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.

Filter by
Sorted by
Tagged with
0
votes
0answers
39 views
+50

Will ranking “correlation” of variables by Pearson's return the same results as chi-square and F stats?

Generally speaking my understanding and experience is that when I have some target variable and want to see which other variables best correlate with it (for instance to build a predictive model), ...
0
votes
0answers
35 views

relation between wald statistic and f statistic

$Y=X_i\beta_i+X_2\beta_2+\epsilon$ Y and $\epsilon$ are n*1 matrix $X_1$ is $n*k_1$ matrix $X_2$ is $n*k_2$ matrix $\beta_1$ is $k_1*1$ matrix $\beta_2$ is $k_2*1$ matrix F is f statistic for testing $...
3
votes
2answers
144 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,...
9
votes
2answers
120 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-...
0
votes
0answers
15 views

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 ...
0
votes
0answers
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 ...
5
votes
2answers
127 views

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{\...
2
votes
1answer
165 views

Why does the J-test yield a $\chi^2$ distribution?

My econometrics professor recently introduced us to the J-test. To perform the J-test, he gave us the following procedure: Estimate $\mathbf{b}^{2SLS}$ and using this, define $\hat{U}_n$ residuals ...
0
votes
1answer
118 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 ...
2
votes
2answers
196 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 $R^2$?
2
votes
1answer
403 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 ...
0
votes
0answers
13 views

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 ̃^...
17
votes
4answers
30k views

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 ...
0
votes
2answers
1k views

The square of each t-statistics is the corresponding F-statistics

The below text is from statistical learning Page 76-77. The data used in the following example can be found here . I just want to know how to calculate $RSS_0$ (It is different from TSS) As ...
1
vote
0answers
130 views

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: ...
1
vote
0answers
65 views

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{\...
0
votes
1answer
70 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 ...
5
votes
1answer
143 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 & ...
0
votes
0answers
38 views

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: ...
0
votes
0answers
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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
17 views

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 ...
2
votes
1answer
1k views

R-squared and F-stat in dummy variables regression vs panel FE model

When estimating a Fixed Effects model on panel data and an equivalent dummy variables regression, the coefficient estimates and associated SEs are identical. However, the R-squared and F-statistic are ...
0
votes
1answer
378 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 ...
1
vote
1answer
80 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 ...
1
vote
0answers
396 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 ...
1
vote
0answers
21 views

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} ...
0
votes
0answers
16 views

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 ...
0
votes
1answer
429 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 ...
25
votes
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)...
0
votes
0answers
367 views

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 ...
2
votes
0answers
58 views

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 ...
1
vote
1answer
738 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, $\beta$ ...
3
votes
2answers
1k views

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 $...
0
votes
0answers
154 views

find F-statistic using R output

I have this R output: ...
0
votes
0answers
247 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 ...
1
vote
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 ...
2
votes
2answers
213 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 ...
1
vote
0answers
591 views

When to include or reject interaction term in two variable linear regression

I am studying a treatment that degrades device quality and performed an independent sample test on two batches that had different initial quality. I analyzed the data with a two variable linear ...
1
vote
1answer
216 views
2
votes
0answers
92 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 ...
0
votes
1answer
728 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: ...
1
vote
0answers
425 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 ...
1
vote
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-...
5
votes
3answers
23k views

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: ...
1
vote
1answer
398 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}} {\...
1
vote
0answers
156 views

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 ...
2
votes
2answers
551 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: $$\frac{\text {variance between groups}}{\text {variance within groups}}$$...
1
vote
0answers
64 views

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 ...
1
vote
0answers
60 views

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 ...