Coefficient of correlation (r) and b1

leaning

Involved In Discussions
#1
Hello!


I found this:

1) the sample correlation coefficient (r) is related to the regression coefficient (b1) by r= b1 (sx/sy) where sx is the standard deviation of x, and sy is the standard deviation of y.

I also found:
2) the simple linear regression model equation is y=b0 +b1x + e

The question I am looking at asks: Which of the following statements about the coefficient of correlation, r, is (are) true?
I. r will have the same sign as b1
II. r equals 0, when b1 = 0
III. When r equals 1, b1 is positive

The answer is that they are all (I,II,III) true.


Is the way to answer this using 1), 2) or are both B1's in 1) and 2) the same?

I appreciate your help.

Regards,
leaning
 
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JeantheBigone

Quite Involved in Discussions
#2
Those are the same b1s.

http://www.stat.ucla.edu/~rosario/classes/091/112-1b/regression

But really, I think this is one of those questions that tempts you into getting snarled up in equations and spending a lot of time filling up the sheet.

Step back and think about what the graph / scatter chart looks like for a positive slope and what that means.

Honestly I wouldn't resort to equations at all for this one. And I passed the ASQ CQE last December. :D
 
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