Question

A manufacturer of optical lenses has the following data on the cost per unit (in Rs.) of a certain custom made lenses and the number of units made in each order:
$\begin{array}{ccccccc}\text{Order No.}& 1& 2& 3& 4& 5& 6\\ \text{Number of units}& 2& 3& 5& 8& 11& 13\\ \text{Cost per unit}& 55& 52& 49& 45& 41& 36\end{array}$
What will be the value of correlation coefficient?

• A. -0.999
• B. -0.990
• C. -0.994
• D. 0.990

Answer 1

The correct option is C -0.994

$\begin{array}{cccccc}\text{Order No.}& x& y& xy& x^2& y^2\\ 1& 2& 55& 110& 4& 3025\\ 2& 3& 52& 156& 9& 2704\\ 3& 5& 49& 245& 25& 2401\\ 4& 8& 45& 360& 64& 2025\\ 5& 11& 41& 451& 121& 1681\\ 6& 13& 36& 468& 169& 1296\\ Total& \sum x=42& \sum y=278& \sum xy=1790& \sum x^2=392& \sum y^2=13132\end{array}$
Correlation coefficient $r=\frac{n\sum xy-(\sum x\left)\right(\sum y)}{\sqrt{[n\sum x^2-(\sum x{)}^2]}\sqrt{n\sum y^2-(\sum y{)}^2}}$
$=\frac{6\times 1790-42\times 278}{\sqrt{(6\times 392-{42}^2)}\sqrt{(6\times 13132-{278}^2)}}$
$r=-0.994$