Compute the correlation coefficient for the data below

$\begin{array}{|c|c|c|c|c|c|}
\hline \text { X values } & -5 & -2 & 1 & 4 & 4 \
\hline \text { Y values } & 3 & -1 & -3 & 3 & -2 \
\hline
\end{array}$
A) 0.521
B) 0.368
C) -0.271
D) -0.058

Question

Compute the correlation coefficient for the data below

$\begin{array}{|c|c|c|c|c|c|}
\hline \text { X values } & -5 & -2 & 1 & 4 & 4 \
\hline \text { Y values } & 3 & -1 & -3 & 3 & -2 \
\hline
\end{array}$
A) 0.521
B) 0.368
C) -0.271
D) -0.058

Quizplus · Accepted Answer

We can use the formula for correlation coefficient:

$r = \dfrac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}}$

First, we need to find the means of x and y:

$\bar{x} = \dfrac{\sum_{i=1}^{n}x_i}{n} = \dfrac{-5 - 2 + 1 + 4 + 4}{5} = \dfrac{2}{5}$

$\bar{y} = \dfrac{\sum_{i=1}^{n}y_i}{n} = \dfrac{3 - 1 - 3 + 3 - 2}{5} = \dfrac{0}{5} = 0$

Next, we can plug in the values:

$r = \dfrac{(-5 - \dfrac{2}{5})(3 - 0) + (-2 - \dfrac{2}{5})(-1 - 0) + (1 - \dfrac{2}{5})(-3 - 0) + (4 - \dfrac{2}{5})(3 - 0) + (4 - \dfrac{2}{5})(-2 - 0)}{\sqrt{((-5-\dfrac{2}{5})^2 + (-2-\dfrac{2}{5})^2 + (1-\dfrac{2}{5})^2 + (4-\dfrac{2}{5})^2 + (4-\dfrac{2}{5})^2)}\sqrt{(3-0)^2+(-1-0)^2+(-3-0)^2+(3-0)^2+(-2-0)^2}} = \dfrac{-\frac{90}{5}}{\sqrt{\frac{598}{25}}\sqrt{23}} \approx -0.271$

Therefore, the best choice is C, -0.271.

Compute the Correlation Coefficient for the Data Below A) 0521 B) 0

Compute the Correlation Coefficient for the Data Below A) 0521
B) 0