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3 questions
9
votes
4
answers
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Why highly correlated means higher variance?
I am reading the book Introduction to Statistical Learning and on page 183, the book states that
Since the mean of many highly correlated quantities has higher variance than does the mean of many ...
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4
votes
2
answers
985
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Intuitive understanding of variance of sum vs variance of difference
$\newcommand{\Var}{\operatorname{Var}}\newcommand{Cov}{\operatorname{Cov}}$Mathematically,
$\Var(X + Y) = \Var(X) + \Var(Y) + 2\Cov(X,Y)$ and
$\Var(X - Y) = \Var(X) + \Var(Y) - 2\Cov(X,Y)$
This ...
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12
votes
1
answer
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Understanding $\operatorname{Cov}(X,X) = \operatorname{Var}(X)$ intuitively
I just saw this question and the wonderful accepted answer in this forum. I was then triggered to try understanding intuitively why division of $S_xS_y$ is normalizing the covariance:
$$\frac{\...
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