Question

Find the correlation coefficient for the data using the shortcut method for the following data.

$\begin{array}{cc}Quantity\left(X\right)& Profit\left(Y\right)\\ 150& 1600\\ 180& 1800\\ 210& 2000\\ 240& 2300\\ 250& 2500\end{array}$

• A. 0.986
• B. 0.945
• C. 0.875
• D. 0.824

Answer 1

The correct option is A

0.986

$Let{A}_x=210\&h_x=10Let{A}_y=2000\&h_y=100$

$\begin{array}{ccccccc}{X}_i& Y_i& U_i=\frac{X_i-A_x}{h_x}& V_i=\frac{Y_i-A_y}{h_y}& U_i^2& V_i^2& U_i{V}_i\\ 150& 1600& -6& -4& 36& 16& 24\\ 180& 1800& -3& -2& 9& 4& 6\\ 210& 2000& 0& 0& 0& 0& 0\\ 240& 2300& 3& 3& 9& 9& 9\\ 250& 2500& 4& 5& 16& 25& 20\\ & & \sum =-2& \sum =2& \sum =70& \sum =54& \sum =59\end{array}$

$r=\frac{N\sum \left(U_i{V}_i\right)–(\sum U_i)(\sum V_i)}{\sqrt{N\sum U_i^2–(\sum U_i{)}^2}\sqrt{N\sum V_i^2–(\sum V_i{)}^2}}=\frac{299}{18.6\times 16.31}=0.986$