# 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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### 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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### 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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### 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  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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### 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) , 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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### 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 ...