Question

The following table contains the quantities of a good produced by a firm and the corresponding profits in rupees. Find the correlation coefficient for the data using the shortcut method.

$\begin{array}{cc}Quantity\left(X\right)& Profit\left(Y\right)\\ 250& 10000\\ 500& 12000\\ 750& 15000\\ 1000& 20000\\ 1250& 17000\\ 1500& 16000\end{array}$

• A. 0.65
• B. 0.75
• C. 0.85
• D. 0.95

Answer 1

The correct option is B

0.75

$Let{A}_x=1000\&h_x=15000Let{A}_y=250\&h_y=1000$

$\begin{array}{ccccccc}{X}_i& Y_i& U_i=\frac{X_i-A_x}{h_x}& V_i=\frac{Y_i-A_y}{h_y}& U_i^2& V_i^2& U_i{V}_i\\ 250& 10000& -3& -5& 9& 25& 15\\ 500& 12000& -2& -3& 4& 9& 6\\ 750& 15000& -1& 0& 1& 0& 0\\ 1000& 20000& 0& 5& 0& 25& 0\\ 1250& 17000& 1& 2& 1& 4& 2\\ 1500& 16000& 2& 1& 4& 1& 2\\ & & \sum =-3& \sum =0& \sum =19& \sum =64& \sum =25\end{array}$

$r=\frac{N\sum \left(U_i{V}_i\right)–(\sum U_i)(\sum V_i)}{\sqrt{N\sum U_i^2–(\sum U_i{)}^2}\sqrt{N\sum V_i^2–(\sum V_i{)}^2}}=\frac{150}{10.25\times 19.6}=0.747$