Compute r, the correlation coefficient, using the following data. x657318y3536103 r=?

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gonjenjemeb

Answered question

2021-11-27

Compute r, the correlation coefficient, using the following data.

\begin{array}{cc} x & 6 & 5 & 7 & 3 & 1 & 8 \\ y & 3 & 5 & 3 & 6 & 10 & 3 \end{array}

r = ?

Answer & Explanation

Roger Noah

Beginner2021-11-28Added 17 answers

Step 1
$M_{x} = Mean of X Values = \frac{\sum_{i}^{x_{i}}}{n} = \frac{(6 + 5 + 7 + 3 + 1 + 8)}{6} = \frac{30}{6} = 5$
$M_{y} = Mean of Y Values = \frac{\sum_{i}^{y_{i}}}{n} = \frac{(3 + 5 + 3 + 6 + 10 + 3)}{6} = \frac{30}{6} = 5$
Step 2
$\begin{array}{cc} X - M_{x} & Y - M_{y} & (X - M_{x})^{2} & (Y - M_{y})^{2} & (X - M_{x}) (Y - M_{y}) \\ 1 & - 2 & 1 & 4 & - 2 \\ 0 & 0 & 0 & 0 & 0 \\ 2 & - 2 & 4 & 4 & - 4 \\ - 2 & 1 & 4 & 1 & - 2 \\ - 4 & 5 & 16 & 25 & - 20 \\ 3 & - 2 & 9 & 4 & - 6 \\ M_{x} = 5 & M_{y} = 5 & \sum = S S_{x} = 34 & \sum = S S_{y} = 38 & \sum = \sum (X - M_{x}) (Y - M_{y}) = - 34 \end{array}$
$r = \frac{\sum (X - M_{x}) (Y - M_{y})}{\sqrt{(S S_{x}) (S S_{y})}} = \frac{- 34}{\sqrt{34 \times 38}} = - 0.9459 \approx - 0.946$
Answer: -0.946

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