Answer:
The correlation coefficient 0.5 depicts that there is moderate positive correlation between y and x.
Step-by-step explanation:
The linear regression equation is
y= a+bx
The given linear equation is
y= 10x
Here, slope=b=10 and intercept=a=0.
From above equation,
ybar=10xbar
We are given that CVx=0.1 and CVy=0.2
where CV=(standard deviation/mean)*100
We know that
b=r(Sy/Sx)
Multiplying by xbar/ybar on both sides
(xbar/ybar)b=r(Sy/Sx)(xbar/ybar)
(xbar/ybar)b=r[(Sy/ybar)/(Sx/xbar))]
(xbar/ybar)b=r[CVy/CVx]
As CVy/CVx=(Sy/ybar)*100/(Sx/xbar)*100=(Sy/ybar)/(Sx/xbar).
By putting ybar=10xbar, b=10, CVx=0.1 and CVy=0.2.
(xbar/10xbar)10=r(0.2/0.1)
1=r(0.2/0.1)
1=r(2)
r=0.5
There is moderate positive correlation between y and x.
