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Year 9AC9M9ST04

Scatter Plots and Correlation

Choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context.

A scatter plot shows two things about each person or item at once. The pattern tells you whether they are linked.

Method

Positive correlation
as x↑, y↑\text{as } x \uparrow,\ y \uparrow
Points rise from left to right.
Negative correlation
as x↑, y↓\text{as } x \uparrow,\ y \downarrow
Points fall from left to right.
No correlation
no pattern\text{no pattern}
Points scattered with no clear direction.
Line of best fit
y=mx+cy = mx + c
A straight line drawn through the middle of the pattern.

Worked example

e.g. hours studied against test score for 8 people\text{hours studied against test score for 8 people}
  1. Plot each pair as one point(1;42), (2;48), …(1;42),\ (2;48),\ \ldots
    Eight points rising from left to righthours studiedscore
  2. Look at the direction. These rise from left to rightpositive correlation\text{positive correlation}
  3. Draw a line of best fit through the middle of the points. Roughly as many above as belowy≈6x+36y \approx 6x + 36
    The same points with a line of best fit drawn through themhours studiedscore
  4. Use the line to predict. At 4.5 hours, read off about 63y≈63y \approx 63
  5. Say how strong it is. Points close to the line means a strong linkstrong positive correlation\text{strong positive correlation}

Common mistakes

WrongCorrelation means one thing causes the other\text{Correlation means one thing causes the other}
RightCorrelation only means they move together\text{Correlation only means they move together}
Ice cream sales and sunburn rise together, but ice cream does not cause sunburn. Hot weather causes both. Never claim cause from a scatter plot alone.
WrongJoining the points dot to dot\text{Joining the points dot to dot}
RightOne straight line through the middle\text{One straight line through the middle}
The line of best fit is a single straight line showing the trend, not a zigzag connecting every point.
WrongPredicting far outside the data\text{Predicting far outside the data}
RightOnly predict inside the range you measured\text{Only predict inside the range you measured}
The line may not continue the same way. Predicting a score for 40 hours of study from data that stops at 8 is not reliable.

Practice

Describe the correlation you would expect:

1
Hours of exercise and resting heart rate\text{Hours of exercise and resting heart rate}
AnswerNegative\text{Negative}
2
Height and shoe size\text{Height and shoe size}
AnswerPositive\text{Positive}
3
Shoe size and test score\text{Shoe size and test score}
AnswerNone\text{None}
4
Age of a car and its value\text{Age of a car and its value}
AnswerNegative\text{Negative}
5
Number of pages and weight of a book\text{Number of pages and weight of a book}
AnswerPositive\text{Positive}
6
Using y=6x+36, predict the score for x=5\text{Using } y = 6x + 36, \text{ predict the score for } x = 5
Answer6666
7
Using y=6x+36, predict the score for x=2\text{Using } y = 6x + 36, \text{ predict the score for } x = 2
Answer4848
8
A plot shows points falling steeply, all close to the line. Describe it\text{A plot shows points falling steeply, all close to the line. Describe it}
AnswerStrong negative correlation\text{Strong negative correlation}
9
Why can you not say more study CAUSES higher marks from this plot?\text{Why can you not say more study CAUSES higher marks from this plot?}
AnswerCorrelation is not causation — something else may explain both\text{Correlation is not causation — something else may explain both}
10
Would you use this line to predict a score for 30 hours?\text{Would you use this line to predict a score for 30 hours?}
AnswerNo — that is far outside the measured range\text{No — that is far outside the measured range}
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