Slope Formula Error

[bigwilly]

In the CFA readings they provide a formula for estimating the slope for Bi = Cov (Y,X)/Var(x)....but later in the solution for a problem at the end of the reading they use Cov(Y,X)/E(X-X)^2

please read E(X-X)^2 as Sum of X minus Xbar squared.

which one is correct? One is using the variance and the other is using just the sum of the deviations from the mean?????

 

[Wheat Field with Crows]

What specific reading and what page?
If you elaborate it could be helpful.

BTW, in the prob theory the formulas Cov (Y,X)/Var(x) and Cov(Y,X)/E(X-Xbar)^2 are identical because Var(X)=E(X-Mean)^2 where "E" is the expectation, not the sum as you stated.

 

[bigwilly]

I meant E as in Sum...i dont have the Sumation letter thingy

 

[bigwilly]

the Problem is #8D on pg 568 in CFA Volume #1. Formula is page 542 Reading 13

 

[Wheat Field with Crows]

in the solution on p. A-62 (1/n) is removed from both the numerator and denominator.

 

[Wheat Field with Crows]

1/n would be for population.
for a sample it is 1/(n-1).

 

[bigwilly]

Your correct...I somehow missed that when I was doing it this morning...good catch.



Edited 1 time(s). Last edit at Wednesday, March 22, 2006 at 10:27AM by bigwilly.

 

[bigwilly]

The problem is that they say Cov (X,Y)/Var (X) but then change the actual values used. I didn't follow it step by step like I should...I just looked at the solution....my mistake. Thanks for the clarification.

 

[cheredayko]

There are no mistakes in formulas:

Slope = Cov (X,Y)/Var(X) = (sum of (X-Xaver)*(Y-Yaver))/sum of (X-Xaver.)^2.

* 1/(n-1) * (n-1)/1 = 1 (that's how the second formula is simplified)



Edited 1 time(s). Last edit at Sunday, April 2, 2006 at 05:03PM by cheredayko.