Does Temperature Predict Energy Use?
Scatter plots, lines of best fit, and correlation using Detroit's 2024 monthly temperatures.
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Class period:
Date:
Standards
SEP 4 & 5 — Analyzing and interpreting data; using mathematics and computational thinking.
HSS-ID.B.6 — Represent data on two quantitative variables on a scatter plot, and describe how the variables are related (Common Core Math). Middle school: 8.SP.A.1–2.
Why Does This Matter?
Detroit swings from well below freezing in January to hot and humid in July. Utilities such as DTE Energy forecast demand using temperature data because home heating and air conditioning respond to the weather. Your household's energy bill follows the same pattern.
Objective
Graph monthly natural gas and electricity use against average monthly temperature, fit a line, and interpret the slope and correlation.
Materials
- Dataset: household_energy_model_2024.csv. Temperatures are real 2024 Detroit monthly averages; the electricity and gas figures are an illustrative model of a typical single-family home, not actual customer data.
- Spreadsheet software (or graph paper, ruler, and calculator)
- Optional: the Fit the Line simulation for practice
Note: This is a computer-based data lab — no physical safety hazards.
Procedure
- Open the dataset. Identify the two variables you will compare: average temperature (x) and natural gas use in therms (y).
- Make a scatter plot of gas use versus temperature. Describe the direction, strength, and shape of the pattern.
- Add a linear trendline with its equation and R² value (or draw a line of best fit by eye and estimate its slope).
- Make a second scatter plot of electricity use (kWh) versus temperature. Notice how its shape differs from the gas plot.
- Fit a separate trendline using only the months warmer than 15°C.
- Use your equations to predict gas use at −10°C and electricity use at 30°C. Mark each prediction as interpolation or extrapolation.
Data Table
| Model | Equation (y = mx + b) | R² or r | Prediction |
|---|---|---|---|
| Gas vs. temperature (all months) | |||
| Gas vs. temperature (months below 16°C) | |||
| Electricity vs. temperature (all months) | |||
| Electricity vs. temperature (months above 15°C) |
Analysis Questions
- Interpret the slope of your gas-versus-temperature line in words, including units.
- Why does electricity use not follow a single straight line across the whole year?
- Is temperature the cause of the change in energy use, or just correlated with it? Describe the physical mechanism that connects them.
- How reliable is your prediction at −10°C? What risk comes with extrapolating beyond your data?
- Describe one way a utility could use a relationship like this to plan for very hot or very cold days.