# Scatter graph relationship

### What is a Scatter Plot and When to Use It

Purpose: Check for Relationship, A scatter plot (Chambers ) reveals relationships or association between two variables. Such relationships manifest. Strength refers to the degree of "scatter" in the plot. If the dots are widely spread, the relationship between variables is weak. If the dots are concentrated around. A scatter plot is a two-dimensional data visualization that uses dots to Scatter plots are used when you want to show the relationship between two variables.

The line of best fit for the scatter graph would look like this: Interpolation and extrapolation From the diagram above, we can estimate how many umbrellas would be sold for different amounts of rainfall. For example, how many umbrellas would be sold if there was 3mm of rainfall? What if there was 10mm of rainfall?

### Scatter (XY) Plots

To estimate the number sold for 3mm of rainfall, we use a process called interpolation. The value of 3mm is within the range of data values that were used to draw the scatter graph.

Find where 3 mm of rainfall is on the graph. Draw a line by going across from 3 mm and then down.

Writing a scatter plot as a relation

An estimated 19 umbrellas would be sold if there was 3 mm of rainfall. If there was 10mm of rainfall, we could extend the graph and the line of best fit to read off the number of umbrellas sold.

This gives a value of approximately 64 umbrellas sold. This process is called extrapolation, because the value we are using is outside the range of data used to draw the scatter graph.

## Scatter Plots

The relationship between two variables is called their correlation. Scatter plots usually consist of a large body of data. The closer the data points come when plotted to making a straight line, the higher the correlation between the two variables, or the stronger the relationship.

If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation. If the line goes from a high-value on the y-axis down to a high-value on the x-axis, the variables have a negative correlation. A perfect positive correlation is given the value of 1.

A perfect negative correlation is given the value of If there is absolutely no correlation present the value given is 0. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables.

## Describing scatterplots (form, direction, strength, outliers)

The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0.

An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go.