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### Types of Correlation

```Date: 06/25/2002 at 15:18:25
From: Katie
Subject: Correlation

Hello! I am really stuck on a question that deals with weak, strong,
positve, and negative correlation in scatter plots. You have a post
didn't help.

In the problem it shows you a scatter plot and it asks you to tell
what kinda of correlation is shown. If you could just tell me what all
this correlation stuff is about I think I can get it from there.

Thanks!
```

```
Date: 06/25/2002 at 22:54:42
From: Doctor Achilles
Subject: Re: Correlation

Hi Katie,

Thanks for writing to Dr. Math.

A correlation is when two variables are related.  That definition is
probably not terribly helpful, so let me give you a few examples.

First, there is a positive correlation between the amount of
education a person has and the amount of money that person makes (at
least I hope there is, since I'm a college student).  That is really
just a fancy way of saying: "On average, if someone has more
education, then that person will make more money."

You might graph that using a scatter plot by taking a random sample
of people, finding out how much money they make and asking how much
education they have.  Then for each person you put a point down.
The farther to the right the point is, the more education that person
has; the higher up the point is the more money that person makes.
I've made up some data that look like this:

|       .
|            . ..
m  |           ...
o  |         .   .
n  |  .    .
e  |          .
y  | ...
| .  .
|   .
-----------------

education

Notice that the highest paid person actually only has about an
average education.  But still, on average more education means more
money.  So there is a POSITIVE correlation between education and
money.

For another example, let's look at the relationship between the
number of cars on the freeway and the average speed.  Here's my

|   .   .
|.
s  |   . .
p  |      .
e  |      .
e  |          .
d  |   .     .
|           ..
|            ..
-----------------

number of cars

Again, there are a few exceptions, but for the most part, the more
cars there are, the slower the average speed. (Think of rush hour,
when there are a lot of cars but everyone goes really slowly.)  This
means that there is a NEGATIVE correlation between the number of cars
and the average speed.

Finally, let's imagine that we go to a mall and take a survey.  What
we do is we ask random people to tell us their height.  Then we look
to see if there is any correlation between the answer they give and
the time of day it is.  Here's my made up scatter plot:

|       .
|    .
h  |    .  ..
e  |         .   .
i  |  .    .
g  |          .
h  |      .     .
t  | .  .
|   .     ..
-----------------

time of day

This time the points are all over.  There doesn't seem to be any
relationship at all.  So we answer that there is NO correlation
here.

As far as strong vs. weak correlations, that just has to do with how
many exceptions there are to the general rule.  The examples of car
speed and money are moderate or weak correlations.  Here's a very
strong (positive) correlation:

|                .
|              .
|            .
|          .
A  |        .
|      .
|    .
|  .
|.
-------------------

B

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/26/2002 at 16:15:36
From: Katie
Subject: Thank you (Correlation)

examples really helped!

-Katie
```
Associated Topics:
High School Statistics
Middle School Statistics

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