Step by step
The question
Question: draw a scatter plot of (1, 7), (2, 3), (3, 6), (4, 2), (5, 4), (6, 1).
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, 7): across to 1, then up to 7.
(2, 3): across 2, up 3.
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 wide: the points are spread out from the line.
So the correlation is weak.
Careful!
A correlation shows that two things move together.
It does not prove that one causes the other.
So the answer: weak negative correlation.
5 Check
Let's check with numbers.
The 3 points on the left have a mean y of about 5.3.
The 3 on the right: about 2.3.
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.