Pearson's correlation coefficient is used to measure the strength of the linear relationship between two variables.
The symbol for the correlation coefficient is r, and r is always somewhere between -1 and 1.
The limitations of r are:
- It can only be calculated for linear relationships.
- It is affected by outliers. An outlier is a number vastly different to all the other results. If you are trying to calculate the average (mean) of numbers, a hugely different number means that the results become skewed and are not necessarily a true representation of the data. This is the same for correlation coefficients. If there is an outlier, the correlation coefficient is unreliable.
What the r Value Means
strong positive linear association
moderate positive linear association
weak positive linear association
weak negative linear association
moderate negative linear association
strong negative linear association
How to Calculate the Correlation Coefficient on Ti-89 Calculator
- Press the APPS button
- Select stats/list editor
- Type the independent variable data into list1. The independent variable causes the dependent variable to change. For example, if you were finding out whether someone's age affects how happy they are, you would make the person's age the independent variable, because you are trying to find out if the age of a person changes their happiness levels.
- Type the dependent variable data into list2.
- Select F4: Calc
- Select 3: Regressions
- Select 2: Lin Reg (ax +b)
- Where it says "X list", type in list1 (with no spaces). You do this because you stored the independent variable in list 1, and the x-axis (the bottom horizontal line of a graph) always shows the independent variable.
- Where it says "Y list", type in list2 (no spaces).
- Where it says "Store RegEan to:", select any of the drop down options. It doesn't make a difference, there are just options so that you can re-access data later if you need it instead of saving on top of previously saved data you may still need.
- Press enter ONCE ONLY.
- After a few seconds, a box should pop up on your calculator screen. The r value is your correlation coefficient.
How to find the coefficient of determination on a TI 89 calculator
The coefficient of determination (r^2) is simply calculated by squaring the correlation coefficient. Just type in your correlation coefficient, then press ^2.
Nolan Wilkicki on March 30, 2017:
I only get R squared... :/
WD Curry 111 from Space Coast on April 10, 2012:
Hey! I am an artist. What do I need math for? You would be surprised.
I found it interesting to think about outliers, and often they affect results.