  Question

# Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations:

Easy

## Solution Verified by Toppr

## \begin{align} 2Y - X - 50 = 0\end{align}...............(i) \ and               \begin{align} 3Y - 2X - 10 = 0\end{align}...............(ii)                                  \begin{align} 2Y - X = 50 \end{align}...............(multiply \ by \ 3 ) \ and                \begin{align} 3Y - 2X = 10 \end{align}...............(multiply \ by \ (-2))                 \begin{align} 6Y - 3X = 150 \end{align}                              \begin{align} -6Y + 4X = -20 \end{align}                 \begin{align} X = 130 \end{align}                                \begin{align} 2Y - 130 = 50 \end{align}                  \begin{align} Y = 90 \end{align}                \begin{align} 2Y - X - 50 = 0\end{align}                \begin{align} - X = 50 - 2Y \end{align}                \begin{align} X = -50 + 2Y \end{align}               \begin{align} 3Y - 2X - 10 = 0\end{align}               \begin{align} 3Y = 2X + 10\end{align}               \begin{align} Y = \dfrac{2}{3}X + \dfrac{10}{3}\end{align} 0 0