Questions tagged [r-squared]

The coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by a regression model. Can also be used for various pseudo R-squared proposed, for instance for logistic regression (and other models.)

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47 views

Why must the R-squared value of a regression be less than 1?

Why must the R-squared value of a regression be less than 1? What does R-Squared value more than '1' indicate? Can a Regression Model with a Small R-squared Be Useful?
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What to do when R-squared is 1?

I want to regressed Set A with Set B; their correlation is 0.88. Set A runs from 1 to 70. Set B runs from 30 to 100. I want to create a Set C from 1 to 100 by using the linear fit between Set A and ...
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Generalization of Adjusted R-Squared to Nonlinear Models

We are in the prototypical machine learning setting. We have a set of random variables $X=X_1,\ldots,X_p$ representing predictors, and a random variable $Y$ representing the dependent variable. We ...
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497 views

Does cross-validation shrinkage of the r-squared have anything to do with LASSO shrinkage?

When you fit a model to a "learning" data set, and then apply the same model to new data, the coefficient of determination shrinks, and this "shrinkage" is a measure of how well a model predicts in ...
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457 views

Pseudo R-squared of averaged model

I am working on model averaging of data collected about bird species and habitat vegetation. I have been using the MuMIn package in R and have taken a subset of all ...
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Simulate data based on linear regression and R squared

I have a small data set of 10 x,y points from which I can derive a simple linear regression. I'm looking to use this data set as a basis to simulate / predict additional "y" points as I have a much ...
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10 views

How are differences in R2 of two models with/without variable A related to the (partial) eta2 of variable A in the extended model?

Assume I have two models: m1: Y = B0 + B1*X1 + e m2: Y = B0 + B1*X1 + B2*X2 + e How is the difference in R-squared between m1 and m2 related to the (partial) eta-squared of B2 in m2?
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Is there within and between R^2 for pooled cross section?

I am writing a referee report for a paper that reports within and between $R^2$ for pooled cross-section regression that includes year fixed effects (but no panel or other fixed effects)so the ...
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How to statistically compare the coefficient of determination (R2) among multiple simple linear models (nonnested) with same scales (IV's)?

I made two simple linear regression models with the same scales (i.e. X variables, sample size and Y variable). The adjusted R2 was used to compare the good of fit between these models. But, how to ...
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Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$

I am interested in the geometric meaning of the multiple correlation $R$ and coefficient of determination $R^2$ in the regression $y_i = \beta_1 + \beta_2 x_{2,i} + \dots + \beta_k x_{k,i} + \...
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920 views

R-squared for glmmTMB with beta distribution and logit link

I'm looking for a method or function for computing R² for glmmTMB models with a beta distribution and a logit link. I am interested in a ratio (%) response in a repeated measures design. I looked ...
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211 views

Generating R squared statistics when carrying out a Firth Logistic Regression

I am using the logistf package available for SPPS to carry out a firth logistic regression, and have results relating to the coefficents, standard errors and p-values associated with each predictor. I ...
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Identify suitable scoring metric for food prediction

I am using GridSearchCV to find the best parameter that help me tune XGBoost for a food prediction algorithm. I am struggling to identify the best scoring metric that would result in the best profit (...
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does r-squared say anything about statistical error?

Can i estimate error bars based on the value of R-squared, when the signal is measured once (no SD)? Normally I do not use statistics but the time has come and i have to calculate error bars.. The ...
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How to simulate the outcome in a simple linear regression given X and R-squared?

Suppose that we have a fixed $R^2$ and one predictor $X$, sample size = $n$. How can we simulate an outcome variable that follows a normal distribution with $\epsilon \sim N(0,1)$ so that in a simple ...
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linear mixed effects models - overfit: how to calculate predictive R squared

I am using R to build the random structure of my model but I am ending up with a very complex model. Currently looks like this: ...
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Driscoll kraay estimator and R squared

I am doing a panel data regression with Driscoll-Kraay standard errors. Do my R-squared and adjusted R-squared stay the same when using Driscoll-Kraay standard errors?
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Koenker & Machado (1999) goodness-of-fit criterion (R1)

Has anyone come across a journal paper or a book providing a rule of thumb regarding what R1 is appropriate in research that focuses on the impact of macroeconomic or bank-specific variables on bank ...
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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
56 views

How to test several predictors' effect when you use means and standard deviations (or SE) from published papers?

For explanatory purposes, I will give a fake example to understand my question (and goal). Let's suppose I get from different published papers data about the concentration of a substance (...
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1answer
26 views

Help with understanding logistic regression's $R^2$ value

I have a set of ordinal varies (0,1,2,3,4) and I'm trying to do binary logistic regression with a dichotomous variable (0,1). These are the values, where the numerator is = 1 and the denominator is = (...
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How to evaluate prediction error from population?

I have data of 30 subjects. For each subject, measurements have been performed every 5 minutes. Due to the different length of the duration of the procedures, each subject has different amount of ...
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790 views

Why are results different between MuMIn::r.squaredGLMM and piecewiseSEM::sem.model.fits?

MuMIn::r.squaredGLMM and piecewiseSEM::sem.model.fits should be preforming the same calculations. They are implementing Schielzeth and Nakagawa's R2 for generalized linear mixed effects models. ...
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Multiple regression with a blockwise manner vs simple multiple regression

Almost all papers I read (in social science) used multiple regression in a "blockwise" manner instead of including all variables at once. I was wondering if it's even possible in our field to not go ...
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How to calculate variance of Y explained by my predictor X when using a gamma GLMM and an identity link?

