| Correlation Coefficient |
What is the correlation coefficient?
Correlation coefficient (r) is a measure of how strong a linear relationship is between two variables. It is always a number between -1 and +1. A value of -1 or +1 indicates a perfectly linear relationship. The +/- only indicates the direction of the slope of the line. A line with a correlation coefficient of +1.0 will be a perfectly straight line sloping upward and to the right. A line with a correlation coefficient of -1.0 will be a perfectly straight line sloping downward and to the right. The closer the correlation coefficient is to 1.0 (or -1.0 for a negatively sloping line), the better the correlation between the two variables. A coefficient of 0 means there is no relationship between the two variables.
Take a look at this correlation coefficient applet to see graph examples for different correlation coefficients.
How is the correlation coefficient determined?
The correlation coefficient can be calculated manually but it is a very involved and tedious process. It involves knowledge of statistics that you could find in any introductory statistics book as well as some high school math text books.
However, students can easily determine the correlation coefficient (r) for each of the 3 graphs if they use a spreadsheet program such as Excel or other computer program that has basic statistics functions.
Computer programs often will find the line of best fit including the equation of the line and correlation coefficient but may display r2 instead of r because it is a common way to measure the strength of a linear relationship without worrying about the positive or negative slope of the line. To find r, just take the square root but don't forget that the square root of a number can be positive or negative! You are welcome to compare either r or r2 for each of the graphs.
To find the correlation coefficient using Excel first make a scatter plot of the data. From the top menu, select CHART/ADD TREND LINE. Under TYPE select LINEAR and under OPTIONS check the boxes that allow you to display the equation and r2 value on chart. Click on OK and you should then see the trend line, equation, and r2 displayed on your graph.
What age student can determine the correlation coefficient?
Determining the correlation coefficient is a good way for students to objectively judge the strength of a linear relationship. Many students find it easier to rely on correlation coefficient comparisons instead of using their eyes to determine the strength of a relationship when determining which factor in the experiment has the greatest correlation to boiling point. Although correlation coefficient typically isn't introduced until high school level math courses, it is possible for younger students to understand what correlation coefficient is and how to use it to judge the strength of a relationship. However, it is up to you if you want your students to do this; it is not a required part of the project.
| "Using the correlation factor was useful even though my students did not understand the math involved. Excel gave R squared, and they used their graphing calculators to obtain R. Then all they really needed to know was that 1.0 meant a perfect correlation. At that point they were on a roll and did not like being unable to find R for the heating device!! "-- Middle School Teacher |
More Info and Examples
You can find out more about how to find correlation coefficient and see examples (including more java applets) using the Mathematics Resources links in the Reference Material section.
| Project Home Page |
Copyright © 2002 Stevens Institute of Technology, Center for Improved Engineering and Science Education, All Rights Reserved