Correlation with two independent variables

In summary, the speaker is seeking help with finding the correlation between XY and Y given the assumption that X and Y are independent. They are unsure how to simplify the equation for covariance and are questioning whether X and Y^2 are also independent. They ask for assistance in proving this.
  • #1
rhuelu
17
0
I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent. If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 
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  • #2


rhuelu said:
I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent.
yes.
If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 
  • #3


how would you prove this?
 
  • #4


rhuelu said:
how would you prove this?

what do you mean by "independent"?
 

1. What is the definition of correlation with two independent variables?

Correlation with two independent variables refers to the relationship between two variables that are not influenced by each other. It measures the strength and direction of the linear relationship between the two variables.

2. How is correlation with two independent variables calculated?

Correlation with two independent variables is typically calculated using a statistical measure called Pearson's correlation coefficient. This involves calculating the covariance and standard deviations of the two variables, and then dividing the covariance by the product of the two standard deviations.

3. What does a correlation coefficient of 0 indicate in correlation with two independent variables?

A correlation coefficient of 0 indicates that there is no linear relationship between the two variables. This means that the two variables are not related to each other and do not influence each other's values.

4. Can correlation with two independent variables determine causation?

No, correlation with two independent variables does not determine causation. Even if a strong correlation is found between two variables, it does not mean that one variable causes the other. Other factors and variables may be influencing the relationship between the two variables.

5. What are the limitations of using correlation with two independent variables?

Correlation with two independent variables only measures the strength and direction of a linear relationship between two variables. It does not account for non-linear relationships or other factors that may influence the relationship between the variables. Additionally, correlation does not imply causation, so it cannot determine cause and effect relationships between variables.

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