Question

The quantity of goods produced and costs incurred by a firm are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

$\begin{array}{cc}\text{Quantity produced}& \text{Total cost}\\ 10& 120\\ 20& 230\\ 30& 315\\ 40& 425\\ 50& 510\end{array}$

• A. 0.85
• B. 0.93
• C. 0.97
• D. 0.99

Answer 1

The correct option is D

0.99

$\begin{array}{ccccc}{X}_i& Y_i& X_i^2& Y_i^2& X_i{Y}_i\\ 10& 120& 100& 14400& 1200\\ 20& 230& 400& 52900& 4600\\ 30& 315& 900& 99225& 9450\\ 40& 425& 1600& 180625& 17000\\ 50& 510& 2500& 260100& 25500\\ \sum =150& \sum =1600& \sum =5500& \sum =607250& \sum =57750\end{array}$

$r=\frac{N{\sum }_{i=1}^n\left(X_i{Y}_i\right)–\left({\sum }_{i=1}^n{X}_i\right)\left({\sum }_{i=1}^n{Y}_i\right)}{\sqrt{N{\sum }_{i=1}^n{X}_i^2–({\sum }_{i=1}^n{X}_i{)}^2}\sqrt{N{\sum }_{i=1}^n{Y}_i^2–({\sum }_{i=1}^n{Y}_i{)}^2}}=\frac{48750}{70.71\times 690.11}=0.999$