**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

**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:

1 |
5 |
6 |
8 |
9 |
12 |
15 |

2 |
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*
= -0.65*x* + 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.