Question

The correlation between two scores X and Y equals 0.92. If both scores were converted to z-scores, then the correlation between the z-scores for X and z-scores for Y would be:

a) 0.92
b) −0.92
c) 0.08
d) −0.08

Answer 1

Answer:

A) 0.92, I took the test and it was right. Vote me brainliest please

Step-by-step explanation:

Answer 2

The correlation between the z-scores for X and z-scores for Y is given by: Option A: 0.92

What is the effect of change in origin and scale on the correlation coefficient?

The correlation coefficient(for two variables) is independent of the change of origin and scale of any or both variables.

Thus, we get:

$Corr(X, Y) = Corr\left(\dfrac{X - a}{b}, Y\right) = Corr\left(X, \dfrac{Y - c}{d}\right) = Corr\left(\dfrac{X - a}{b},\dfrac{Y - c}{d}\right)$

where a, b, c and d are constants.

How to find the z-scores for a random variable?

Suppose the considered random variable be X.

Then, we get the z-scores for X as:

$Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - E(X)}{\sqrt{E(X^2) - [E(X)^2]}}$

where $\mu = E(X)$ and $\sigma = \sqrt{Var(X)}$ (both are constants).

For this case, we're specified that:

• $Corr(X,Y) = 0.92$

The correlation coefficient for the z-scores of X and Y would be:

$Corr\left(\dfrac{X -\mu_X}{\sigma_X}, \dfrac{Y - \mu_Y}{\sigma_Y}\right)$

Using the property that origin and scale change doesn't affect correlation coefficient, we get:

$Corr\left(\dfrac{X -\mu_X}{\sigma_X}, \dfrac{Y - \mu_Y}{\sigma_Y}\right) = Corr(X,Y) = 0.92$

Thus, the correlation between the z-scores for X and z-scores for Y is given by: Option A: 0.92

Learn more about correlation coefficient here:

https://brainly.com/question/10725272