Problem

Find the correlation coefficient using the following information: \[ \begin{array}{l} S_{x x}=26 \\ S_{y y}=40 \\ S_{x y}=-4 \end{array} \] NOTE: Round your answer to TWO decimal places.

Solution

Step 1 :Given the following information: \(S_{xx} = 26\), \(S_{yy} = 40\), and \(S_{xy} = -4\).

Step 2 :We need to find the correlation coefficient, which is given by the formula \(r = \frac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}}\).

Step 3 :Substitute the given values into the formula: \(r = \frac{-4}{\sqrt{26 \cdot 40}}\).

Step 4 :Calculate the value of \(r\) and round it to two decimal places.

Step 5 :Final Answer: The correlation coefficient is \(\boxed{-0.12}\).

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Source: https://solvelyapp.com/problems/qPK8yqIXuw/

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