# Questions tagged [f-distribution]

The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.

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### Intuitively, why do F distributions not have a peak when df1 is 1 or 2?

In the context of the variance ratio F test, I'd like to understand intuitively why the F curves have no peak when the degree of freedom for the numerator variance is 1 or 2, but instead increase ...
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### Sampling distribution of Coefficient of determination in general

I was studying the properties of multiple linear regression, and stumbled across the F statistics often used for the tests. We are testing for the regression coefficients (let's say there are $p$ ...
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### F-distibution only depends on degrees of freedom

I am reading ISLP Chapter 3.2 on multiple linear regressions. They define the F-statistic as $S_1$, the variance of sample 1 from population 1, divided by $S_2$, the variance of sample 2 from ...
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### Distribution of $\frac{X^2}{Y^2}$ where $X$ and $Y$ are iid standard normal

Let $X,Y\in \mathcal{N}(0,1)$ with $X$ and $Y$ independent. I am interested in the pdf of $Z=X^2/Y^2$ which has a $\mathcal{F}(1,1)$ Fisher distribution. I know that his can be done by first finding ...
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### ratio of 2 chi square to get f-distribution

How can I use two chi square functions to make a f function? I only see invchisquare functions in some languages when I need to use an inv f-dist to get the exact binomial CI. So, looking to figure ...
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### $F$-test with a variance being $C$ times as large as the other

I am familiar with $F$-tests in which the alternative hypothesis is defined as $H_a=\{\sigma^2_1/\sigma^2_2>C\}$ (the sign "$>$" can be either "$<$" or "$\ne$" as well), where $C=1$. If I ...
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