Simulations / Data Science

Fit the Line

Choose a Detroit dataset, adjust a line until it matches the pattern, and compare your error with the best-fit (least-squares) line.

Controls

Residual = actual y minus the line's y. The best-fit line minimizes the sum of squared residuals (SSE). Datasets: model energy data (illustrative home), real freeze–thaw counts from Open-Meteo daily temperatures (winters 2016–2024), and real annual mean Detroit River levels from NOAA (1970–2024).
Your line
y = m·x + c
Your error (SSE)
Best-fit error
Correlation r

Try this

  • On the electricity data, can a single line fit well? What does the best-fit line miss?
  • For freeze–thaw days, how close can you get? Does a nonzero slope mean there is a real trend?
  • For water levels, compare the slope with the multi-year ups and downs.

What to notice

  • Low r means the points are far from a line, not that there is no pattern.
  • Squared errors punish far-away points most, which is why outliers pull the line.
  • Correlation is not causation.

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