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

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.

Applied to 14 Wa In Fong East

For our Sheung Wan case study, the regression inputs would be:

Variable	Data Source	Value
Market size (X₃)	Census population within 500m	~28,000 residents
Competition (X₂)	FEHD restaurant licenses in C&W	208 licensed restaurants
Affluence (X₄)	Median household income	HK$30,000–40,000/mo
Store size (X₁)	Site-specific	Depends on lease

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 Agent Simulation to model actual consumer behaviour.

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

Source

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