The Regression Line and Making Predictions
Fit the least-squares line through the data, read its gradient and intercept in the units of the problem, and predict only inside the range the data covers.
What a learner can do afterwards
- Interpret the gradient of a fitted line in the units of the situation
- Predict a value for an x inside the range of the data
- Explain why a prediction well outside that range is not supported
1 · Read
A fitted line reads y equals a plus b x. The intercept a is the predicted y when x hits zero. The gradient b is the predicted change in y for each extra unit of x. Both live in the units of the story, such as marks per hour. The line sums up average drift, and no single pupil must obey it.
A class line for marks on hours studied is y equals 5 plus 2 x. For 6 hours, swap in 6 to get 5 plus 12, which is 17 marks. The data cover x from 1 to 8, and 6 sits inside that range, so the value is supported.
Outside the observed range the line guesses into unknown land. Curves and ceilings may lurk there. Kim predicts at x equals 30 and trusts it fully, but 30 sits far past 8. State the value, then judge it: supported inside, unsupported outside.
Read the gradient in story units, predict inside the range, and distrust guesses far outside it.
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.