Practice Test
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The calculator will provide the slope and the y-intercept of the line of best fit. Use these values to write the equation.
Line of Best Fit: y=255.5x+622.2
Correlation Coefficient: 0.999
Interpretation: See solution.
Graphing calculators use linear regression to find a line of best fit. Calculators also give the correlation coefficient r. The value of r ranges from - 1 to 1, indicating how strong the correlation is and whether it is a positive or a negative correlation.
| Value of r | Type of Correlation |
|---|---|
| Close to - 1 | Strong negative correlation |
| Close to 1 | Strong positive correlation |
| Close to 0 | No correlation |
Let's start by considering the given data.
| Year, x | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|
| Number of AP Exams, y | 3698 | 3938 | 4176 | 4479 | 4705 |
We will use a calculator to find the equation of the line of best fit for the data points. Our first step is to enter the data from the table into our calculator. We do this by pressing the STAT button followed by ENTER. Enter the x-values in the first list and the y-values in the second list.
Next we press STAT again, go to the CALC menu, and press 4, which corresponds to linear regression.
Then, we scroll down and press ENTER on the option Calculate.
By doing this we obtain the slope and the y-intercept of the line of best fit, as well as the correlation coefficient.
To obtain the correlation coefficient using our calculator, we first need to make sure that we have turned on the proper settings. To do so, we push 2ND followed by . Then, we scroll down to DiagnosticOn
and push ENTER.
Now we are good to go!