1. ## F distribution

Can someone please explain to me what's the use of f distribution. I cannot understand how to derive it from a normal distribution.

2. The main link between F and Normal distributions is:

The Quotient to two Chi-square distributed variables (each divided by their degrees of freedom) follows an F distribution

The sums of squares of k independant normal variables follows a chi square distribution with k degrees of freedom.

So, if you have 5 normally distributed independant Variables (N1...N4)

$\displaystyle \frac{(N_1^2 + N_2^2 + N_3^2)/3}{(N_4^2 + N_5^2)/2} \sim F$

Its often used in testing the goodness of fit of regression models.

3. Standard normals
and it's real value is in ratio of variances,
which allows you to obtain confidence intervals and hypothesis testing for comparing standard deviations
and also in regression, which are also chi-square random variables