**Scatterplots, Association, & Correlation**

**AP Stats - Chapter 7**

What are scatterplots?

Here's a short example of a scatterplot if you need it.

At the end, they talked about "correlation". What's that all about?

IMPORTANT!!!!

The term "correlation" is one of the most misused words in the English language.

Here are some examples that describe assiciation in direction and strength.

This scatterplot has a strong positive association.

This scatterplot has a strong negative association.

This scatterplot has a weaker positive association than the first example.

This scatterplot has no assiciation.

For each of these you should also say that they have a LINEAR association.

Here's an example of a scatterplot that does NOT have a linear association.

Describing the Variables

The x-variable is called the EXPLANITORY variable.

The y-variable is called the RESPONSE variable.

So if I'm supposed to use "association" to describe the direction and strength of a scatterplot. When do I use "correlation", what is correlation, and how do I find it?

The Correlation Coefficient!

Here are some other characteristics of the Correlation Coefficient, r

1. Correlation is sensitive to outliers.

2. It can only go from -1 to 1.

3. The closer to -1 or 1 the stronger the linear association.

4. The sign on the correlation coefficient gives the direction.

How do I calculate r, the correlation coefficient?

TIME OUT!!!!

Before you are allowed to find and use the correlation coefficient you need to check 3 conditions.

1. The quantitative variables condition - Make sure your data are quantitative variables. r only works for quantitative data.

2. The straight enough condition - Look at the scatterplot and make sure it is straight enough for you. It shouldn't have an obvious curve.

3. The Outlier Condition - If there is an outlier, you need to find r for the data with AND without the outlier.

If I check all of those conditions, THEN can I find the correlation coefficient, r?

Yes! Mr. Mays will show you how it is found by hand, but most of the time you will find it with your calculator.

5. Correlation has no units.

"Correlation" is a precise term describing the strength and direction of the linear relationship of two quantitative variables.

"Association" is a deliberately vague term describing teh relationship between two variables.

For example, if someone were to say, "There appears to be a strong correlation between wearing glasses and being color blind." They would be using the term correlation in the wrong way.

What should be said is, "There appears to be a strong ASSOCIATION between wearing glasses and being color blind." Correlation is a number that give direction and strength.

Here's a video showing how to make scatterplots on your calculator. We will cover the stuff after the 2:10 mark in the video at a later time.

This flipped lecture had videos with someone other than Mr. Mays. What did you think of that?

Mr. Mays is curious.

See you in stats class.