- 2008 Bk2 page 193: …suffice to say that the coefficient standard error is calculated using the standard error of estimate (SEE)… Does it mean coefficient standard error = SEE? 2. what’s the connection between regression coefficient (b1) and correlation coefficient? b1=Cov(x,y)/Sx^2 vs. r = Cov(x,y)/ Sx*Sy Thanks.
for question 1) Yes for large enough N, the messy formula for CSE reduces to SEE
- Standard error of estimate is the standard deviation of the error term, while the coefficient standard error is the sampling error of the coefficient estimate. I don’t know the formula for finding coefficient standard error but I know they are not equal. If you need formulas you can go to the url mentioned below: http://www.gseis.ucla.edu/courses/ed231a1/notes2/slr0.html 2. Correlation coefficient measures the strength of the linear relationship between two variables while b1 is the slope of the regression line. Actual derivation is also shown at the website mentioned above. Hope it clears your doubt.
kabhii, Is b1 = the strength of the linear relationship between x and y? That’s why I wondered. What I don’t understand is why the difference in the bottom part of the formulas (Sx^2 vs. Sx*Sy).
No, b1 is not the strength of linear relationship between X&Y but it is the slope of fitted regression line. As far as the difference in denominator is concerned I don’t know the answer, if you can google then you might find lot of articles which discusses about the derivation of slope.
I searched the net and found the following solution to that question, Joey says it isn’t technically correct… but it does seem to spit out the right solution and is intuitive. COR (X,Y) = COV (X,Y) / std X*std Y Beta = COR (X,Y) * std Y / std X which gives you the formula above. The standardized covariance between the stock and the market multiplied by the ratio of how much the stocks value varies in proportion to the market. Kerry.
I said that isn’t technically correct? Those are correct formulas. I probably said they weren’t correct in some situation like CAPM.
I must have misunderstood you, you said: Read more carefully - beta isn’t that at all. An estimate of beta might be that but beta is a parameter and mixing your estimators and your parameters is bad medicine. So… it is correct? I’m obviously still missing something here.
Kabhii I thought b1 = (coefficient) slope = strength of linear relationship between X&Y. This is why we use t-test to see if b1 is significantly different from zero (correlation of zero means no relationship). Our goal is to prove that a linear relationship exists between X&Y, which is Assumption#1 of multiple linear regression model. Kerry1 Where did you get the second formula? Can you provide the website? Since b1 = Beta, and it involves COR(X, Y), I conclude that it is still a measurement of linear relationship between X&Y. And therefore we use the t-test to prove that.
Ahh… I remember writing that. It was about CAPM. I just looked at your readings and there is a point here that I don’t want to make here. You should regard those statements above as correct and applicable in all the portfolio analysis stuff on the exam.
Sleepy bird, I think if the slope of the regression line (for Y and X) is significant then correlation between the two variables will also be significant. So in a way you are correct that testing significance of regression coefficient can also be used to determine the strength of the linear relationship. what I wanted to make clear was the correlation coefficient can only tell about the strenght of linear relationship but if you want to predict Y using X then you need slope for that which is derived from correlation. I hope it makes some sense.
Kerry1, I am little confused, Can you please tell which relationship is technically incorrect?
kabhii, thanks.
That Beta = [COV(X,Y) / std X, std Y] * std Y / std X = COV(X,Y) / VAR X It was on Wikipedia, I have just had a look for it and cant find it. If I do see it later I’ll post it. sleepybird, b1 isnt always beta, thats only in the CAPM model. Still use the t-test for significance but test if it is significantly different from 1.
Hey there, It was a link from wikipedia http://viking.som.yale.edu/will/finman540/classnotes/class5.html
kerry1, thanks.
Kerry1 Wrote: ------------------------------------------------------- > That Beta = * std Y / std X > > = COV(X,Y) / VAR X > > It was on Wikipedia, I have just had a look for it > and cant find it. If I do see it later I’ll post > it. > > sleepybird, b1 isnt always beta, thats only in the > CAPM model. Still use the t-test for significance > but test if it is significantly different from 1. Yes - use that. I’m sorry for the confusion of posts leaking into other posts.