Question 3 of 7: Trip generation by cross-classification and by regression

Question 3: Trip generation by cross-classification and by regression (20 marks)

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 base‑year survey of households and trips cross‑classified by persons/household (1–5+) and vehicles/household (0, 1, 2+), and a forecast household count for each of the 15 cells.

Find. Forecast trips per cell by (a) cross‑classification rates and (b) the regression rate, plus (c) a comparison of the two methods.

Approach. For (a) the trip rate of a cell is its surveyed trips divided by its surveyed households; multiply by the forecast households. For (b) compute each cell’s rate from the regression formula (capping NPERSON at 5 and NVEH at 2) and multiply by forecast households.

1. Cross‑classification rates. Rate $r_{ij}=\text{trips}_{ij}/\text{HH}_{ij}$. For example the (1 person, 0 veh) cell gives $r=220/95=2.32$ trips/HH and the (4, 0) cell gives $1008/122=8.26$ trips/HH.
2. Forecast trips, method (a). Multiply each rate by that cell’s forecast households, e.g. $(1,0):2.32\times120=278$ and $(3,1):8.09\times190=1536$. The full grid is tabulated below; the zonal total is $\boxed{T_a\approx 12{,}427\text{ trips}}$.
3. Regression rates. $r=0.47+2.02\,\mathrm{NPERSON}+1.39\,\mathrm{NVEH}$ with the stated caps. For instance $(1,0):0.47+2.02(1)+1.39(0)=2.49$ and $(5\text{+},2\text{+}):0.47+2.02(5)+1.39(2)=13.35$ trips/HH.
4. Forecast trips, method (b). Multiply each regression rate by the forecast households, e.g. $(1,0):2.49\times120=299$ and $(4,1):9.94\times180=1789$. The zonal total is $\boxed{T_b\approx 12{,}369\text{ trips}}$.

(c) Comparison of the two methods

The two methods give almost the same zonal total (12,427 versus 12,369 trips, a difference well under 1%), but they rest on different assumptions. Cross‑classification makes no functional‑form assumption: it simply reuses each cell’s observed average rate, so it captures any non‑linear or interaction effect between household size and car ownership that is present in the data. Its weaknesses are that it needs a large, well‑populated sample in every cell to give stable rates (a cell surveyed from only 11 households, like (5+, 0), yields a noisy rate), it cannot produce a rate for an empty cell, and it assumes the base‑year rates transfer unchanged to the forecast year.

The regression method assumes a specific linear, additive relationship between the trip rate and the two variables, with no interaction term. Its advantages are that it smooths sampling noise, gives a rate for every cell (even unsampled ones), and is compact. Its limitations are that the linear‑additive form may misrepresent reality (the true effect of an extra person or car may taper off, which is partly why the formula caps NPERSON at 5 and NVEH at 2), and it too assumes the fitted coefficients are stable over time. In practice cross‑classification is preferred when the sample is large and category‑rich, and regression when the sample is thinner or a continuous predictive equation is wanted.