Worked examples
The question
Question: draw a scatter plot of (1, 2), (2, 4), (3, 5), (4, 4), (5, 7), (6, 8).
What is the correlation?
(1, 2) (2, 4) (3, 5) (4, 4) (5, 7) (6, 8)
Correlation tells if y goes up or down as x goes up, and how closely.
correlation: does y go up or down as x goes up?
1 Draw the axes
x goes along the bottom.
y goes up the side.
2 Plot the points
(1, 2): across to 1, then up to 2.
(2, 4): across 2, up 4.
And so on, one dot for each point.
3 Find the direction
We draw a line along the points.
It goes uphill: from bottom left to top right.
As x goes up, y goes up too.
That is a positive correlation.
uphill ↗ → positive
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.
narrow band → strong
Careful!
A correlation shows that two things move together.
It does not prove that one causes the other.
Careful: correlation does not prove one causes the other
So the answer: strong positive correlation.
= strong positive correlation
5 Check
Let's check with numbers.
The 3 points on the left have a mean y of about 3.7.
The 3 on the right: about 6.3.
The right is higher: it goes up.
So it is right!
mean y: left ≈ 3.7, right ≈ 6.3
Let's look back.
First: draw the axes.
Then: plot the points.
Then: find the direction.
Then: find the strength.
Last: check.
Answer = strong positive correlation
▶ Watch it solved
The question
Question: draw a scatter plot of (1, 3), (2, 6), (3, 2), (4, 7), (5, 4), (6, 8).
What is the correlation?
(1, 3) (2, 6) (3, 2) (4, 7) (5, 4) (6, 8)
Correlation tells if y goes up or down as x goes up, and how closely.
correlation: does y go up or down as x goes up?
1 Draw the axes
x goes along the bottom.
y goes up the side.
2 Plot the points
(1, 3): across to 1, then up to 3.
(2, 6): across 2, up 6.
And so on, one dot for each point.
3 Find the direction
We draw a line along the points.
It goes uphill: from bottom left to top right.
As x goes up, y goes up too.
That is a positive correlation.
uphill ↗ → positive
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.
wide band → weak
Careful!
A correlation shows that two things move together.
It does not prove that one causes the other.
Careful: correlation does not prove one causes the other
So the answer: weak positive correlation.
= weak positive correlation
5 Check
Let's check with numbers.
The 3 points on the left have a mean y of about 3.7.
The 3 on the right: about 6.3.
The right is higher: it goes up.
So it is right!
mean y: left ≈ 3.7, right ≈ 6.3
Let's look back.
First: draw the axes.
Then: plot the points.
Then: find the direction.
Then: find the strength.
Last: check.
Answer = weak positive correlation
▶ Watch it solved
The question
Question: draw a scatter plot of (2, 9), (3, 4), (5, 8), (6, 3), (8, 6), (9, 2).
What is the correlation?
(2, 9) (3, 4) (5, 8) (6, 3) (8, 6) (9, 2)
Correlation tells if y goes up or down as x goes up, and how closely.
correlation: does y go up or down as x goes up?
1 Draw the axes
x goes along the bottom.
y goes up the side.
2 Plot the points
(2, 9): across to 2, then up to 9.
(3, 4): across 3, up 4.
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.
downhill ↘ → negative
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.
wide band → weak
Careful!
A correlation shows that two things move together.
It does not prove that one causes the other.
Careful: correlation does not prove one causes the other
So the answer: weak negative correlation.
= weak negative correlation
5 Check
Let's check with numbers.
The 3 points on the left have a mean y of about 7.
The 3 on the right: about 3.7.
The right is lower: it goes down.
So it is right!
mean y: left ≈ 7, right ≈ 3.7
Let's look back.
First: draw the axes.
Then: plot the points.
Then: find the direction.
Then: find the strength.
Last: check.
Answer = weak negative correlation
▶ Watch it solved
