Contents
What is the correlation of X with itself?
The more widely-scattered the (X,Y) pairs are about a line, the closer the correlation is to 0. (Notice that the covariance of X with itself is Var (X), and therefore the correlation of X with itself is 1.)
What is the minimum value of Corr ( x, y, z )?
Assume X, Y, Z are three random variables, what is the minimum value of corr (X,Y)+corr (X,Z)+corr (Y,Z), here corr (X, Y) means the correlation between X and Y. Since the correlations are defined, we may assume the variances are all finite and nonzero.
Do you know the cause and effect of a correlation?
The key point is that is impossible just from a correlation analysis to determine what causes what. You don’t know the cause and effect relationship between two variables simply because a correlation exists between them. You will need to do more analysis to define the cause and effect relationship.
When is there no correlation between two variables?
There is no correlation if a change in X has no impact on Y. There is no relationship between the two variables. For example, the amount of time I spend watching TV has no impact on your heating bill. There are two straightforward ways to determine if there is a correlation between two variables, X and Y.
What is the formula for the correlation formula?
The correlation analysis enables us to have an idea about the degree & direction of the relationship between the two variables under study. The formula for correlation is equal to Covariance of return of asset 1 and Covariance of return of asset 2 / Standard Deviation of asset 1 and a Standard Deviation of asset 2.
Show that X − Y and X + Y are uncorrelated. The solution is below, however, I am confused about a portion of the explanation. Because the covariance remains unchanged when we add a constant to a random variable, we can assume without loss of generality that X and Y have zero mean.
Negative Correlation – There said to exist a negative correlation between two variables when the variable change in the opposite direction. For example, the law of demand, quantity, and supply. No Correlation – There exists no correlation between two variables when there is no movement of a direct relationship between the two variables.