Question

Find the correlation coefficient using Karl Pearson's formula for the following data.
$\begin{array}{cc}X& Y\\ 10& 2\\ 20& 7\\ 30& 9\\ 40& 11\\ 50& 16\\ 60& 21\end{array}$

• A. 0.588
• B. 0.785
• C. 0.894
• D. 0.986

Answer 1

The correct option is D

0.986

$\begin{array}{ccccc}{X}_i& Y_i& X_i^2& Y_i^2& X_i{Y}_i\\ 10& 2& 100& 4& 20\\ 20& 7& 400& 49& 140\\ 30& 9& 900& 81& 270\\ 40& 11& 1600& 121& 440\\ 50& 16& 2500& 256& 800\\ 60& 21& 3600& 441& 1260\\ \sum =210& \sum =66& \sum =9100& \sum =952& \sum =2930\end{array}$

$r=\frac{N{\sum }_{i=1}^n\left(X_i{Y}_i\right)–\left({\sum }_{i=1}^n{X}_i\right)\left({\sum }_{i=1}^n{Y}_i\right)}{\sqrt{N{\sum }_{i=1}^n{X}_i^2–({\sum }_{i=1}^n{X}_i{)}^2}\sqrt{N{\sum }_{i=1}^n{Y}_i^2–({\sum }_{i=1}^n{Y}_i{)}^2}}=\frac{3720}{102.47\times 36.82}=0.986$