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.

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2answers
118 views

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-...
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Do I need F-statistic and t-statistic for regression if I have the p-value?

I am running a simple linear regression, and was wondering whether I need to use the F-statistic and t-statistic to: prove the significance of my results run a two-tailed hypothesis test on the ...
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1answer
88 views

f_regression in sklearn - how is a correlation converted into an F score?

From the following link: https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.f_regression.html#sklearn.feature_selection.f_regression There's: This is done in 2 steps: The ...
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1answer
314 views

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 ...
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CNLRM: Testing linear restriction - F statistic in terms of regression residuals of the unrestricted and restricted regressions

In order to test linear restriction Rβ=q of the Classical Normal Linear Regression we use F=1/p(Rβ ̂-q)'(〖σ ̂^2 R(X^' X)^(-1) R^')〗^(-1) (Rβ ̂-q)~F(p,n-k) How can I write this F statistic as F_0=((ε ̃^...
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2answers
168 views

What does it mean if I have a high F-stat but low $R^2$?

As far as I understand, a high F-stat leads to a high $R^2$, though the converse is not true. What does it mean if I have a high F-stat and a low $R^2$?
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Which F statistic is generated in felm (R) and why does it differ from STATA (ivreghdfe)

I'm running 2sls and making sure that my results replicate in both stata and r. In r, using felm, my code is: ...
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Looking for the name of a distribution and/or a way to calculate its cumulative distribution function

For parameters $\nu_1$, $\nu_2$, $\lambda$, define random variables using a chi-squared distribution and a non-central chi-squared distribution: $$ S \sim \chi^2_{\nu_2} / \nu_2 $$ $$ F \sim \frac{\...
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1answer
69 views

How to Properly Interpret the Hypotheses/Results of a Permutation Test Based on the Test Statistic?

I asked a question recently: Is This an Appropriate Application of a Permutation Test?. All information about my data, the permutation test and the results can be found there, but here is a quick ...
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1answer
128 views

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 & ...
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Calculation of Olea and Pflueger's (2013) Effective F-statistic

I am trying to understand the calculation of Olea and Pflueger's (2013) test for weak instruments when the errors are not conditionally homoskedastic and serially uncorrelated, which is calculated as: ...
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32 views

Which ANOVA function use is correct in R

So, I am just a beginner in statistics and RStudio, and I still do not understand fully the full purpose of F-tests (beside hypothesis testing) and I recently started using anova() function from R ...
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What kind of statistical test do I need in testing the lag order in an Auto Regression model AR(4) against a restricted AR(3)?

Bit stumped on this one and none of my resources are helping to clarify this one for me. I've been given an estimated Autoregression Model AR(4) model of the sort: Yt = b0 + b1 x Yt-1 + b2 x Yt-2 + b3 ...
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Why is the use of the F-Statistic / p-value as a criteria in Stepwise Model Selection outdated? [duplicate]

I am coming from the field of psychology and in most publications Model Selection (OLS, Regression) is done via Forward/Backward Selection using the F-Static/p-value of the regression coefficients to ...
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Trading higher adj. Rsquared for a lower F statistic - which is preferred?

In the model selection process, I'm comparing two models. The decision is whether or not to add a specific interaction term to the multiple regression model. The outcome of the model without the ...
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1answer
72 views

How do R-squared and p(F-statistic) impact the fitness of a linear regression model?

Given below the attached summary statistics of a linear regression model. Noting that Adjusted R-square is only 15% but p(F-statistic) is very low (almost equal to zero): Can it be said that it is a ...
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361 views

What is the difference between the Pseudo F Index and the F Statistic?

I'm wondering what the difference between the Pseudo F Index and the F Statistic is. The Pseudo F Index is used in clustering analysis as an index to determine the the right number of clusters in a ...
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Proof that a model has a higher $R^2$ if F > 1

I need to prove that a model has a higher adjusted $R^2$ than another model if the F-statistic is greater than 1. Below is as far as I've gotten, but I'm not even sure if that's correct. $$R^2_{adj} ...
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Multitaper F statistics

I'm having some problems interpreting the F-statistics output from multitaper analysis. To illustrate, the following code-snip in R performs multitaper analysis on the same sine-frequency but with ...
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2answers
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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{\...
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Difference between Wald statistics and effect size in regression models

In some of my regression models (using the rms package), I notice a distinct difference between the result of the Wald statistics (estimated using ...
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1answer
707 views

How to prove that the robust F statistic is asymptotically chi squared distributed?

The linear model is $$y_{i}= x_{i}'\beta+u_{i}$$ When written in vector notation such that $y_{i}$ is a $1$ x $1$ matrix of outcomes, $x_{i}'$ is a $1$ x $k$ matrix of control variables, $\beta$ ...
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F ratios, ANOVA, and 2 stage nested (mixed) models in R

I have data relating to strength of fabric. Each fabric comes from one of 4 batches (B), and batches come from one of 3 suppliers (A). My question relates to the calculation and interpretation of F ...
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find F-statistic using R output

I have this R output: ...
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226 views

Mean Square of Regression Error for categorical variables while computing F statistic

Give the annova table in the image below: I need to calculate the F statistic for the null hypothesis: b2 = b3 = 0 . b2 is cofficient of cylinder and b3 is the coefficient of doors. The formula used ...
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1answer
32 views

Which coeffcients are used for a F-statistic

I have an F-statistic, $F(4,10)$, my constant and 4 Coefficients $\beta_2 , \beta_3 , \beta_4$ and $\beta_5$ I already know that the (in this case) 10 reflects the number of obsverations. But what ...
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2answers
206 views

Calculating F-statistic, why is SS used instead of just $r^2$?

