Correlation and linear regression

Read correlation with the scatter · Diagrams

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Five coefficient cases

Compare five correlation cases

Compare the patterns below.

Perfect negative · r = −1

3 points

Perfect negative · r = −1. Inspect the shape as well as the direction.

Negative · −1 < r < 0

3 points

Negative · −1 < r < 0. Inspect the shape as well as the direction.

Zero linear correlation · r = 0

8 points

Zero linear correlation · r = 0. Inspect the shape as well as the direction.

Positive · 0 < r < 1

3 points

Positive · 0 < r < 1. Inspect the shape as well as the direction.

Perfect positive · r = +1

3 points

Perfect positive · r = +1. Inspect the shape as well as the direction.

Schematic illustrations: positions are not measured observations. No numerical data or calculated correlation is implied.
The coefficient labels retain the roles stated in the source, not values computed from these schematic positions.
Zero linear correlation does not imply independence or no relationship.

Five schematic panels reproduce the source roles: perfect negative, imperfect negative, zero linear correlation with a curved arrangement, imperfect positive, perfect positive. The imperfect panels show scatter around the drawn line. These are schematic, not supplied numerical observations.

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