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.

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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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$R^2$ of Log transformed data is positive, however that of reversed transformed data is negative

I am running an XGBoost model with a continuous target variable. With ~200 features I am getting a Test $R^2$ of 0.54. By looking at the distribution of the target variable, it appears it's highly ...
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R square output in lrm function : Is it a pseudo or not? [closed]

Using rms package, I was wondering if the r-squared in the output of the lrm function in R is a pseudo-R or just a R-square like for a linear regression? Thank you,
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$R^2$ is too high- reasons? [closed]

What are the reasons of too high values of $R^2$? I only know that its value increases when the number of independent variables increases. What are the other factors?
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Weighted regression - How does weighing observations of different magnitude affect the results of Multiple Linear Regression analysis?

I am working on a dataset that contains some statistics for each county in the US. I am trying to predict the amount of people with diabetes based on all the other predictors. The counties are of ...
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Can R^2 be used as the metric for model/parameter selection (grid search)?

I have a simple model with 3 free parameters to fit, and wanted to try estimating those parameters via grid search. I was wondering -- what is the convention for selecting the best model in this case? ...
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How can I calculate Nagelkerke pseudo r2 with glmmkin object from GMMAT package in R?

I have used glmmkin function from GMMAT package to fit a logistic mixed model with the binary phenotype 'disease', one fixed variable 'PRS' and one kinship matrix 'GRM' to model the covariance ...
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How do I understand “Ballentine” diagrams of variance for a univariate OLS regression?

I recently learned about the use of Ballentine [sic] diagrams to illustrate some principles of linear regression. There appear to be a few different implementations of this principle. Notably, in some ...
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Why is R-squared equal to the sum of standardized coefficients times the correlation?

Reading about standardized coefficients I came across the following formula: $$R^2=\sum\beta_ir_{yi}$$ Where $\beta$ is the standardized coefficient for the independent variable $i$ and $r_{yi}$ is ...
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R - factor model - R-squared calculation

I am trying to recalculate in R an example of a factor model presented in the Zivot, Wang book (Modeling Financial Time Series with S-PLUS) p.548 (link) I am looking for an explanation of the ...
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If the coefficient of determination is a measure based on variance, then what about standard deviation instead?

Background: I've been teaching a very simple course of introductory Statistics for a few years now and we cover linear correlation and the Correlation Coefficient ($r$). I want to introduce the ...
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Hayes Mediation Tables with binary outcome variable

I am trying to put together mediation tables for my study which has a binary outcome variable. Normally, I report the R-squared and F statistics for my mediation model. However, SPSS Process does not ...
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multicollinearity high R squared

I understand that one of the ways to detect multicollinearity would be to observe low t-stats and high r squared. t-stats will will be low because the standard errors of the coefficients will be high, ...
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Trying to understand partial R-squared

I'm trying to understand partial R-squared as computed by package rsq. See the reproducible example on the standard data set: ...
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AUC or $R^2$/RMSE for binary classification

I am using doing a binary classification to classify things 0 or 1 using a set of features with LightGBM and XGBoost. Both models give AUC scores roughly in the <...
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Transformed data due to non-normal residuals - how to see if it actually improved the model?

I am trying to run a linear regression model (ideally) to see whether age (continuous variable) affects levels of stress hormone (also continuous, dependent variable), i.e. hypothesis testing. My ...
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$R^2$ and adjusted $R^2$ in presence of overlapping observations

Given a linear model $$ y=X\beta+\varepsilon, $$ the population value of $R^2$ is $$ R^2=1-\frac{\text{Var}(\varepsilon)}{\text{Var}(y)}. $$ The vanilla estimator of $R^2$ is $$ \hat R^2=1-\frac{\...
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Why is Out of sample R^2 inappropriate for Time Series Forecasting?

I've been reading a few posts from distinguished members of this community about R^2 and time series forecasting: 1.What is the problem with using R-squared in time series models? 2.R-squared to ...
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How to compute RSquare from GLS regression in a Fama Macbeth procedure

I am trying to compute the RSquared from the Fama Macbeth procedure using GLS regression, but for some reason I get negative values, so I was wondering what the problem might be. The Fama Macbeth ...
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R^2 value more than one [duplicate]

I have a question about the R^2 value equation given on page 112 (Forecasting Principles and Practice) by Dr. Hyndman. I am working with a dataset with 100 samples and the R^2 using gives me a value ...
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Why are the R-squareds of the subsamples much smaller than the R-squared of the full sample? [duplicate]

I'm hoping to get some intuition on what is happening. My R-squared in the full sample is 10%. When I split my sample into two subsets, my R-squared in each subset is about 1%. I thought the R-...
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Can you compare coefficient of determination $R^2$ fitted to two distinct sets of data?

I have a simple linear regression model, $\textrm{Weight} = \beta_0 + \beta_1 \cdot \textrm{Height}$. Can I pick only men, fit model 1, get an $R_{\rm men}^2$, and do the same for women with $R_{\rm ...
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A question about regression analysis: invariance of partial R2?

