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### Why is correlation formula the way it is? Or Say how it formed? [duplicate]

I am really being confused by why the correlation formula is called the correlation of two variables $X$ and $Y$. Also how is it derived? The part where we divide covariance by product of standard ...
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### How would you explain covariance to someone who understands only the mean?

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
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### What is covariance in plain language?

What is covariance in plain language and how is it linked to the terms dependence, correlation and variance-covariance structure with respect to repeated-measures designs?
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### Does correlation = 0.2 mean that there is an association “in only 1 in 5 people”?

In The Idiot Brain: A Neuroscientist Explains What Your Head is Really Up To, Dean Burnett wrote The correlation between height and intelligence is usually cited as being about $0.2$, meaning ...
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### Prove the equivalence of the following two formulas for Spearman correlation

From wikipedia, Spearman's rank correlation is calculated by converting variables $X_i$ and $Y_i$ into ranked variables $x_i$ and $y_i$, and then calculating Pearson's correlation between the ranked ...
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### Do correlation or coefficient of determination relate to the percentage of values that fall along a regression line?

Correlation, $r$, is a measure of linear association between two variables. Coefficient of determination, $r^2$, is a measure of how much of the variability in one variable can be "explained by" ...
Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares. Suppose you have $y=\beta_0+\beta_1x_1$, ...