Step by step
The question
Question: draw a scatter plot of (1, 9), (2, 8), (3, 8), (4, 5), (5, 6), (6, 3).
What is the correlation?
Correlation tells if y goes up or down as x goes up, and how closely.
1 Draw the axes
x goes along the bottom.
y goes up the side.
2 Plot the points
(1, 9): across to 1, then up to 9.
(2, 8): across 2, up 8.
And so on, one dot for each point.
3 Find the direction
We draw a line along the points.
It goes downhill: from top left to bottom right.
As x goes up, y goes down.
That is a negative correlation.
4 Find the strength
Two lines hold all the points.
The band is narrow: the points stay close to a straight line.
So the correlation is strong.
Careful!
A correlation shows that two things move together.
It does not prove that one causes the other.
So the answer: strong negative correlation.
5 Check
Let's check with numbers.
The 3 points on the left have a mean y of about 8.3.
The 3 on the right: about 4.7.
The right is lower: it goes down.
So it is right!
Let's look back.
First: draw the axes.
Then: plot the points.
Then: find the direction.
Then: find the strength.
Last: check.