Correlation tests for a relationship between two variables.

Causation means that one thing "causes" another

Study Time and Grades

As study hours increase, grades increase. There is a positive correlation between hours and grades.

So....Do hours spent studying cause higher grades?

Ice Cream Sales and Shark Attacks

As ice cream sales increase, shark attacks increase. As ice cream sales decrease, shark attacks decrease.

So....ice cream sales cause shark attacks?

​Correlation vs. Causation

​Causation means that x makes y happen. For example, the more cash you spend, the less cash you will have. This example has a correlation AND causation.

BUT… Correlation ≠ Causation.

Example: There may be a correlation between the number of glue sticks in a classroom and the number of students in a classroom. However, adding glue sticks to a classroom does not make more students be in the classroom.

​Types of Correlation

​Correlation Coefficient (r)

Correlation Coefficient ​(r) describes the strength and direction of the correlation.

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​r values can not be less than -1 or greater than +1. This can be written as the inequality  -1 < r < 1

The closer to 0, the weaker the correlation. Very close to 0 is no correlation. The closer to -1 or 1, the stronger the correlation. -1 and 1 are perfect.

Correlation coefficient (r) formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where:

• 1 indicates a strong positive relationship.

• -1 indicates a strong negative relationship.

• A result of zero indicates no relationship at all.

To show the overall trend of a data set, we can use a ​Line of Best Fit.

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A line of best fit should:

• Follow the trend of the data

• Split the data in half

• Help to estimate or predict values that are not already given in the set.

Line of Best Fit

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​outlier

cluster