Why is correlation only defined between two variables? I am an MBA student is taking statistics courses.
Our statistics prof was teaching us about correlations in statistics. We learned about Pearson's Correlation of Coefficient which is defined as the correlation between only two variables.
I am asked the prof if the correlation can be calculated between more than two variables and he said "no". But I am struggling to understand why this is the case?
For example: Hurricanes are correlated with Wind Speed, Hurricanes are also correlated with Temperature - Although I am not a meteorologist don't actually know if this is true (I just assumed this to show a point), we can see that in theory more than two variables can be correlated.
Therefore, why do we only evaluate the correlation between two variables and not more than two variables?

Pearson correlation is defined as a measure of the linear relationship between two variables.
For other relationships, like multidimensional relationships, we use other names. For instance:

*

*one could use the eigenvalues of a principal component analysis to express a degree of correlation in a multivariate case.

*Another related concept is the variance inflation factor.

*In the case of the hurricanes example that you mention, one might also think of multiple correlation and this gives the $R^2$ value or coefficient of determination for a linear model where hurricanes
are predicted by temperature and windspeed.

In addition there are constructs similar to Pearson correlation that use multiple variables. I have seen on this website before an expression like $E[(X-\mu_X)(Y-\mu_Y)(Z-\mu_Z)]/(\sigma_X\sigma_Y\sigma_Z)$. (but I can not find the original post)
