A *scatter plot* shows the relationship between two variables. When looking at a scatter plot, you look at the *correlation*, which gauges the strength of the relationship and the direction. This means a correlation can be strong or weak and can be positive, negative, or neither.

Depending on the strength of the correlation, you can infer a trend in the relationship. The figure shown here illustrates some examples of scatter plots and the types of correlations that can appear. Notice how when there is a correlation, the points tend to line up in one direction.

A common example of a scatter plot is the relationship between people’s shoe sizes and their IQs. When a large data collection is analyzed, you see that there’s no correlation. If there were one, you could make a statement like “People with bigger shoe sizes are smarter.” However, there’s a wide range of IQs and shoe size combinations, and you can’t gauge a person’s intelligence based on his or her shoe size (no correlation).

## Practice question

- What statement corresponds to the relationship illustrated by the following scatter plot?
**A.**The longer you study, the worse you will do on the test.**B.**The longer you study, the better you will do on the test.**C.**The amount of time studying does not affect the score on the test.**D.**Not enough information can be gathered.

## Answer and explanation

- The correct answer is
**Choice (B).**Because the trend line, or line of best fit, of this scatter plot has a positive slope, there is a positive relationship between the variables. This means as one increases the other increases: the longer you study, the better you will do on the test, Choice (B) is correct. For there to be no relationship, the line of best fit would be a “flat” horizontal line. For a negative relationship, the slope would be negative or “pointing down.”