Example
Before we look at real data, let’s talk about a different way of looking for relationships between variables. This is done by plotting the values of one variable on a graph where the X or horizontal axis represents one variable and the Y or vertical axis represents the other. This is called a scatterplot. Here is the scatterplot for the graph above with a special line fitted to it:
One way of measuring the strength of the relationship between two variables is to fit a line or curve like the one above and then measuring how close all the real points are to this line. If all of the points fell exactly on the line, the two variables are said to exactly correlated – a change in one variable produces an exactly known change in the other. To illustrate this correlation, go to:
https://www.stat.berkeley.edu/~stark/Java/Html/Correlation.htm
Drag the slider next to the "r" all the way to the right so that r = 1.0. Note that this shows a correlation of 1.0 and that the points all line up on the line. Now drag theslider until it is in the middle near 0.0. Notice that the points are scattered randomly and almost none are on the line. This is a correlation of 0 or there is no relationship. Now drag to -1.0. Notice that the points line up on the line again but the line is sloped in the opposite direction. As the first variable goes up, the other goes down. This is a perfect, negative correlation. Move the indicator around some more and see what the scatter looks like between 0 and 1 and 0 and -1. Numbers from 0.3 to 0.7 are called weak correlations and above 0.7 are called strong correlations.
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