Question

The following table contains the cost of 5 motorcycles and their corresponding mileages in (km/litre). Find the correlation coefficient using the shortcut method.

$\begin{array}{cc}\text{Cost (X)}& \text{Mileage (Y)}\\ 50000& 40\\ 100000& 30\\ 150000& 25\\ 200000& 15\\ 250000& 10\end{array}$

• A. 0.95
• B. -0.95
• C. 0.99
• D. -0.99

Answer 1

The correct option is D

-0.99

$Let{A}_x=150000\&h_x=50000Let{A}_y=25\&h_y=5$

$\begin{array}{ccccccc}{X}_i& Y_i& U_i=\frac{X_i-A_x}{h_x}& V_i=\frac{Y_i-A_y}{h_y}& U_i^2& V_i^2& U_i{V}_i\\ 50000& 40& -2& 3& 4& 9& -6\\ 100000& 30& -1& 1& 1& 1& -1\\ 150000& 25& 0& 0& 0& 0& 0\\ 200000& 15& 1& -2& 1& 4& -2\\ 250000& 10& 2& -3& 4& 9& -6\\ & & \sum =0& \sum =-1& \sum =10& \sum =23& \sum =-15\end{array}$

$r=\frac{N\sum \left(U_i{V}_i\right)–(\sum U_i)(\sum V_i)}{\sqrt{N\sum U_i^2–(\sum U_i{)}^2}\sqrt{N\sum V_i^2–(\sum V_i{)}^2}}=\frac{-75}{7.07\times 10.68}=-0.993$