Today is rung 4 of 5 on this topic
Data, regression and interpreting a model
Can do: Fits a line to real data, interprets the parameters, and knows the limits of the fit.
Why it matters
It's the maths behind every claim from a study, and the limits are more important than the calculation.
What it looks like when it's wobbly
Reports a correlation coefficient with no sense of what it means or what the model can't do.
⏱️ Two-minute check
"What does r = 0.8 tell you? What does it not tell you?"
Solid looks like: Strong positive association, and explicitly not causation, nor validity outside the data range.
The full activity for this topic · 30 minutes
Fit It and Break It
- 1Collect or find a real paired data set of at least twenty points.
- 2Plot it, fit a line, and record the equation and r.
- 3Interpret the slope in real units.
- 4Predict a value inside the data range and one far outside it, and discuss which is defensible.
- 5Remove one outlier and refit — see how much the model moves.
If it's too hard
Fit by eye and interpret the slope.
If it's too easy
Compare a linear and an exponential fit to the same data and argue for one.
Say this
"That prediction is thirty years past your data. On what basis do you believe it?"