City of Brampton data projectCan a straight line predict a City of Brampton building’s emissions from its energy bills?
The City of Brampton publishes the yearly electricity use, natural gas use and greenhouse gas emissions of the buildings it operates, from offices and libraries to fire stations and arenas. Our students fit a two-input linear model to it. The figures in this section are our own output, not the City’s.
Our least squares results on the City of Brampton’s Energy Consumption and Greenhouse Gas Emissions file (711 rows fetched 22 October 2026; fitted on 503 rows from 2013 to 2017, tested on 208 rows from 2018 and 2019)| Model | What it assumes | Average miss on the 2018 and 2019 rows |
|---|
| Mean guess | Every building emits the 2013 to 2017 average | 196,390 kg a year |
| Two-input line, fitted on 2013 to 2017 | Emissions = 1.885 kg per cubic metre of gas + 0.0491 kg per kWh of electricity | 10,928 kg a year |
| Two-input line, fitted on 2017 only | The same shape of model, learned from the most recent training year alone | 8,390 kg a year |
Here is the program. It downloads the whole layer in one request, solves the two least squares equations by hand (no libraries, so the algebra is visible), and prints the fitted factors for each year as well as the errors in the table. We ran it on 22 October 2026 with the output shown in the table and the list below:import json, urllib.request
URL = ("https://services3.arcgis.com/rl7ACuZkiFsmDA2g/arcgis/rest/services/"
"Environment/FeatureServer/0/query?where=1%3D1&returnGeometry=false"
"&outFields=REPORT_YEAR,NATURAL_GAS_M3,ELECTRICITY_KWH,GHG_EMISSIONS_KG"
"&resultRecordCount=5000&f=json")
rows = [f["attributes"] for f in json.load(urllib.request.urlopen(URL))["features"]]
data = [(r["REPORT_YEAR"], r["NATURAL_GAS_M3"] or 0, r["ELECTRICITY_KWH"] or 0,
r["GHG_EMISSIONS_KG"]) for r in rows]
def fit(points):
# least squares for kg = a * gas + b * kwh (two equations, two unknowns)
gg = sum(g * g for _, g, e, _ in points)
ee = sum(e * e for _, g, e, _ in points)
ge = sum(g * e for _, g, e, _ in points)
gy = sum(g * y for _, g, e, y in points)
ey = sum(e * y for _, g, e, y in points)
det = gg * ee - ge * ge
return (gy * ee - ey * ge) / det, (ey * gg - gy * ge) / det
def miss(points, a, b):
return round(sum(abs(a * g + b * e - y) for _, g, e, y in points) / len(points))
train = [p for p in data if p[0] <= 2017]
test = [p for p in data if p[0] >= 2018]
a, b = fit(train)
avg = sum(p[3] for p in train) / len(train)
print(len(data), "rows;", len(train), "train (2013-2017),", len(test), "test (2018-2019)")
print("kg per m3 of gas:", round(a, 3), " kg per kWh:", round(b, 4))
print("average miss, guessing the mean:", round(sum(abs(avg - p[3]) for p in test) / len(test)))
print("average miss, two-input line:", miss(test, a, b))
for year in range(2013, 2020):
ya, yb = fit([p for p in data if p[0] == year])
print(year, round(ya, 3), round(yb, 4))
a17, b17 = fit([p for p in data if p[0] == 2017])
print("trained on 2017 only:", miss(test, a17, b17))
Our per-year fits from the same program: the factor the line learns for each input, year by year (711 rows, our calculation)| Report year | Rows | kg per cubic metre of gas | kg per kWh of electricity |
|---|
| 2013 | 97 | 1.891 | 0.076 |
| 2014 | 101 | 1.891 | 0.04 |
| 2015 | 103 | 1.899 | 0.043 |
| 2016 | 102 | 1.891 | 0.0355 |
| 2017 | 100 | 1.899 | 0.043 |
| 2018 | 106 | 1.888 | 0.03 |
| 2019 | 102 | 1.891 | 0.0305 |
1. Ask why it fits so well
A line that misses by about 11,000 kg on buildings that emit hundreds of thousands looks brilliant. The City’s own description explains it: “The software calculates the annual energy consumption and greenhouse gas emissions”. The emissions are worked out from the energy use, so the model is mostly rediscovering a formula.
2. Read the coefficients
The gas factor barely moves, between 1.888 and 1.899 kg per cubic metre every year. The electricity factor falls from 0.076 in 2013 to about 0.03 by 2018. The data does not say why; a student should find out what factor the reporting software used before claiming a cause.
3. Watch the rule change
Because the electricity factor dropped, a line trained on 2013 to 2017 overestimates 2018 and 2019. Training on 2017 alone cuts the miss from 10,928 to 8,390 kg. Old data is not always better data when the rule behind it shifts.
Gaps a careful student flags
The item says the City submitted datasets for 2010 to 2019, yet the rows we downloaded run only from 2013 to 2019. Forty-three rows record zero electricity and 123 record zero gas; some buildings may genuinely use no gas, but a building with a gas bill and no electricity at all is more likely a missing record than a fact. A model trained without checking those rows learns from the gaps as well as the data.
The City notes that the reports are prepared under Ontario Regulation 25/23 and that “The City receives utility bills that contain energy consumption data.” Its item page adds: “Last updated: August 30, 2021 with 2018 & 2019 report values.”, so this is a historical file, ideal for practice and not a current account of any building. The dataset carries the licence label CC BY, credited to the City of Brampton; the Creative Commons deed says that licence allows use “for any purpose, even commercially.” Source: City of Brampton, Energy Consumption and Greenhouse Gas Emissions, GeoHub item. The City has not endorsed this page, our courses or our results.
