Mistake Master
Predicted, On Average, Inside the Range
You'll learnwhat the hat on a predicted value means, the four elements a slope interpretation is graded on, when the intercept means something and when it is an extrapolation in disguise, how to make a prediction, and why the arithmetic keeps working long after the prediction stops meaning anything.
A regression line turns an association into a prediction rule: score = 58.5 + 3.5 · hours. The two sentences that interpret it are graded on two words each — predicted, and on average — and this page lets the data do the grading. The line says 83 at seven hours, and the seven-hour student scored 86, so "will score 83" is refuted by the very cloud the line came from. Then the other boundary: at 20 hours the equation returns 128.5 points on an exam whose maximum is 100. The arithmetic is fine and the prediction is worthless, and where those two facts part company is what this topic is about. Twelve short steps; press Next for each one.