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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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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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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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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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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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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1answer
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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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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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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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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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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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1answer
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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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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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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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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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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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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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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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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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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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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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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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1answer
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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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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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conditional and marginal R² in r.squaredGLMM always the same

I get exactly the same values for conditional and marginal R² from the r.squaredGLMM in the MuMIn package. I tried this with various similar data sets. I wonder whether there is a bug within the ...
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R square and R square adjusted

As $R^2$ increases, $R^2_{adj}$ increases too. Is that statement true?
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How to improve the adjusted R squared value in R?

In my model target variable is continuous variable, 32 independent variables with categorical and 106 observations. I build a linear regression model with lm() function. I tried in 2 ways. First, I ...
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32 views

Does R-squared help assess statistical significance?

I have a R-squared of 0.4787. I know it indicates the model does not fit very well with the observations, but that is what I got so far using R. My question is: does R-squared help to access ...
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Coefficient of Determination for multiple regression models

I was wondering if it's possible to calculate one (global) coefficient of determination for multiple regression models. Context: I've set up a batch regression process which generates sales ...
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What happens when we introduce more variables to a linear regression model?

Let’s consider the following regression model: y = B0 + B1*x where B0 — represents the intercept B1 — represents the coefficient x — represents the independent variable y — represents the output or ...
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Odd results of AUC and McFadden R2 on insure tech article

I was reading this article entitled: Usage-Based Vehicle Insurance: Driving Style Factors of Accident Probability and Severity (Korishchenko et all., 2019) [1], and watching the results section, I saw ...
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low marginal and high conditional R2 for mixed models

I have a suspicious output in my linear mixed model lmer() (lmer package), where I have marginal r2 of 0.08 and conditional of 0.8. I am not surprised by the low marginal r2, however, I am puzzled ...
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What is the coefficients of determination of prediction?

I have never seen this term mentioned before. Yet this study uses it: https://www.econstor.eu/bitstream/10419/204328/1/ifro-wp-2011-12.pdf Is it any different than the typical R^2, i.e. ...
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1answer
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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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Degree of Freedom of Null Model in Logistic Regression

I built a logistic regression in R using 6 predictor variables and the output is as shown: ...
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Under what circumstances can you compare the $ R^2 $ value of two models? [duplicate]

When you different models that are trying to establish the relationship between the same variables -- but these models have different structural forms, when can you compare the $R^2 $ of these models? ...
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Determin the determination coefficient R square

I have the following question and I couldn't figure out how to solve it. The given is the following: The model is: Yi = B0 + B1 Xi + Ei I have the following dependent variables 2, 4 and 8 (3 ...
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What is the main difference between multiple R-squared and correlation coefficient?

I have a R code that runs lm function and get the summary. What is the meaning of multiple R squared? And is there any relationship between multiple R-squared and ...
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Multiple regression $r^2$ as a function of single regression $r^2$

Let $Y, X_1, X_2 \in \mathbb{R}^n$ be random variables, and let $r_i^2$ be the proportion of variance explained by the linear regression $Y \sim X_i$. Let $r_{12}^2$ be the proportion of variance ...
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How to find in-sample sum-of-squared errors and $R^2$ after glm?

My formula is: glm(formula = total ~ yr * mnth, data = daytots) yr and mnth are factors, ...
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What to make of high R-squared and non-significant p-value of a linear model?

I am using doc2vec to produce $\mathbb{R}^{50}$ vector representations of short bits of text. I am then using those vectors in a linear model to predict a continuous outcome variable. The R^2 is .25 ...
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R² for a negative binomial regression model

I have been searching quite a while to find a useful way for calculating (an estimate for) the explained variance for a negative binomial regression model in R... Knowing that the "explained variance" ...
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Prediction model clarification

I have the following formula and I'm trying to understand whether the square root, Rˆ2 the coefficient of determination is and whether sdev(y) the standard deviation of the outcome variable is. Please ...

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