I want to assess how well my variable X explains Y. As far as I know, I have to use mixed-effects models since what I have is data over time from 6 individuals. Below I show the relationship between X ...
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Informational value of R squared and correlation? [closed]

Taleb has previously undermined the typical interpretation of correlation with regards to the informational value it carries, showing how the uncertainty is reduced in a non-linear fashion. With ...
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21 views

R mgcv::gam or mgcv::gamm - Difference in Rsquared

I am fitting a predictive model on spatial distribution of a species according to environmental variables with gam from mgcv, but I have some difficulties with the results I obtained. My model used a ...
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1answer
985 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 ...
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How to compute R-squared value when doing cross-validation?

I am using multiple linear regression with a data set of 72 variables and using 5-fold cross validation to evaluate the model. I am unsure what values I need to look at to understand the validation ...
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515 views

Coefficient of determination $R^{2}$ for each variable in multiple regression

In multiple linear regression, is the coefficient of determination calculated for each independent variable, or is it only for the model obtained, that is, in relation to all the independent variables?...
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Compare Residual Standard Error / r-squared to Accuracy

Using machine learning and having a data set with a target that can be both seen as a numerical value or a class, how could you compare the outcomes of the two possible type of models. For example: ...
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Pseudo R squared formula for GLMs

I found a formula for pseudo $R^2$ in the book Extending the Linear Model with R, Julian J. Faraway (p. 59). $$1-\frac{\text{ResidualDeviance}}{\text{NullDeviance}}$$. Is this a common formula for ...
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Most likely sources of divergence between (adjusted)-R squared and out-of-sample predictive performance

I'm wondering which invalid assumptions are most likely to explain the wild discrepancies between a model's R-squared as a measure of predictive performance, and the actual out-of-sample predictive ...
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Strategies to achieve a near-perfect Adjusted R square (0.99<=) with only the lm function in R while only using 25 variables?

The simulated data has 9 (All continuous) independent variables and 500 observations, the given response variable is a continuous variable. Currently, I am at an R squared of 0.965 with 22 variables. ...
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What is the main difference between Multiple R squared and Adjusted R squared?

How can we use this as a basis to decide the best regression fit model? Not many question posts included the concept of Adjusted R-squared for understanding.
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How to plot density for repeated k-fold cross validation?

Long story short, I conducted regression using repeated k-fold cross validation. While messing around I decided to plot the density of the R-squared distribution for the resampling. Obviously there ...
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Regressing predictions on corresponding observed values, does that make any sense? If so, would this be a reasonable proposition?

I have a list with around 100 different dependent variables, for each of them I have around 35 observed values with 12 explanatory variables (it’s the same 12 explanatory variables for all dependent ...
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McFadden's pseudo-$R^2$ based on reduced instead of intercept-only model?

McFadden's pseudo-$R^2$ is defined as difference in the log-likelihoods of the full and intercept-only model $1 -(loglik(full)/(null)) $ Given a multiple regression scenario (ordinal regression in ...
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Why the focus on variance reduction for $R^2$?

It seems to odd to me that we measure the explanatory power of a regression model in "percent of variance explained", or $R^2 = {\rm cor}(\hat{y},y)^2 = r^2$ even though we all know that variance is ...
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35 views

Missing R squared value from STATA output, what does that mean?

I ran a 2SLS regression in STATA, and there is no R squared value given in the output (only a dot where the value should be). What could this be interpreted as? Is it missing because it may be a ...
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Is `p` in the formula for adjusted R-square defined for tree models?

Let $R^2$ be the R-squared defined for regression models. Given a vector x, the target, and a vector, y, the prediction of the ...
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615 views

R-squared or ICC or Kappa or pairwise t-test comparisons to compare ratings

I would like to compare the scores (0-100 scale) of students who are rated by three different examiners. The correct score is assigned by fourth examiner. I would like to quantify how different the ...
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Higher $r^2$ value on test data than training data?

I am trying to create a linear regression model. I split my data into training and testing data, and built a model. The $R^2$ value on the training data is 0.840. Then I ran the model on the test ...
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Multiple R-squared from bootstrap in R

I am fairly new to R and am having issues with my bootstrapped linear model. I'm using non-parametric case re-sampling to account for some skewed variables. Here is what I have done so far: ...
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Can the multiple linear correlation coefficient be negative?

I am using IDL regression function to compute the multiple linear correlation coefficient... ...
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Why to report R squared?

If adjusted R squared is superior to R squared, then why do statistical software continue to report the latter? Is there any kind of situation when a researcher may prefer to use R squared instead of ...
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calculate R² as a function of μ,σ

Suppose I fit the sum of $t$ iid random variables $$y_t=\sum_{i=1}^t{x_i} \space \space \space\space\space x_i \text{ i.i.d} \sim N[\mu,\sigma]$$ to a linear regression model $$f_t=a\space t +b$$ ...
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How arbitrary is adjusted r-squared as a measure of fit?

I came across the adjusted $R^2$ for multivariate linear models, $R^{2}_{adjusted} = 1 - \frac{SSE / (n-p-1)}{SSTO / (n-1)}$, and I was curious what kinds of properties this satisfies. (Googling was ...
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Proportion of variance unexplained by one variable but explained by another variable

Suppose you have an dependent variable $ Y $ and two dependent variables $ X_2 $ and $X_3$. You want to know the proportion of variance unexplained by $ X_2 $, but explained by $X_3$. How will you ...
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How to adjust R^2 and the Coefficient of Determination when using Overlapping Observations?

I am currently working through the paper Improved Inference and Estimation in Regression With Overlapping Observations [1] which presents an elegant way to do inference on $\beta$ in a linear ...

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