Say we're given a design matrix $X$ as well as some invertible matrix $H$. I'm interested in the partial $R^2$ of $X_{i}$ given $X_{1}, X_{2}, ..., X_{i-1}$. $H$ is such that $e_{i}^{T}H = e_{i}^{T}$, ...
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Does the high coefficient of determination in this graph predict a huge spike in global warming? [closed]

I have had three semesters of college statistics as part of my BSBA degree. From what I recall from regression analysis the graph seems to show a very high coefficient of determination between CO2 ...
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Partial R2 for factors in nlme

I need to obtain partial R2 for all explanatory variables of a mixed model, which should also include a correlation structure. For instance: ...
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incremental $R^2$ update at every new sample [duplicate]

I am sampling from a random process $X$ and I would like to calculate $R^2$ for the cumulative sum of the samples: $$x_1,..x_n$$ $$y_n=\sum_0^n x_i$$ $$R^2_n=RSQ( [1,2,...n], [y_1,y_2,..,y_n])$...
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1answer
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correlation coefficient in pandas (pearson) [duplicate]

I have divided my data into training and testing, and I am outputting the error metrics on the testing data. This is what I get: ...
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1answer
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$R^2$ of 1 but RMSE > 0

I am running k-fold cross validation on my training data, and then choosing the best set of hyper parameters, re-training on the training data and testing on a new (unseen) testing data. I am getting ...
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Help on R squared, Mean Squared Error (MSE), and/or RMSE as individual measures in regression model perfomance evaluation?

Just a question on regression model evaluation statistics. Here we go. I seem to be under the impression that $R^2$, MSE, and RMSE are all very closely related and essentially all play a part in ...
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Question about R squared ratio in model comparisons

I am currently working with a few different regression models (regression trees, GBT, linear, etc) in the platform KNIME and now that I have computed the following statistical measures: $R^2$, mean ...
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Overall score in cross-validation

I am using Repeated K-folds (RepeatedKFold(n_splits=10, n_repeats=10, random_state=999) from sklearn) to provide reliable scores for a linear regression on my ...
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Is there a distinction between the “squared semi-partial correlation” and the “semi-partial R squared” of a fixed predictor?

The package 'r2glmm' in R calculated the "semi-partial R squared" of each fixed predictor in a mixed effects model. The package describes this as "The semi-partial R squared statistic corresponds ...
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R-squared interpretation

Does the R-squared provide an indication of the degree of endogeneity? For example, does a low R-squared suggest there is more correlation with the error term? If so, why? If not, why not?
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Sum R-Squared over uncorrelated features

I am currently developing an automatic approach to eliminate noisy samples from a data set. I clustered all the samples, and then I am iterating over all the clusters, eliminate the samples of the ...
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1answer
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Can adjusted r-squared (or r-squared) be used to compare the strength of independent variables in linear multiple regression?

Relative newbie with quantitative analysis here, so forgive me if the question is naive or ill-specified. I have argued in a manuscript that along with using Beta values in linear multiple regression ...
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1answer
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Out of sample and In sample forecasting - R squared

Can anyone explain why R2 (R-squared) for out of sample forecasting is likely to be smaller than R2 for in-sample forecasting?
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regressions with common domain: upper bound on r squared

Heres a conjecture I'm struggling to prove / disprove: Let $X \in \mathcal{R}^{N \times a}$ represent a set of $N$ observations, each having $a$ features. Paired with each observation $x_i$ are ...
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1answer
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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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Does over fitting a model affect R Squared only or adjusted R Squared too?

The total sum of squares for the variable being predicted is as the following: $$\mathrm{TSS}=\sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^2$$ and the residual sum of squares from the predictions from ...
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MAPE vs R Squared, and their Interpretation in Regressions

So, I'm somewhat familiar with R squared and MAPE, and their usage to qualify the goodness of fit for a regression model. My question is not about when to use one or another (like in this post) but ...
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calculate a variance for a given R-squared [duplicate]

I am trying to replicate a study that has generating simulated data with the following variables and assumptions $x_j\sim U[0,1]$, and $j = (1,2,\dots,N)$ with $$z_j = x_j + \sigma_z \epsilon_j$$ ...
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magnitude of correlation

Another question has gotten me thinking about testing more than just correlated/not correlated. Let's say that I have some data and find the correlation to be $0.15$. However, I then realize that ...
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1answer
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R-squared and sample size

I was wondering if R-squared is affected by the sample size? Is adjusted R-squared also affected? The reason behind this though is, that i have run a multiple linear regression on two samples. The R^...
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How to measure explained variance in y in the case of regression dilution bias?

I would like to find the explained variance in y by x when both y and ...
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Adjust for confounder in calculating explained variability in cox-regression

My question is closely related to this one. I am interested in the proportion of variability which is explained by a certain covariate X in a cox-model. So I have the cox-model “outcome ~ X”, for ...
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$R^2$ can be negative, but can it be -100% or lower? [closed]

I saw an $R^2$ statistic being reported as $-115\%$. I thought $R^2$ must be between $[-1, 1]$ so can it be negative to beyond $-1$?
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Can I ignore the negative R-squared value when I am using instrumental variable regression?

I am running an instrumental variable regression using 'ivreg' command in R program. I find that all my validity tests related to endogeneity are satisfied only except the R-squared value which is ...
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R-squared unbiased when F-test is biased in heteroscedasticity?

If R2 and F-statistic are in functional relationship, is it possible, that in case of heteroscedasticity F-test is biased but R-squared is not?
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Time series Data : Regress absolute values or regress the %growth of the values?

I am doing a time-series data analysis. The idea is to produce a forecast from the regression output. I am regressing Air traffic passengers of country A with GDP/capita of country A. I am getting ...
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Multiple Linear regression: inverse the y value

I have a dataset of 3500 samples where delay (dependent variable) depends on multiple system variables,such as cpu, memory, etc. I can use a multiple regression model and predict the delay against a ...