Math PicnicEvery sheet is a promise

The line of best fit, step by step

A line through a scatter plot is only useful once you can say what its two numbers mean.

Practice Practice sheetNew questions
The question
Practice and test scores
Hours practicedScore

In y = 0.25x + 4, what does 4 mean?

points at 0 hourspoints per hourhours at 0 pointstotal points

In y = 0.25x + 4, what does 4 mean?

Hours practicedvsScore
In y = 0.25x + 4, what does 4 mean?
points at 0 hours
points at 0 hours
  1. A scatter plot puts two measurements against each other: Hours practiced along the bottom, Score up the side, and one dot for each thing measured. A line has been drawn through them — the line of best fit — and this question is about THAT line rather than about any one dot.
  2. The number on its OWN is the intercept — what the line says when x is nothing at all. Put a zero in for x and every term with an x in it disappears, leaving just that number.
  3. So it is points at 0 hours: the value the line gives at zero Hours practiced. Worth asking whether zero is a sensible thing to have here — often the line is only honest across the range the dots actually cover.
  4. So the answer is "points at 0 hours". Say what that means for the two things rather than for the graph — and remember it is not a claim that one CAUSES the other. Two measurements can move together for a reason that is nothing to do with either of them.

How it works.

  1. 01

    A scatter plot puts two measurements against each other: Hours practiced along the bottom, Score up the side, and one dot for each thing measured. A line has been drawn through them — the line of best fit — and this question is about THAT line rather than about any one dot.

  2. 02

    The number on its OWN is the intercept — what the line says when x is nothing at all. Put a zero in for x and every term with an x in it disappears, leaving just that number.

  3. 03

    So it is points at 0 hours: the value the line gives at zero Hours practiced. Worth asking whether zero is a sensible thing to have here — often the line is only honest across the range the dots actually cover.

  4. 04

    So the answer is "points at 0 hours". Say what that means for the two things rather than for the graph — and remember it is not a claim that one CAUSES the other. Two measurements can move together for a reason that is nothing to do with either of them.

Pick another skill