16-Civ-A6 Highway Design, Construction, and Maintenance · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, 98‑Civ‑A6 Transportation Planning & Engineering (May 2013). Closed book, one two‑sided aid sheet, 3 hours. Seven questions; any five constitute a complete examination and each is 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. Survey counts (households, trips) and target‑year household forecasts, tabulated below. The 56 sampled households check the sample size.
| Size | 0 autos | 1 auto | 2+ autos |
|---|---|---|---|
| 1 | 5 / 30 → 6.00 | 3 / 12 → 4.00 | — (no sample) |
| 2 | 3 / 21 → 7.00 | 8 / 46 → 5.75 | 3 / 24 → 8.00 |
| 3 | 2 / 15 → 7.50 | 5 / 42 → 8.40 | 5 / 52 → 10.40 |
| 4 | 4 / 34 → 8.50 | 2 / 20 → 10.00 | 5 / 55 → 11.00 |
| 5+ | — (no sample) | 3 / 33 → 11.00 | 8 / 96 → 12.00 |
| Size | 0 autos | 1 auto | 2+ autos |
|---|---|---|---|
| 1 | 500 | 425 | 75 |
| 2 | 375 | 725 | 225 |
| 3 | 350 | 525 | 475 |
| 4 | 50 | 250 | 550 |
| 5+ | 25 | 200 | 775 |
Find. The category (cross‑classification) trip rates and forecast trips (a), the regression‑based forecast trips (b), and a comparison of the two methods (c).
Approach. For (a) divide sampled trips by sampled households in each cell to get a rate, then multiply by the forecast households. For (b) evaluate the linear rate for each (size, auto) cell and multiply by the forecast households.
| Size | 0 autos | 1 auto | 2+ autos |
|---|---|---|---|
| 1 | 4.74 | 5.58 | 6.42 |
| 2 | 6.17 | 7.01 | 7.85 |
| 3 | 7.60 | 8.44 | 9.28 |
| 4 | 9.03 | 9.87 | 10.71 |
| 5+ | 10.46 | 11.30 | 12.14 |
| Method | Target‑year trips |
|---|---|
| (a) Category analysis (13 populated cells) | 45 743.75 |
| (b) Regression (all 15 cells) | 46 623.75 |
Check / assumption: The survey has no household in two categories that the forecast nevertheless populates (size 1 with 2+ autos; size 5+ with 0 autos). Category analysis has no rate for them, so their trips are omitted from the method‑(a) total. In practice one would borrow the rate of an adjacent category or note the data gap; the regression method has no such gap, which is one of its advantages [part (c)].
Category analysis (cross‑classification) makes no assumption about the mathematical form of the relationship: it simply reads an empirical average trip rate for each homogeneous household stratum. Its strengths are transparency and the fact that it captures non‑linear and interaction effects automatically. Its limitations are that it needs an adequate sample in every category (the two empty cells above are a direct symptom), the rates are assumed stable over time, and the number of strata multiplies quickly as variables are added.
The regression method assumes a specific functional form — here trip rate is linear and additive in household size and auto ownership. Its strengths are that it needs far fewer parameters, interpolates and extrapolates smoothly (so it fills the empty cells and can be applied to categories not surveyed), and gives a statistically testable model. Its limitations are that the imposed linearity may be wrong (real trip rates often saturate at large household size and high auto ownership), it forces additivity and so misses interaction effects, and it can predict implausible values outside the calibration range. Reassuringly, the two totals here agree to within about 2 %, which is expected when the survey rates are themselves close to linear.
