What is the logical bacground behind regression and corellation, what do they actually mean and what makes it useful

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I am a third year student studying Electronics Engineering. Over trial and Error, reading and repetation, I finally understand what Variance is and why we use it. We want to find just how much are sample values differ from some mean value. I can intuitively explain it, tell you ways that it’s useful and all that good stuff.

Corellation and Regression don’t make sense. I see their equations a lot. I can spout out the formulae given a few seconds to remember which is which. But for the life of me, I can’t explain too much about it apart from saying “regression to the mean” and “two values are highly correlated”.

ELI5 what the underlying logic is, what the equation is doing and all that jazz

In: Engineering

Correlation is kind of like taking two variances and multiplying them together. That’s why correlation of something with itself is its variance squared. A big correlation tells you that if A is higher than its mean, B probably is too. Ex: Cloudy days and rain.

A negative correlation tells you that is A is higher than its mean, B is probably lower than its mean (and vice versa). Ex: Cloudy days and sunburn.

Zero correlation means there’s zero relationship between A and B. Ex: Cloudy days and the phase of the moon.