ISI questions on correlation

[deepak]

Could someone please explain how to solve the 2 questions (see attached image)? I haven't studied correlations so would greatly appreciate if someone could suggest an online resource for this.

Thank you!

[neha]

Question 1: i think the answer should be (b) as the var(x bar) will be (n*sigma^2 +(n^2-n)*row))/n^2 , so it will approach to ow as n approaches infinity.

Question 2 : it will be (1) as all the  points are on lines but x and y are related positively in one and negatively in another, ergo (1).

[deepak]

Thanks Neha, but I'm not too sure I understand.

For question 1, how did you arrive at the formula for Var (Xbar)? After that your explanation sounds perfect, but I couldn't understand how you got that expression.

For question 2, I get the +vely correlated in the 1st, -vely correlated in the 2nd funda, but I don't understand how the correlation coefficients are equal. And um, how do I figure out what the correlation coefficient between 2 variables is, from the linear equation?

[neha]

okay,,,, for question 2: i think explaining it via scatter diagram would help,, so if all the points lie on a linear equation , we say that the variables are perfectly related,, since thats the case here ,, x and y will be perfectly related,,, will have same signs in absolute terms but opposite in signs..

for question1, actually i had some difficulty in typing,, but let me try,,

Var ( n variables) = sum (i over the range 1 to n)(sum(j over the range 1 to n) of co variance of (xi,xj) ,,,,,,,,, there will be n^2 terms.
Now when u use this formula there will be n times when sigma^2 will be used for example for cov(x1,x1) and cov(x2,x2) and in rest of the cases which are n^2 -n row will be used, for instance cov (x1, x2) ,, cov(x5,x8),,, so this is how u get it,,,

hope it helps

[deepak]

Brilliant! Thanks very much for the clarifications. Much appreciated