**Testing for Significant Linear Correlation; Regression
Lines; Coefficients of Determination and Correlation**

**Brief Instructions**

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 *TESTS*, then *LinRegTTest* and press *ENTER*. The *X-list* is L1, the *Y-List* is L2 and the *Freq* is 1. Choose ≠0 next to *β & ρ*: and leave the space next to *RegEQ:* blank. Choose *Calculate* and press *Enter*.

The test statistic is next to *t = and* the
P-value is next to *p =*. If the null hypothesis is rejected, the evidence
is strong enough to say there is significant linear correlation. If the null hypothesis is kept, the evidence is not strong enough to say there is significant linear correlation.

The *y-intercept*
of the regression is *a*
and the slope is *b*. Write the equation of the regression line in
the form of a linear equation without using *a* or *b*.

The coefficient of determination is *r ^{2}* and the correlation
coefficient is

**Detailed Instructions**

The TI 83/84 calculator is set up so that when you test for significant linear correlation, the equation of the regression line and the coefficients of determination and correlation are presented as by-products. To test for significant linear correlation, you need to be working with two variables such that each value of the first variable is paired with one value of the second variable. 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 *LinRegTTest* using the up-arrow or
down-arrow buttons. Pressing *Enter*
will bring up the following display:

Make sure L1 is next to *XList**:*, L2 is next to *YList**:* and 1 is next to *Freq:*. If your first variable is in some other list besides L1,
then you would enter that list next to XList. Similarly, if your second variable is in some
other list besides L2, you would enter that list next to YList.
Choose ≠0 next to *β &
ρ:* and leave the space next to *RegEQ:*
blank.

After highlighting *Calculate* and pressing *ENTER*,
you should have the following output on your calculator.

You will need to use the down-arrow and up-arrow buttons to see the entire output.

Since *a*
= 13.85 and *b* = -0.65, the equation
of the regression line is *y* = 13.85 -
0.65*x*. Notice that the equation of the regression
line does not contain *a*
or *b*.

The coefficient of determination, *r ^{2}* = 0.507, says that about
50.7% of the variation in the data is determined by the regression line.

The correlation coefficient, *r* = -0.715, indicates a moderate
negative correlation.