# Correlation Exploration

- Author:
- Steve Phelps, Tim Brzezinski

- Topic:
- Algebra, Correlation, Linear Regression

## Drag these points around. What do you notice? What do you wonder about? Enter your noticings and wonderings after the applet.

## Arrange these points so the value of r is as large as possible.

Describe the configuration or pattern of the points that produced the largest value of r you could find. What is this value of r?

## Arrange these points so the value of r is as small as possible.

Describe the configuration or pattern of the points that produced the smallest value of r you could find. What is this value of r?

## Arrange these points in a circle.

What is the value of r when the points are arranged in a circle? Try changing the radius of the circle on which your points are arranged. Does that change the value of r? What information do you think r is conveying?

## Arrange these points in the shape of the letter "V".

What is the value of r when the points are arranged in the shape of the letter "V"? Try changing the width of the "V" on which your points are arranged. Does that change the value of r? What information do you think r is conveying now? Have your changed your mind about what information r is conveying?

## Arrange these points on a horizontal line.

What is the value of r when the points are arranged in a horizontal line? What information do you think r is conveying now? Have your changed your mind about what information r is conveying?

## Arrange these points in the shape of the letter "U".

What is the value of r when the points are arranged in the shape of the letter "U"? Try changing the width of the "U" on which your points are arranged. Does that change the value of r? How does this compare to the letter "V" from above? What information do you think r is conveying now? Have your changed your mind about what information r is conveying?

## Arrange these points in the shape of a square.

What is the value of r when the points are arranged in the shape of a square? Does changing the size of the square change the value of r? What information do you think r is conveying now? Have your changed your mind about what information r is conveying?

## The values of r for different scatterplot shapes.

What information is conveyed by the value of r? What do all the patterns in the bottom row have a value of r equal to zero?

What is YOUR definition of r after completing this classroom activity?