Question on Correlation (from Elan) Slope vs. correlation coefficient

CFA Level II Quant
#1

Hi all,

In Elan Notes on correlation analysis Figure 2 shows correlation of +1.

Why is the slope different to +1? (here it is +0,6)

Can I interpret that if the correlation coefficient is +1 and the slope is +0,6 that they are perfectly related and if A moves +1 B moves +0,6 ?

If so, what would be the message if correlation coefficient is +0,5 and slope is +0,6?

Sorry - but this is somehow confusing to me …

Thanks!

#2

A slope of +0.6 means that (on average) Y changes +0.6 when X changes by +1. The correlation coefficient (ρ) simply tells you how close the (X, Y) points plot to the regression line: if ρ is near +1 or -1, then the points lie very close to the regression line; if ρ is close to 0, then the points are scattered far from the regression line.

#3

if the dots form a straight line, it’s perfectly correlated. slope doesn’t matter

#4

Many thanks, very helpful!

#5

Correlation 1 means: When a variable moves by 1 standard deviation in one direction, the other variable also moves by 1 standard deviation in same direction. (nothing to do with slop)

Now if variable 1 has standard deviation of 1 unit and variable two has standard deviation of 0.6 unit, the slop can be 0.6 or 1.67 based on which axis you plot your variables.

Correct me if I am wrong.

#6

The only error you made is in spelling _slop e _.

#7

lol… thanks!