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Use the table to answer the question.

This table shows the corresponding y-values for a given set of x-values.
x-Value 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.

(1 point)
r=

1 answer

To calculate the correlation coefficient (r) using a set of data, you can use technology like GeoGebra, Excel, or a scientific calculator. However, since I'm unable to compute directly here, I can guide you through how to find it.

  1. Enter Data: Input your x-values and y-values from the table into the software.

    • x-values: [1, 5, 7, 11, 15, 17]
    • y-values: [23, 27, 32, 35, 39, 43]

  2. Use the Function for Correlation:

    • In Excel, you would use the function =CORREL(array1, array2), where array1 is the range of x-values and array2 is the range of y-values.
    • In GeoGebra, you can use the command CorrelationCoefficient(list1, list2) where list1 and list2 are your data lists.

  3. Calculate: After inputting the data and invoking the correlation function, you will receive a value.

Based on the provided data, you should find the correlation coefficient (r). The expected result, given the linear trend visible in your data, is likely to be close to 1.

If you ran these calculations, you could expect a high positive correlation indicating that as x increases, y also increases.

For clarity, if you find the correlation coefficient \( r \) using technology, it is expected to be approximately:

  • r = 0.99 (as a sample value based on a presumed strong positive linear relationship).

Ensure you input and calculate accurately with your chosen technology!