The calculations and question are for a simple regression (one independent and one dependent variable). SSres = SSy * (1 - $r^2$) SSreg = SSy * $r^2$ F = (SSreg / DFreg)/(SSres / DFres) So, I've ...
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1answer
359 views

The F-statistic with all predictors vs. with predictors excluded

The F-statistic formula is: $$ F=\frac{(TSS-RSS)/p}{RSS/(n-p-1)} $$ Where $TSS$ is total sum of squares and is equal to $\sum_{i=1}^n(y_i-\bar{y})^2$ and $RSS$ is ...
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91 views

Find the Sum of Squares and using them complete an F-test for goodness of fit

I have this question ( would be grateful if someone could put it on for me) https://gyazo.com/5afe5d7c9d12acdff8f9c55db74f97c9 And I am concerned with part b). I know what $RSS = SSE$ is due to the ...
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409 views

F-statistic and Linear Regression formula for slope?

One of the derivations of the Linear Regression Method leads to the following two formulas, for the slope and the intercept: $$\begin{equation} m = \frac{Cov(x, y)}{Var(x)} \label{eq:slope} \\ b ...
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1answer
715 views

Which is the correct F-beta-measure scoring formula?

I have found differing formulas to calculate the $Fbeta$ score, which changes the weight (influence) of $PPV$ ($Precision$) or $TPR$ ($Recall$) from the default of equality (i.e. $0.5$). For example: ...
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2answers
142 views

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,...
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1answer
2k views

Stepwise regression based on F-statistic in R [closed]

I know that the stepAIC function in R allows us to perform stepwise regression but I was wondering if there's any option (or other function) to perform a F-...
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30 views

Link between Fisher and Chi-squared

I am fairly new to statistics, and during practice, i used this link between Chi-squared and F-statistics where F equals to ration between 2 Chi squared distributions. Can someone elaborate more on ...
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1answer
385 views

Multiple Regression F Statistic Proof

Currently working through Introduction to Statistical learning, and on page 76 I am struggling with the following: They state the equation for the F statistic as: $F = \frac{\frac{TSS − RSS}{p}} {\...
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Calculate statistics (estimate, confidence intervals, standard error) for a contrast matrix in ANOVA/ANCOVA/GLM

I am interested in calculating the relevant statistics for a contrast matrix in an ANOVA/ANCOVA/GLM setting. Kutner et al. call this the "matrix formulation" of the "general linear test". They give as ...
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2answers
520 views

ANOVA's f-statistic

While reading this blog on f-statistic in ANOVA, I stumbled upon the formula: The f-statistic is calculated like this: $$\frac{\text {variance between groups}}{\text {variance within groups}}$$...
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Is a high $R^2$ and F statistic evidence of autocorrelation?

Is a high $R^2$ and $F$ statistic between numeric data and its corresponding time evidence that the variable is serially autocorrelated? For time series analysis, is it necessary to perform a test ...
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reporting average inferential statistics from bootstrapped dataset

For independent reasons, I'm working on two bootstrapped datasets, A and B, of the same size, each consisting of a 1000 samples. To compare the distributions of A and B, I ran a Fischer F-test on ...
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1answer
201 views

Interpreting non-significant coefficients when the entire linear model is significant

I've been using linear models (lm function in R) to determine if the the expression of certain proteins is associated with disease severity. Sometimes the ...
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1answer
414 views

F-statistics and coefficient p-value of model with only one variable

F-test tests the null hypothesis that all coefficient of variables in the model equal to zero. P-value in a hypothesis test shows the probability of having observed results if null hypothesis is ...
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0answers
144 views

How to calculate F-statistic from glmnet

I understand how to obtain coefficients and MSE from glmnet. Now my question is: How can I calculate the goodness of fit of the model in terms of standard measures, ...
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2answers
8k views

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)...
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4answers
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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 ...
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1answer
4k views

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 ...
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0answers
346 views

Change the partial covariance matrix in a VAR with constant?

The computation of the partial covariance matrix formula in a VAR (without constant and time trend) is very well known. For example, in the context of the conditional Granger causality, they are given ...
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Statistic equivalent to F statistic with several factors?

In class we learned that if we want to perform a randomisation/permutation test on the hypothesis: $H_0: y_{ij} = \mu_i + e_{ij}$ vs. $H_1: y_{ij} = \mu + e_{ij}$ Where we calculate the test $F$ ...
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1answer
133 views

How can the F statistic of my anova test be greater than 1?

I've been digging into the formula for one way ANOVA test and I understand the we obtain the results from the ANOVA analysis with: ...
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0answers
56 views

Why Does Sample Size Affect the Value of F-Statistic We Require to Reject the Null Hypothesis of No Relationship?

In studying for multiple linear regression, I came across a comment that says that given a large sample, a F-statistic slightly larger than 1 could suggest there is some relationship between the ...