Scatter-graphsHow to produce, describe and interpret a

scatter-graph

- Correlation - Line of Best Fit

Positive correlation

As one goes up...As one goes up...

The other goes upThe other goes up

Negative correlation

As one goes up...As one goes up...

The other goes downThe other goes down

Perfect positive correlationPerfect positive correlation

Weak positive correlationWeak positive correlation

No correlationNo correlation

Weak negative correlationWeak negative correlation

No correlationNo correlationNo correlationNo correlation

Line of Best FitLine of Best Fit““A line as close as possible to all A line as close as possible to all

points”points”

How?How?1) The line should have an equal number of points either side of it.

2)The line should go throughthe mean point(x-coordinate: mean of all x values,

y-coordinate: mean of all y values)

Optional

Line of Best FitLine of Best Fit““A line as close as possible to all A line as close as possible to all

points”points”

Why?Why?The line can be used to predict values:

Interpolation: Predicting values within the range covered.

Extrapolation: Predicting values outside the range covered.

Line of Best FitLine of Best Fit““Post hoc, ergo propter hoc”Post hoc, ergo propter hoc”

““After it, therefore because of it”After it, therefore because of it”Rarely trueRarely true

Just because two things are correlated doesn’t mean one causes the other.

Discuss

“If you spend a lot of time on the phone, you have a better chance of ending up in a high-paying job”

“The larger your shoe-size, the greater your bank overdraft”

“Learning maths makes you a better musician”

Positive, Negative or None?Remember: correlation doesn’t mean one thing causes the other – it just means there is a relationship between them.

Time spent travelling Distance covered

Level of education Level of income

Amount of clothing worn Temperature outside

Number of pages in a book Copies sold

Cost of car insurance Age of driver

Number of socks owned Number of cars owned