Question

The following table contains the data of monthly salaries and percentage of the income saved. Find the correlation coefficient using the shortcut method.

$\begin{array}{cc}Salary& \%ofincomesaved\\ 10000& 5\\ 20000& 8\\ 30000& 10\\ 40000& 12\\ 50000& 20\end{array}$

• A. 0.92
• B. 0.95
• C. 0.98
• D. 0.99

Answer 1

The correct option is C

0.98

$Let{A}_x=30000\&h_x=10000Let{A}_y=0\&h_y=1$

$\begin{array}{ccccccc}{X}_i& Y_i& U_i=\frac{X_i-A_x}{h_x}& V_i=\frac{Y_i-A_y}{h_y}& U_i^2& V_i^2& U_i{V}_i\\ 10000& 5& -2& 5& 4& 25& -10\\ 20000& 8& -1& 8& 1& 64& -8\\ 30000& 10& 0& 10& 0& 100& 0\\ 40000& 12& 1& 12& 1& 144& 12\\ 50000& 20& 2& 20& 4& 400& 40\\ & & \sum =0& \sum =55& \sum =10& \sum =733& \sum =34\end{array}$

$r=\frac{N\sum \left(U_i{V}_i\right)–(\sum U_i)(\sum V_i)}{\sqrt{N\sum U_i^2–(\sum U_i{)}^2}\sqrt{N\sum V_i^2–(\sum V_i{)}^2}}=\frac{170}{7.07\times 25.3}=0.95$