Multiple Regression Model

The multiple regression model is the most straightforward way to predict a store’s revenue from measurable site characteristics. It’s a statistical workhorse: you feed it data from existing stores, and it tells you what drives sales.

The Formula

Y = a + b₁X₁ + b₂X₂ + b₃X₃ + b₄X₄

Where:

• Y = predicted annual turnover
• X₁ = store size (sq ft)
• X₂ = competition index (nearby competing stores)
• X₃ = market size (population within catchment)
• X₄ = affluence index (household income)
• a, b₁…b₄ = coefficients fitted from existing store data

“Multiple regression is used to combine different attributes into the same regression equation… The model is usually built up sequentially (‘stepwise’), starting with the most important variable.” — Birkin & Clarke, Retail Geography, Ch. 7

Data Requirements

Dataset	What We Use	Link
FEHD Restaurant Licences	Competitor count as independent variable	View →
Rental Indices (RVD)	Rent cost as independent variable	View →
Census Population	Population density as independent variable	View →
Household Income	Area spending power as independent variable	View →
Employment by District	Worker density predicting lunch revenue	View →
Consumer Price Index	Inflation-adjust historical revenue data	View →
Restaurant Receipts	Revenue benchmarks from census data	View →
Building Information	Building usage mix as predictor (commercial ratio → lunch crowd)	View →

How It Works

1. Collect data from existing stores: turnover, size, competition, market size, affluence
2. Run stepwise regression — each variable enters the model in order of explanatory power
3. Read the coefficients — they tell you which factors matter most
4. Apply to new sites — plug in the new location’s attributes, get a turnover prediction

Real Example: Birkin & Clarke’s Store Network

From the book (Table 7.3), a UK retailer’s regression output:

Variable	Slope	Contribution to Variance
Market size	5.8	0.33
Store size	125	0.20
Competition	116,448	0.18
Income	17,956	0.09
Total R²		0.80

Market size alone explains 33% of turnover variation. Store size adds 20%. Together with competition and income, the model explains 80% of all variance.

Tip

The stepwise approach is key. You don’t throw everything in at once — you add the most important variable first, then see what residual the next variable can explain. This prevents multicollinearity from blowing up your coefficients.

Caution

The regression model needs training data — actual turnover figures from comparable stores. Without that, the coefficients are theoretical. For a real deployment, you’d need at least 20–30 comparable outlets with known revenue.

Strengths & Limitations

Strengths:

• Simple, transparent, explainable to stakeholders
• Quick to compute — runs in milliseconds
• Good for portfolio benchmarking (which stores underperform their attributes?)

Limitations:

• Requires training data (actual revenue from comparable stores)
• Assumes linear relationships (diminishing returns not captured)
• Doesn’t model consumer choice — treats each site independently
• Can’t simulate “what-if” scenarios (new competitor, road closure)

When to Use It

The regression model is best as a first filter — screening many potential sites down to a shortlist. For the shortlist, you’d graduate to the Spatial Interaction Model or LLM Agent Simulation to model actual consumer behaviour.

“Two important applications of the model are performance assessment and evaluation of potential.” — Birkin & Clarke, Ch. 7

Implementation Notes

Implementation vs Theory

This section documents the actual implementation in functions/api/analyze.ts, including calibration decisions and bug fixes. The theoretical formula above is the target; the implementation below is what currently runs.

Current Implementation (2026-03-25)

Current formula:

Y = (a + b1×area + b2×compIdx + b3×market + b4×transport%) × priceMult

Coefficients:

• a = 20000 (base; every restaurant has some baseline revenue)
• b1 = 120 (area: 500 sqft → +60K contribution)
• b2 = -80 (competition drag: compIdx 100 → −8K)
• b3 = 0.3 (market size, capped at 100K; max contribution = +30K)
• b4 = 30000 (transport: full score = +30K)

Competition index: compIdx = min(100, round(100 × log(1 + competitors) / log(1001))) — uses log(1001) as denominator so only 1000+ competitors reach 100.

Price multipliers: Budget 0.7, Mid 1.0, Premium 1.5, High-end 2.2.

Revenue floor: Math.max(30000, predicted) — no restaurant prediction goes below HK$30K/month.

Changelog

Date	Change	Why
2026-03-25	Competition index denominator changed from log(81) to log(1001)	log(81) saturated at ~81 competitors; urban locations all hit 100 and became indistinguishable
2026-03-24	b2 (competition drag) changed from -200 to -80	At b2=-200, competitionIndex ~100 subtracted 20K from prediction, driving everything to the floor
2026-03-24	Revenue floor lowered from Math.max(500000, ...) to Math.max(30000, ...) (via 50K intermediate)	500K floor meant all predictions were identical regardless of inputs
2026-03-24	b3 (market size) changed to 0.3 with 100K cap	Uncapped market contribution was dominating predictions in dense districts

Source

📖 Birkin, M. & Clarke, G. (2023). Retail Geography. Chapter 7: Store Performance Modelling.