Applied case · Retail · about 60 minutes
Estimate the sales lift of a chain-wide discount promotion fairly — separating it from holidays and store mix — put an honest interval on it, and decide whether it pays for itself.
Lumen Bay Stores (a fictional home-goods chain) ran a recurring discount promotion across its 40 stores during 2023–2024. Each week, individual stores could opt in. The commercial director wants to make the promotion a permanent part of the calendar and has a slide that says “promoted weeks sell 19.6% more”.
Before the board approves the budget, the finance team has asked you — the chain's analyst — three questions:
The data. retail_weekly has 4,160 store-weeks (40 stores × 104 weeks) with region, store size, a holiday-week flag, a promotion flag, footfall and net weekly sales in SAR. 661 store-weeks were promoted. The dataset is synthetic: it was generated to behave like real retail data (trend, seasonality, holiday peaks, a promotion effect), but it describes no real company, and its numbers are not evidence about real promotions.
Stakeholders. The commercial director (wants the promotion), the finance controller (owns the budget), and regional managers (want to know whether their region is different). Your deliverable is a one-page recommendation to the finance controller.
Dataset
Weekly store sales
4,160 rows · one row = one store-week · synthetic data
| Store | Region | Store size | Floor area (m²) | Week number | Week start | Holiday week | Promotion | Footfall (visitors) | Weekly sales (SAR) |
|---|---|---|---|---|---|---|---|---|---|
| ST01 | Central | Small | 954 | 1 | 2023-01-01 | false | true | 1986 | 214951.9 |
| ST01 | Central | Small | 954 | 2 | 2023-01-08 | false | false | 1811 | 201838.41 |
| ST01 | Central | Small | 954 | 3 | 2023-01-15 | false | true | 2045 | 217021.33 |
| ST01 | Central | Small | 954 | 4 | 2023-01-22 | false | true | 1947 | 212706.67 |
| ST01 | Central | Small | 954 | 5 | 2023-01-29 | false | false | 1798 | 193921.23 |
| ST01 | Central | Small | 954 | 6 | 2023-02-05 | false | false | 1894 | 201477.48 |
Stage 1 of 4
Open retail_weekly in the lab. Before computing any lift, find out when promotions happened and what one row is. A promotion that mostly runs in already-busy weeks will look better than it is.
Exercise 1 · Application, difficulty 1 of 3
In retail_weekly, what percentage of store-weeks were promoted (a) among holiday weeks and (b) among non-holiday weeks? Give both to 2 decimal places.
Data: retail_weekly · Open in the lab to explore and calculate.
Exercise 2 · Interpretation, difficulty 2 of 3
Which features of this dataset could make a simple “average promoted week vs average non-promoted week” comparison misleading? Select all that apply.
Stage 2 of 4
Reproduce the commercial director's number, then make the comparison fairer one step at a time: first hold the holiday effect fixed, then look at regions.
Exercise 3 · Application, difficulty 2 of 3
The lift is the percentage by which mean weekly sales in promoted store-weeks exceed mean weekly sales in non-promoted store-weeks:
(a) Compute the naive lift using all store-weeks. (b) Compute the lift using non-holiday weeks only. Give both as percentages to 2 decimal places.
Data: retail_weekly · Open in the lab to explore and calculate.
Exercise 4 · Practice, difficulty 2 of 3
Regional managers want their own numbers. Using non-holiday weeks only, compute the raw lift (same formula as before) separately for each region. Give each to 1 decimal place.
Data: retail_weekly · Open in the lab to explore and calculate.
Exercise 5 · Interpretation, difficulty 3 of 3
Within each region, a regression of log(sales) on promotion, holiday and store size gives these promotion lifts (with 95% intervals):
| Region | Adjusted lift | 95% CI |
|---|---|---|
| Central | 12.7% | 10.1% to 15.4% |
| Eastern | 13.7% | 10.7% to 16.7% |
| Western | 12.6% | 9.7% to 15.6% |
| Southern | 13.9% | 11.7% to 16.1% |
The raw lifts you computed ranged from 7.1% to 14.3%. What is the best explanation?
Stage 3 of 4
A model can hold several things fixed at once. Because sales are multiplicative (a big store gains more SAR than a small one from the same promotion), model the logarithm of sales: a coefficient then means a lift of about .
Exercise 6 · Application, difficulty 3 of 3
In the lab's Model panel, fit a linear regression of log(sales_sar) (tick “Model log(response)”) on promotion, holiday, region and store_size (all as categories). Report:
(a) the promotion coefficient (4 decimal places); (b) the estimated lift (2 decimal places); (c) the lower and upper ends of the 95% interval for the lift, transforming the coefficient's interval the same way (2 decimal places).
Data: retail_weekly · Open in the lab to explore and calculate.
Exercise 7 · Interpretation, difficulty 2 of 3
The model's 95% interval for the lift is 11.7% to 14.7%. Which statement should go into the board paper?
Stage 4 of 4
Statistical significance is not the decision. Translate the lift into money using finance's figures: gross margin 38% on net sales, and about SAR 22,000 of extra cost per promoted store-week. As the baseline, use the mean weekly sales of non-holiday, non-promoted store-weeks: SAR 305,997.
Exercise 8 · Application, difficulty 2 of 3
Using the model's lift of 13.19% and the baseline of SAR 305,997 per store-week, compute for one average promoted store-week:
(a) the incremental sales (SAR); (b) the incremental gross profit at a 38% margin (SAR); (c) the net contribution after the SAR 22,000 promotion cost (SAR; negative if it loses money).
Round each to the nearest riyal.
Exercise 9 · Challenge, difficulty 2 of 3
What lift (in %) would a promoted store-week need for its extra gross profit to exactly cover the SAR 22,000 cost? Use the same baseline (SAR 305,997) and margin (38%). Give the answer to 1 decimal place.
Exercise 10 · Interpretation, difficulty 3 of 3
Write a 3–5 sentence recommendation to the finance controller. State the lift and its uncertainty, compare it with the break-even lift, give a clear recommendation, and name at least one limitation of the analysis.
Write up your analysis. Your report is saved to your account; you can download it at any time. Written reports are not graded automatically — compare your reasoning with the worked solutions above.
State the decision (make the promotion permanent or not) and the three questions you answered: is the lift real, how big, does it pay.
Describe retail_weekly (40 stores × 104 weeks, synthetic). Explain the two traps you found: promotions concentrated in holiday weeks, and repeated weeks per store.
Explain why you moved from the naive comparison to a non-holiday comparison and then to a log-sales regression with holiday, region and store size. Say what a log-scale coefficient means.
Report the naive, non-holiday and adjusted lifts side by side, the adjusted 95% interval, the regional picture, and the incremental profit and break-even lift.
Clustering (repeated weeks per store, and what the within-store check showed), self-selected promotion weeks (observational), effects outside the promoted week (pull-forward, halo), and cost estimates you took from finance.
One clear recommendation with the next step (for example a randomised pilot of a cheaper design), and what result would change your mind.