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$\newcommand{\Cov}{\operatorname{Cov}}$ Let $u_1=ax+cw$ and $u_2=by+dz$. Then we have \begin{align*} \rho(u_1,u_2) &=\frac{\Cov(u_1,u_2)}{\sqrt{V(u_1)}\sqrt{V(u_2)}}. \end{align*} Let $C=\dfrac{1}{\sq …

Here's some Python code I wrote once to test out the max correlation method. … 0][1])) print("Now we find max correlation coefficient:") # Create a vector of correlation coefficients. …

The usual "post hoc ergo propter hoc" fallacy is the fallacy that says correlation always implies causation, or even that you can infer causality. This is still a fallacy. … However, if you add another condition to the correlation - namely, that of mechanism - then you get Reichenbach’s common cause principle: "No correlation without causation." …

This is the reason the aphorism, "Correlation does not imply causation" ought to be replaced with Reichenbach's principle: "No correlation without causation." … Or at least, "Correlation usually implies causation." Causation is more fundamental than correlation, and it's certainly much easier for humans to reason about than correlation. …

I agree with the other answers, but I would like to add that in the New Causal Revolution, particularly with the highest level of reasoning - the counterfactual - it is possible to reason about indivi …

You can interpret the correlation as a measure of how well a straight line (linear relationship) fits the data. If you have a correlation of $\pm 1,$ then it is a perfect linear relationship. … You can introduce a new feature, call it square-of-velocity, and then do a correlation with that new feature. …

Let $\rho$ denote the correlation coefficient of $Y_1$ and $Y_2.$ Using the inequality $$[E(Y_1Y_2)]^2\le E\!\left(Y_1^2\right) E\! …

Find the correlation coefficient for $Y_1$ and $Y_2.$ (Let $p_i=N_i/N$ for $i=1,2,3.$) This is Exercise 5.110 in Mathematical Statistics with Applications, 5th Ed., by Wackerly, Mendenhall, and Scheaffer …