.84 | 161.20 (1.55)
226.92 | 211.11 (2.27)
4 or more
51.50 | 58.00 (1.16)
260.26 | 289.52 (1.88)
304.20 | 304.20 (2.60)
At cell level the two methods differ far more than the totals suggest: the regression over-predicts the small-household cells (size 1, High: 51.5 vs 38.4 trips) and the large Medium-income cell (289.5 vs 260.3), and under-predicts the size-2 cells in every income group (e.g. Medium 268.4 vs 303.6). These offsetting errors are why the zonal totals differ by only about 2.5%.
