16-Civ-A6 Highway Design, Construction, and Maintenance · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, 98-Civ-A6 Transportation Planning & Engineering, May 2014 — 3 hours, closed book (one two-sided aid sheet). Seven questions; any five constitute a complete examination and all are of equal value (20 marks). All seven are solved below as a study resource.
Reference texts (subject).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. A cross‑classification matrix of household trip rates (trips/household) and a matching matrix of forecast household counts, indexed by persons/household (1–5+) and autos/household (0, 1, 2+); plus a fitted regression rate $=-0.52+2.55\,\text{PERSON}+1.75\,\text{AUTO}$ (PERSON capped at 5, AUTO capped at 2). Total forecast households $=1680$.
Find. Zone trip production by (a) category analysis and (b) the regression rate, and (c) a comparison of the two methods.
Approach. For each of the 15 household cells, multiply the applicable per‑household trip rate by the forecast number of households and sum; do this once with the tabulated rates (category analysis) and once with the regression rate.
(a) Category (cross‑classification) analysis. Trips in a cell $=$ rate $\times$ households; the zone total is the sum over all cells, $\sum_i \text{rate}_i \times HH_i$. Carrying out the 15 products gives the table below.
| Autos \ Persons | 1 | 2 | 3 | 4 | 5+ | Row total |
|---|---|---|---|---|---|---|
| 0 | 260 | 528 | 666 | 1380 | 224 | 3058 |
| 1 | 1200 | 1675 | 2300 | 575 | 685 | 6435 |
| 2+ | 600 | 405 | 530 | 798 | 0 | 2333 |
| Zone total (a) | 11 826 | |||||
The category method predicts $\boxed{11\,826\ \text{trips}}$ from the zone.
(b) Regression‑rate estimate. Applying $\text{rate}=-0.52+2.55\,\text{PERSON}+1.75\,\text{AUTO}$ to each cell (e.g. a 3‑person, 1‑auto household: $-0.52+2.55(3)+1.75(1)=8.88$ trips) and multiplying by the same household counts:
| Autos \ Persons | 1 | 2 | 3 | 4 | 5+ | Row total |
|---|---|---|---|---|---|---|
| 0 | 203.0 | 503.8 | 641.7 | 1452.0 | 244.6 | 3045.1 |
| 1 | 1134.0 | 1582.5 | 2220.0 | 571.5 | 699.0 | 6207.0 |
| 2+ | 829.5 | 404.0 | 531.5 | 790.8 | 0 | 2555.8 |
| Zone total (b) | 11 807.9 | |||||
The regression method predicts $\boxed{11\,808\ \text{trips}}$ — within about 0.2 % of the category total. The close agreement of the zone totals is partly compensating error, however: cell by cell the two methods differ by as much as 38 %, as the comparison in (c) shows.
(c) Comparison. Both methods relate household trip‑making to the same explanatory variables (household size and auto ownership), and here they agree closely. They differ in structure and in what they assume. Category analysis makes no functional‑form assumption: each cell carries its own empirically observed rate, so it can capture non‑linear and interaction effects (for example the way the marginal effect of an extra car differs across household sizes). Its costs are that it needs a sufficient sample in every cell to give a stable rate — sparse survey cells give unstable rates — and it cannot extrapolate beyond the categories tabulated. Regression imposes a smooth linear relationship, which economises on data, fills gaps by interpolation, and lets each variable's effect be stated as a coefficient; but it forces additivity and constant marginal effects, so it will misfit wherever the true response is non‑linear or the variables interact, and it can predict implausible values outside the calibration range (note the fitted intercept is negative). The cell comparison shows this directly. For one‑person households the table gives the same 4.0 trips for 1 and for 2+ autos (the rate saturates), but the additive equation must add 1.75 trips for every car, so the 1‑person/2+‑auto cell rises from 600 to 829.5 trips (+38 %) and the 1‑person/0‑auto cell falls from 260 to 203 (−22 %). Conversely, the table's car effect grows with household size (+1.4 trips per first car at 1 person but +2.5 at 5+ persons), an interaction the constant 1.75 coefficient cannot represent. The 0.2 % agreement of the zone totals therefore hides offsetting cell errors, so it should not be read as validation of the regression. In practice category analysis is preferred when data are plentiful and interactions matter, and regression when data are limited or a compact transferable model is required.
| Method | Forecast zone trips |
|---|---|
| (a) Category / cross‑classification | 11 826 |
| (b) Linear regression rate | 11 808 |
