 # what is correlation?

Lol, I set the post to attract those who will come come to laught at my ignorance.

I forgot this Level II material, my books are in a different country. I know how to calculate it, however I just need someone to refresh me on practical meening of it.

I saw I CFAI text an example that said correlation bettwen US bonds and French bonds is 0.4, which mathmaticlly seems to be is also the correlation bettwen French bonds and US bonds, ie cor(x,y) = cor(y, x)

Does it imply that for change in return on US, return on frensh will change by 40%, of it simply sais that maybe 40% of the change of one can be explained by the other, with a Beta like measure (slope of regression) measuring the relationship

WOuld appreciate a nice refresher on the topic, no need for complex, just enough to get me on Level III, i will redo teh level II material later

okay i feel like it is comming back to me

the slope is basiclly the best preictor of the relationship, so if i regress the gas consumption of cars against engine size, i might get a slope of close to 1, which would means that if you double the engine size gas consumption doubles, the correlation would be 0.9 which means engine size explains most of gas consumption except for a small portion that is explained by car weight, engine design etc…

Am I close?

Now my question is, to get negative correlation you got to have negative slope in regression right?

Correlation measures of how two securities move in relation to each other.

Correlation is computed into what is known as the correlation coefficient, which ranges between -1 and +1. Perfect positive correlation (a correlation co-efficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction. If the correlation is 0, the movements of the securities are said to have no correlation; they are completely random.

okay some of you might be anoyed by me trying to answer my own question, but hey at least i put some effort before i ask silly questions:

so what i arrived at is

since slope is covar(x,y)/var(x)

and var(x) can not be negative, the only way to get a negative slope is with a negative covar(x,y)

and since correlation is covar(x,y)/(sd x * sd y), and sd x and sd y must be positive, when slope is negative, covar (x,y) will be negative and thus correlation will be negative as well.

So correlation will always have the same sign as the slope.

Now I have seem statistical software that report R^2 always as positive, they simply do that cause they use it as a measure of strength, with 1 being the best, they assume it is obvioous from slope that relationship is negative?

Thank you guys

Slope is actually the correlation times the ratio of Steve’s. Slope is the beta we have seen and come to love . But correlation expresses that and the variability in the fit at the same time . You can see it on a regression line of two variables if they have a relationship but also it’s strength

thanks mr z and anyone else who helps alzimers dislexic me

Coefficient of determination (R^2) is always positive, because it explains the amount of variance in the dependent variable that is explained by the independent variable. Even if the relationship between your independent and dependent variables is negative the degree to which the relationship is explained will always be positive.

okay i also see why r^2 is always reported positive, dah it is squaring r, so it will have to be positive

now my last question is on r vs r^2, i was thinking correlation ie r as the strength of the fit, forgetting about r^2

so if someone can contrast the 2 for me and what each practicly means

Also, R^2 is always positive because you’re squaring R…so if your correlation is -.43, then you’d get an R^2 of (-.43) * (-.43) = .18.

r tells you whether a change in A means a same direction change in B or if it is an opposite direction … based on sign of r (Correlation)

r^2 tells you how strong a change it is … does A explain a Lot of change in B or is it only some of the change… (coefficient of determination).

quick refresher

present in the Elan Guides Quantitative material for Level II which they provide for free.

Correlation = slope of regression line

R^2 = When you plot the data, this shows how well your X,Y points follow your regression line

For example, if you had a high R^2 you’d have all your data points clustered around your regression line, but a low R^2 they would appear more random

It’s probably easier to see this graphically, I’d try searching on Google for R^2 and see if you can find a visual representation…

^ correlation is not the slope, you can have a slope of 0.5 and correlation of 1, not that i knew this ten mins ago, we all forget…

r tells you whether a change in A means a same direction change in B or if it is an opposite direction … based on sign of r (Correlation)

r^2 tells you how strong a change it is … does A explain a Lot of change in B or is it only some of the change… (coefficient of determination).

cp, many thanks , great guide

however i am still not clear on oen point, correlation seems to tell me about the strength of the relationship, why do i need R^2, what is the meaning of each i guess for value of 0 and 1 it is clear since both will be the same, indicating 100% prediction or 0% predciction, but for values in bettwen when the two are not the same, what is each one telling me

the two combined together tell you what should happen

R < 0, R2 = 0.9 -> strong negative relationship

R > 0, R2 = 0.9 -> strong positive relationship

i see, so mostly i am looking at the r for its sign, which is also the sign of the slope cofficent, so it seems r on its own is not telling me much ?

which makes me wonder why cfa is showing me r of bonds returns in different countries, why not show me r^2 r^2 loses its sign … so you do not know whether it is going to add on, or subtract.

covariance has the sign of the correlation.

so you know whether there is a diversification benefit or not. …

Don’t you guys remember level 2…

R^2 can actually be negative for multiple regressions…

r^2 cannot be negative … r only can be .

you need to remember basic math …