Correlation coefficients provide us with a single number that summarizes the relationship between two variables. We can also examine this type of relationship visually by creating a scattergram. A scattergram, which is also known as a scatterplot, shows the relationship between two variables graphically. A scatter plot is designed to show the relationship between two quantitative variables.
Usually, the graph is arranged with one variable running up and down the left side (the vertical or y-axis) and another variable runs along the bottom (the horizontal or x-axis). A dot is placed where the two variables intersect for each case. The final pattern we notice in the dots can reveal much information about the relationships between the two variables. If the dots form no discernable pattern and have a circular appearance on the graph, then we can say there is little or no relationship between the two variables.
If the dots form a line, then we have a strong relationship. Perfect relationships will form a perfect line, and moderate relationships will form a shape somewhat like a football. Because these relationships tend to form lines when graphed (or represented mathematically), they are known as linear relationships. We can determine the nature of the relationship by examining the slope of the line. If the pattern of dots forms a line from the lower left to the upper right side of the graph, then the relationship between the variables is a positive one. If the line runs from upper left to lower right, then the relationship is a negative one.
It is often helpful to draw a line through the center of the cluster of dots. This line gives us a clearer indication of the relationship between the two variables when the pattern of the dots is somewhat scattered out. The best such line—the one that fits best—can be determined mathematically. A line so determined is called a regression line. We will discuss regression in much more detail in a later section.
Last Modified: 06/03/2021