whenever A increases by 1 unit, B increases by 0.5 unit, and C decreases by 0.5 units. What are the correlation for A&B, and A&C? The answer is 1 and -1. Can somebody pls explain how and why? Thanks.
b always goes in the same direction as A, therefore corr a,b=1 a and c always go in the opposite direction, therefore corr a,c=-1 thats my best guess
they ask about the correlation coefficient not beta meaning: A increases, B increases - perfect positive correlation… A increases, C decreases - perfect negative correlation… the units do not matter. messed this on the cfai exam also up. edit: the correlation coeff is bound between -1;+1. beta is not. they want the correlation coefficient.
by the way, another pair of other choices are +0.5 for A&B, -0.5 for A&C. And that’s what I chose. I know A&B are positively correlated and A&C are negatively correlated, but the problem is how do you know they’re perfectly correlated? If they are perfectly correlated, then if A goes up by 1, then shldn’t B goes up by 1 and C goes down by 1? That’s what I don’t understand
no that is the point. perfect positive correlation (+1) does not imply A increases 1cent and B increases 1cent. it rather says: when A increases (decreases) B increases (decreases). for negative correlation it is vice versa. A increases… B decreases - EVERY TIME! That what correlation says. It does say NOTHING about the magnitude of the movement!
got it…thanks so much
The regression coeffiecients are 0.5 and -0.5 in this question. A unit change in the independent variable A changes dependent variable to vary by 0.5 units B/C. Note that this is specified in units. The correlation coefficient measures the strength and direction of the relationship between 2 variables.
can you show the calculation? Thanks. I’m really weak in quant. I’m looking thru regression chapter now (Schweser 2007), but I don’t find “regression coefficients.” It’s embarrassing to tell you that I never heard of it. (I know coefficient of determination and correlation coefficient). Thanks.
I think perfectly correlated are those variables when 1% movement in 1 causes a 1% change in the other, if postively in the same direction or else in the opp direction
So, am i correct to say that correlation coefficient measures the direction and not the magnitude? By contrast, regression coefficients measure both? Thanks.
smeet Wrote: ------------------------------------------------------- > I think perfectly correlated are those variables > when 1% movement in 1 causes a 1% change in the > other, if postively in the same direction or else > in the opp direction Nope barthezz Wrote: ------------------------------------------------------- > no that is the point. > > perfect positive correlation (+1) does not imply A > increases 1cent and B increases 1cent. > it rather says: when A increases (decreases) B > increases (decreases). > Nope Correlation measures the strength of a linear relationship. That means that if correlation is 1 or -1 then all the points lie along a line which is much more strict than one increases implies the other increases. For example, if I drew a bunch of points from A = Log(B), they would not have a correlation of +1 although if B increased then A would increase. If a unit increase in A cause a 1/2 increase in B then A and B lie along the line B = intercept + 1/2 * A so the correlation is 1.
if questions like these are the real deal then it looks i don’t have much of a shot, coz i would have chosen the 0.5 and -0.5 option in a heartbeat in the heat of the moment. now i’m really nervous…
JoeyDVivre, How do you arrive at +1 from B=intercept+1/2A? Where in the question do you find the value of the intercept? Or is it based on the answers since it has to be greater than 0.5?Thank you.
You don’t need to know the value of the intercept to know it falls on a line. A increase in 1 in A causes an increase of 1/2 in B means they are on a line because there is no uncertainty, no error term, etc…
In case there is an error term, the correlation coefficient would have been less than 1?
Yes. An error term means there is spread about the line.
Good explanation. Thanks.
JoeyDVivre Wrote: ------------------------------------------------------- > You don’t need to know the value of the intercept > to know it falls on a line. A increase in 1 in A > causes an increase of 1/2 in B means they are on a > line because there is no uncertainty, no error > term, etc… Ok, so am I correct to say that if they change the problem to “if A goes up by 1 unit, B goes up by 0.2 (or any number) and C goes down by 0.2 (or any number)”, the answer would still be the same?
Yep
Am I correct in saying that if the connecting the points (graphically) make a straight line (and always will make a straight line) that they are perfectly correlated?