Question

Find the value of the correlation coefficient from the following table :-

$\begin{array}{ccc}\text{S No}& \text{Age 'X'}& \text{Glucose Level 'Y'}\\ 1& 43& 99\\ 2& 21& 65\\ 3& 25& 79\\ 4& 42& 75\\ 5& 57& 87\\ 6& 59& 81\end{array}$

Answer 1

$\begin{array}{cccccc}\text{S No}& \text{Age 'X'}& \text{Glucose Level 'Y'}& XY& X^2& Y^2\\ 1& 43& 99& 4257& 1849& 9801\\ 2& 21& 65& 1365& 441& 4225\\ 3& 25& 79& 1975& 625& 6241\\ 4& 42& 75& 3150& 1764& 5625\\ 5& 57& 87& 4959& 3249& 7569\\ 6& 59& 81& 4779& 3481& 6561\\ Total& 247& 486& 20485& 11409& 40022\end{array}$

From our table :

$\sum x=247,\sum y=486,\sum xy=20,485,$

$\sum x^2=11,409,\sum y^2=40,022,{}^{\prime }{n}^{\prime }=6$

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x{)}^2\left]\right[n\sum y^2-(\sum y{)}^2]}}$

$r=6(20,485)-(247\times 486)/\left[6\right(11,409)-({247}^2\left)\right]\times \left[6\right(40,022)-{486}^2]$

$r=2868/5413.27=0.529809$

r = 0.5298

The range of the correlation coefficient is from -1 to 1.

Our result is 0.5298, which means the variables have a moderate positive correlation.