Montreal data lessonDo busier Montreal libraries lend more books? Correlation on city data
The Ville de Montréal publishes yearly statistics for its public libraries as open data. Secondary IV students plot visits against loans, measure the correlation, fit a regression line and argue about what it proves. We computed every coefficient and residual shown here ourselves.
The dataset is the Bibliothèques de Montréal statistics on loans, collections and attendance; the City describes it, in French, as tables presenting those statistics for Montreal’s 45 libraries (the English rendering is ours). We used the consolidated workbook covering 2012 to 2020, downloaded on 23 October 2026, and its 2018 sheet. Of 49 numbered rows, 45 libraries across 19 boroughs report visits, loans and floor area; the four we left out are two mobile services and two sites with missing figures.
Visits and loans at selected Montreal libraries in 2018, from the Ville de Montréal workbook, with our residuals from the regression line (loans are non-digital loans including renewals)| Library | Visits | Loans | Residual from our line |
|---|
| Benny | 611,789 | 580,620 | −167,753 |
| Ahuntsic | 306,670 | 670,189 | +272,282 |
| Marc-Favreau | 297,265 | 637,137 | +250,033 |
| Pierrefonds | 20,469 | 105,095 | see note below |
| Median of the 45 | 175,292 | 226,952 | |
Across the 45 libraries our correlation between visits and loans is r = 0.825, a strong positive linear relationship, and r squared is 0.681, so about two thirds of the variation in loans lines up with variation in visits. The regression line is loans = 1.1486 × visits + 45,658. At 150,000 visits, an interpolation well inside the data, it predicts about 217,952 loans. The Python reads the 2018 sheet and does the rest:import openpyxl, statistics
book = openpyxl.load_workbook("bm_stats-consol.xlsx", data_only=True)
branches = []
for row in book["2018"].iter_rows(values_only=True):
if isinstance(row[0], int): # numbered library rows only
loans, visits, area = row[8], row[19], row[33]
if all(isinstance(v, (int, float)) for v in (loans, visits, area)):
branches.append((row[4], visits, loans))
visits = [b[1] for b in branches]
loans = [b[2] for b in branches]
line = statistics.linear_regression(visits, loans)
print("libraries:", len(branches))
print("r:", round(statistics.correlation(visits, loans), 3))
print("loans = ", round(line.slope, 4), "x visits +", round(line.intercept))
Residuals tell stories
Benny had the most visits in 2018, 611,789, yet lent about 167,753 fewer items than the line predicts. Ahuntsic lent about 272,282 more. Libraries are used for study, events and computers as well as borrowing, and the residual shows how differently branches are used.
One number to question
Pierrefonds recorded only 20,469 visits in the 2018 sheet but 365,408 in the 2019 sheet. The file does not say why. A careful student flags that point before fitting anything, and checks how much the line moves without it.
A third variable
Visits also correlate with floor area, r = 0.661 in our calculation. Bigger buildings draw more people and hold more books, so size may drive both visits and loans. That is the program’s point about dependent or causal relationships.
Correlation is not a cause
A strong r does not mean that visiting causes borrowing, or the reverse. It says the two rise together across these 45 libraries in 2018. Extending the line to a library with three million visits would be extrapolation far outside the data, and the program asks students to say exactly that when they extrapolate.
Source: Ville de Montréal, Bibliothèques de Montréal statistics, used under the Creative Commons Attribution 4.0 International licence, which the licence deed says allows use for any purpose, even commercially (licence, dataset page). We changed the data by selecting one sheet and computing our own statistics. The Ville de Montréal does not endorse this page or our classes.
