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Find the correlation coefficient of the following table using technology (such as GeoGebra). Round your answer to the nearest hundredth.

x y
2.3 19
3.1 28
4.5 33
6.6 82
(1 point)
Responses

1
1

0.88
0.88

−0.95
−
0.95
negative 0 point 9 5

0.95

1 answer

To find the correlation coefficient of the given data, we can use technology such as GeoGebra, Excel, or a calculator. However, I can guide you through the process conceptually and provide you with the expected answer.

Here are the steps to calculate the correlation coefficient (usually denoted as \( r \)) using a calculator or software:

  1. Input the Data: Enter the x and y values into your chosen software.

    x: 2.3, 3.1, 4.5, 6.6
y: 19, 28, 33, 82

  2. Calculate the Correlation Coefficient: Most tools have a function or formula for calculating correlation coefficients:

    • In GeoGebra, you can use the CorrelationCoefficient command.
    • In Excel, use the formula =CORREL(A1:A4, B1:B4) where A1:A4 are your x values and B1:B4 are your y values.

  3. Get the Result: After running the correlation function, you will retrieve the correlation coefficient \( r \).

When you calculate the correlation for the provided data, you should find that the correlation coefficient rounds to approximately 0.95.

So, the answer to the rounded nearest hundredth would be:

0.95