Question

Use the table to answer the question.
This table shows the corresponding y-values for a given set of x -values.
x-values y-value
1 23
5 27
7 32
11 35
15 39
17 43
Find the correlation coefficient of the data using technology ( such as GeoGebra). Round your r- value to two decimal places, if necessary.

Answer 1

To find the correlation coefficient \( r \) for the given data, you will typically use a calculator or software that supports statistical functions, such as GeoGebra, Excel, or a graphing calculator. Here, I'll outline how to find the correlation coefficient using general steps:

1. **Input the Data**: Enter the x-values and y-values into the software you are using. For your data:

| x | y |
|---|---|
| 1 | 23 |
| 5 | 27 |
| 7 | 32 |
| 11 | 35 |
| 15 | 39 |
| 17 | 43 |

2. **Calculate the Correlation Coefficient**: Look for the statistical function that calculates the correlation coefficient. In most software, this will involve selecting the dataset and choosing an option for correlation or regression analysis.

3. **Retrieve the Result**: After performing the calculation, the software will return the correlation coefficient \( r \).

Since I cannot run software directly, I suggest using the steps above with GeoGebra or your preferred software. If you were to run the calculations properly, you’d find that the correlation coefficient for the provided dataset is approximately:

\( r \approx 0.99 \)

This indicates a very strong positive linear relationship between the x-values and y-values in the dataset. Always remember to round to two decimal places as instructed if necessary.