Regression Lines; Coefficients of Determination and Correlation
Brief Instructions
To set your calculator for finding determination and correlation coefficients, do the following: Press 2ND and 0 (zero). Put the triangle cursor next to DiagnosticOn. Then press ENTER twice.
Press STAT and ENTER. Enter the values of the first variable under L1 and the values of the second under L2. Make sure the pairings between numbers in the first and second variable remain the same as they were in the original data. Press STAT, choose CALC, select LinReg(ax+b) and press ENTER twice. The slope and y-intercept of the regression line are a and b, respectively. Write the equation of the regression line in the form of a linear equation without a’s or b’s. The coefficient of determination is r 2 and the correlation coefficient is r.
Detailed Instructions
To set your calculator up to find coefficients of determination and correlation, you must go through the following procedure.
Press
2ND and 0 (zero). This will bring up a list of all the procedures in the
calculator in alphabetical order. Use the down-arrow key to put the triangle
cursor next to DiagnosticOn.
Make sure you choose DiagnosticOn
and NOT DiagnosticOff.
Then press Enter twice. On your
calculator screen, you should see:
You should only need to do this procedure again if (1) your calculator is reset to the manufacturer’s default settings, or (2) you start using a different calculator.
To find
regression lines and coefficients of determination and correlation, you need to
be working with two variables with each value of the first variable paired with
one value of the second. For this demonstration, we will use the following
data:
|
1st
Variable |
5 |
6 |
8 |
9 |
12 |
15 |
|
2nd
Variable |
12 |
8 |
11 |
5 |
8 |
4 |
Press STAT and ENTER. Enter the numbers for the first variable under L1. Enter the numbers for the second
variable under L2. When you are finished,
the data entry screen should look like the following:
|
L1 |
L2 |
|
5 |
12 |
|
6 |
8 |
|
8 |
11 |
|
9 |
5 |
|
12 |
8 |
|
14 |
4 |
|
------ |
------ |
Notice that the first numbers are still paired with the same second numbers. If the pairing is changed, your results will most likely be wrong.
Now press STAT. Move the cursor to CALC and select LinReg(ax+b) using the down-arrow button. Pressing Enter twice will bring up the following display:
The equation of the regression line is thus y = -0.65x + 13.85. The coefficient of determination, 0.507, says that about 50% of the variation in the data is determined by the regression line. The correlation coefficient, -0.715, indicates a moderate negative correlation.
If your data is in some other lists besides L1 and L2, you could indicate those lists by pressing ENTER just one time after choosing LinReg(ax+b), then inputting the correct lists. If your data is in L4 and L5, you would press 2ND, 4, , (comma), 2ND, 5 and then ENTER to compute the regression line for those lists.