Step by step
The question
Question: find the correlation coefficient r for (2, 5), (4, 1), (6, 7), (8, 3).
r is a number from negative 1 to 1.
It tells how close the points are to a straight line, going up or down.
1 Find the means
The mean of the x numbers: 20 divided by 4 is 5.
The mean of the y numbers: 16 divided by 4 is 4.
2 Make the table
A table with the points.
How far each point is from the means.
2 minus 5 is −3, and 5 minus 4 is 1.
These distances always add up to 0.
A good check.
The product: the two distances multiplied.
−3 times 1 is −3.
And each distance squared.
−3 squared is 9.
1 squared is 1.
We add the last three columns: 0, 20 and 20.
3 Put them in the rule
The rule: the total of the products, over the square root of the two totals of squares multiplied.
We put the totals in: 0 on top.
20 times 20 under the root.
Careful!
Do not forget the square root.
Without it, r comes out far too small.
4 Work it out
20 times 20 is 400.
The square root of 400 is 20.
So r is 0/20.
0 divided by 20 is 0.
5 What r tells us
On a scale from negative 1 to 1.
r is here, at 0.
r is close to 0: no correlation.
The points do not follow a line.
6 Check
Let's check.
The products add up to 0, so r must be 0.
It is.
And r is between negative 1 and 1.
So it makes sense!
Let's look back.
First: find the means.
Then: make the table.
Then: put them in the rule.
Then: work it out.
Then: what r tells us.
Last: check.