STA015 · Probability & statistics · Classes 11–12
Regression line
The regression line (line of best fit) minimises the squared vertical distances from the points. Use it to predict y from x within the data range.
ŷ = mx + cRegression line
📐 Formula
slope = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)²; line passes through (x̄, ȳ)
✏️ Worked example
For the 10 points shown the least-squares line is y = 0.98x + 1.15.
🌍 Where it is used
Forecasting sales, estimating growth.
❓ Quick check
The regression line always passes through…
🏋️ Practice
EasyPredict y at x = 5 with y = 2x + 1.
Answer: 11
MediumIs predicting far outside the data safe?
Answer: No (extrapolation)
ChallengeSlope of y = 0.98x + 1.15?
Answer: 0.98