math
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math [2020/09/26 17:12] – raju | math [2023/08/12 04:40] (current) – [pages in this wiki] raju | ||
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+ | ==== correlation ==== | ||
+ | t-statistic for correlation, | ||
+ | \[ | ||
+ | t = r \sqrt{\frac{n-2}{1-r^2}} | ||
+ | \] | ||
+ | |||
+ | The reverse equation is | ||
+ | \[ | ||
+ | r = \frac{t}{\sqrt{t^2 + n-2}} | ||
+ | \] | ||
+ | |||
+ | Derivation of the reverse equation: | ||
+ | \begin{align*} | ||
+ | & t = r \sqrt{\frac{n-2}{1-r^2}} & \\ | ||
+ | & \frac{t^2}{r^2} = \frac{n-2}{1-r^2} & \\ | ||
+ | & \frac{t^2}{n-2} = \frac{r^2}{1-r^2} & \\ | ||
+ | & \frac{t^2}{t^2 + n-2} = r^2 & \\ | ||
+ | & r = \sqrt{\frac{t^2}{t^2 + n-2}} & | ||
+ | \end{align*} | ||
+ | |||
+ | See also: | ||
+ | * https:// | ||
==== sec(x) + tan(x) ==== | ==== sec(x) + tan(x) ==== | ||
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I came across this simplification while reading https:// | I came across this simplification while reading https:// | ||
+ | |||
+ | ==== pages in this wiki ==== | ||
+ | * [[fibonacci sequence]] | ||
+ | * [[Leibniz integral rule]] | ||
+ | |||
+ | ==== links I came across ==== | ||
+ | * What is the formula for sum of the p-th powers of the first n positive integers? | ||
+ | * Use Faulhaber' | ||
+ | * The formula involves binomial coefficients and Bernoulli numbers. | ||
+ | * See also: https:// | ||
+ | |||
+ | ==== pages with math outside of this wiki ==== | ||
+ | use cases | to copy paste syntax | ||
+ | * https:// | ||
+ | * https:// | ||
+ | * https:// | ||
+ |
math.1601140332.txt.gz · Last modified: 2020/09/26 17:12 by raju