if two variables are linearly correlated with y=50-2x then what will be the value of correlation coefficient
Answers
Answer:
Explanation:
Step 1 : Write the given regression equations .
$$\begin{align} 2Y - X - 50 = 0\end{align}...............(i) \ and$$
$$\begin{align} 3Y - 2X - 10 = 0\end{align}...............(ii)$$
Step 2 : Determine means of X and Y by solving two regression equation .
$$\begin{align} 2Y - X = 50 \end{align}...............(multiply \ by \ 3 ) \ and$$
$$\begin{align} 3Y - 2X = 10 \end{align}...............(multiply \ by \ (-2))$$
we get , $$\begin{align} 6Y - 3X = 150 \end{align} $$
$$\begin{align} -6Y + 4X = -20 \end{align}$$
⇒ $$\begin{align} X = 130 \end{align}$$
put X = 130 in eq (i) we get ,
$$\begin{align} 2Y - 130 = 50 \end{align}$$
⇒ $$\begin{align} Y = 90 \end{align}$$
Step 3 : Determining b
xy
and b
yx
.
Consider equation (i)
$$\begin{align} 2Y - X - 50 = 0\end{align}$$
$$\begin{align} - X = 50 - 2Y \end{align}$$
$$\begin{align} X = -50 + 2Y \end{align}$$
∴ b
xy
=2
Consider equation (ii)
$$\begin{align} 3Y - 2X - 10 = 0\end{align}$$
$$\begin{align} 3Y = 2X + 10\end{align}$$
$$\begin{align} Y = \dfrac{2}{3}X + \dfrac{10}{3}\end{align}$$
∴ b
yx
=
3
2
Step 4 : Determining the correlation coefficient .
Correlation coefficient =
b
yx
×b
xy
=
3
2
×2
=
3
4
=
3
2
∴Correlation coefficient is
3
2
Hence , Means of X = 130 and Y = 90 , and correlation coefficient is
3
2