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Year 10AC9M10ST03

Scatterplots and Association

Construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity.

A scatterplot shows whether two variables move together. Describe it three ways: strength, direction, linearity.

Builds onYr 9 · Comparing Multiple Data Sets

Method

Explanatory variable goes on the horizontal axis
The one you think does the influencing.
Describe all three every time
strength⋅direction⋅linearity\text{strength} \cdot \text{direction} \cdot \text{linearity}
Direction alone is a partial answer.
Direction
positive: both risenegative: one falls\text{positive: both rise} \quad \text{negative: one falls}
Strength: how close to a line
Tight cluster is strong. Wide scatter is weak.
A line of best fit follows the trend
Roughly equal points above and below. It need not touch any.
Association is not causation
The single most misused conclusion in statistics.

Worked example

e.g. Hours studied against test score. Describe the association.\text{Hours studied against test score. Describe the association.}
  1. Put the explanatory variable on the horizontal axis.hours studied\text{hours studied}
  2. Plot the points and look at the overall pattern.
    A scatterplot of hours studied against test score with a line of best fitxyline of best fit
  3. State the direction. As hours rise, score rises.positive\text{positive}
  4. State the strength. The points sit close to a line.strong\text{strong}
  5. State the linearity. The pattern is a straight line, not a curve.linear\text{linear}
  6. Add the caution. This does not prove studying causes the score.association≠causation\text{association} \neq \text{causation}

Practice

Give strength, direction and linearity. Then state the caution.

1
Points scattered widely but trending down. Describe it.\text{Points scattered widely but trending down. Describe it.}
AnswerWeak, negative, roughly linear.\text{Weak, negative, roughly linear.}
2
Points forming a tight upward curve. Describe it.\text{Points forming a tight upward curve. Describe it.}
AnswerStrong, positive, non-linear.\text{Strong, positive, non-linear.}
3
Points with no pattern at all.\text{Points with no pattern at all.}
AnswerNo association.\text{No association.}
4
Ice cream sales and drownings both rise. Cause?\text{Ice cream sales and drownings both rise. Cause?}
AnswerNo. Hot weather drives both.\text{No. Hot weather drives both.}
5
Which variable goes on the horizontal axis?\text{Which variable goes on the horizontal axis?}
AnswerThe explanatory one.\text{The explanatory one.}
6
Must a line of best fit pass through a point?\text{Must a line of best fit pass through a point?}
AnswerNo. It follows the trend.\text{No. It follows the trend.}
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