query: how can I prove the value of correlation coefficient $r$ ranges between $-1$ and $1$?
positive_passages.docid: 150482
positive_passages.text: Proving that the magnitude of the sample correlation coefficient is at most $1$
negative_passages.docid: 95145
negative_passages.text: Does $\exp(2ir\pi)$ equal $1$? What's wrong?
negative_passages.docid: 40724
negative_passages.text: AR(1) coefficient is correlation?
negative_passages.docid: 84662
negative_passages.text: Question on the correlation between two dependent variables
negative_passages.docid: 79138
negative_passages.text: Correlation between a nominal (IV) and a continuous (DV) variable
negative_passages.docid: 82729
negative_passages.text: Prove that $\mathrm E\left({\max}\left\{X^2 , Y^2\right\} \right) \leq 1 + \sqrt{1 - \rho^2}$ where $\rho$ is their correlation.
negative_passages.docid: 45632
negative_passages.text: Correlation coefficient contradicts t-test
negative_passages.docid: 85992
negative_passages.text: how to prove the chain rule?
negative_passages.docid: 142785
negative_passages.text: How can I prove Holder inequality for $0<p<1$?
negative_passages.docid: 89125
negative_passages.text: Prove that $r \in R$ such that $0 \lt r \lt 1$ then $\frac{1}{r (1 - r)} \ge 4$
negative_passages.docid: 9934
negative_passages.text: $P(X>0,Y>0)$ for a bivariate normal distribution with correlation $\rho$
negative_passages.docid: 123929
negative_passages.text: What is the correlation if the standard deviation of one variable is 0?
negative_passages.docid: 104490
negative_passages.text: Range of $\operatorname{arccot}(x)$
negative_passages.docid: 105697
negative_passages.text: How do I evaluate $\prod_{r=1}^{\infty }\left (1-\frac{1}{\sqrt {r+1}}\right)$?
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$
negative_passages.docid: 48252
negative_passages.text: Range of function Involving Modulus Quantity.