Answer:
The correlation between two variables, let's say A and B, is given by:
[tex]r(A.B) = \frac{ \sum{A*B}}{ \sqrt{\sum{A^2}* \sum{B^2}}}[/tex]
In our case, we know that:
y = 2*x
And:
r(X, Z) = 0.45
Then:
Now we want to find:
r(Y, Z)
Let's start with r(X, Z)
We know that:
X = Y/2
Then we can replace that in the correlation equation:
[tex]r(X.Z) = \frac{ \sum{X*Z}}{ \sqrt{\sum{X^2}* \sum{Z^2}}} = 0.45 \\[/tex]
[tex]r(Y/2.Z) = \frac{ \sum{(Y/2)*Z}}{ \sqrt{\sum{(Y/2)^2}* \sum{Z^2}}} = 0.45 \\[/tex]
[tex]r(Y/2, Z) = \frac{ (1/2)*\sum{Y*Z}}{\sqrt{ (1/4)\sum{(Y)^2}* \sum{Z^2}}} = \frac{ \sum{(Y)*Z}}{ \sqrt{\sum{(Y)^2}* \sum{Z^2}}} = 0.45[/tex]
And in the third part, we have r(Y,Z), then:
[tex]r(Y, Z) = \frac{\sum{Y*Z}}{\sqrt{\sum{Y^2}*\sum{Z^2}}} = 0.45[/tex]
The correlation of z with y is 0.45
