Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [f-statistic]

An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different.

The F value is the ratio of the mean regression sum of squares divided by the mean error sum of squares. Its value will range from zero to an arbitrarily large number. The value of Prob(F) is the probability that the null hypothesis for the full model is true (i.e., that all of the regression coefficients are zero). In order to reject the null hypothesis that the group means are equal, we need a high F-value.

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Proof that F-statistic follows F-distribution

In light of this question : Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom I would love to understand why $$ F = \frac{(\text{TSS}-\text{RSS})/(p-1)}{\text{RSS}/(n-p)},$$ where $p$ is the number of…
user1627466
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Linear regression what does the F statistic, R squared and residual standard error tell us?

I'm really confused about the difference in meaning regarding the context of linear regression of the following terms: F statistic R squared Residual standard error I found this webstie which gave me great insight in the different terms involved…
KingBoomie
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Why is the F-Statistic $\approx$ 1 when the null hypothesis is true?

I'm currently reading through the section on linear regression in ISLR, and the authors use the F-Statistic to determine if we should reject the null hypothesis (well they use the p-value of the F-Statistic). I understand that, when the null…
BeepBoop
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Why ever use F-statistic?

We can use F-statistic for determining whether at least one of the predictors has an effect on the response. But why just not take minimal p-value across all predictors? It doesn't require introducing a new concept.
Yurii
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Intuitive explanation of the F-statistic formula?

Introduction to Statistical Learning defines the F-statistic as follows: $$\frac{(TSS - RSS) / p}{RSS / (n - p - 1)}$$ I am trying to interpret this formula intuitively - the numerator looks like the $ESS$ per regressor, and the denominator looks…
kitedancing
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Calculate the F1 score of precision and recall in R

Alright so I want to calculate the F1 score for four pair of values for Precision P and Recall R. These pairs are: Precision = (54.54, 60.0, 91.3, 95.23) Recall = (0.02, 2.10, 0.18, 5.3) The above is the percentage of these values Precision1 = (…
forgotten_novel_char
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AR(q) model with F-test

I am wondering that if we have an AR($q$) model for time series: $$X_i=\beta_1X_{i-1}+..+\beta_{p}X_{i-p} + \beta_{p+1} X_{i-p-1} +...+\beta_{q} X_{i-q}+\epsilon_i,\epsilon_i \;\text{iid}\; N(0,\sigma^2)$$ Does the F-statistic for the F-test to…
Brian Ding
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Is this an Appropriate Application of a Permutation Test?

Suppose I have count data between three groups, each with a different number of observations: $n_1 = 11, n_2 = 6$ and $n_3 = 5$. My data is listed below: \begin{array} {|r|r|}\hline group 1 & group 2 & group 3 \\ \hline 9 & 8 & 6 \\ \hline 9 & 8 &…
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Why is this statistic F-distributed?

A book I'm reading claims that the statistic: $\frac{(RSS_0 - RSS_1) / (p_1 - p_0)}{RSS_1 / (N - p_1 - 1)}$ has an F distribution. Why is this? I know that an F distribution is something like $\frac{\chi^2_p / p}{\chi^2_q / q}$, where the two…
serendipity
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Is it possible to get a negative F-statistic (e.g. in ANOVA)?

If so, why? If not, why not? I'm thinking of an ANOVA context, but if the answer changes depending on context I would also be interested to know why that is.
user1205901 - Reinstate Monica
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Conceptual/Math/brainteaser Question: Multiple Linear Regression

This is kind of a brainteaser and I'm struggling to solve it, any ideas on approaching this would be valued: I thought about using substitution of the different x and z into the third regression equation to get a value in terms of x and z but I…
delucaenzo
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Interpretation of F-statistics in a linear mixed model

I was reading a paper yeaterday, and in their results they reported an F-score for each of their fixed effects in a linear mixed effect model. Here, lux is a catagorical variable, but the rest are continuous. I haven't come across this before. …
RTbecard
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Does Newey-West standard errors affects the significance level of R2?

General question: I use the linear regressions with the OLS method to check whether cross-sectional standard deviation is able to describe future sumed excess returns or not. Because of autocorrelation there is the need to update the summary with…
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Use of the F statistic in logistic regression

This paper uses a generalised linear mixed model assuming a binomial distribution for the errors. In the results section, the F statistic and associated P-value is used for the model (page 2150, paragraph beginning 'Males and females also…
luciano
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F-statistics based method out of fashion?

I'm reading Elements of Statistical Learning and come across this paragraph right before section 3.3.3: Other more traditional packages base the selection on F -statistics, adding “significant” terms, and dropping “non-significant” terms. These are…
James LT
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