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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Is the adjusted R square good for the interpretation prediction accuracy of machine learning regression model and how to interpret it?

Is the adjusted R square good for the interpretation of machine learning regression (SVM, Random Forest, Elastic Net, etc) model prediction accuracy? How to interpret machine learning regression ...
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Source for how to Interprete Results with Extremely Low p-values and Coefficient of Determinations [duplicate]

I finished doing a bunch of data analysis and my results have very impressive p-values and absolutely horrible coefficients of determinations. The way I want to interpret this is that my methodology ...
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Statsmodels OLS R^2 calculation

I understand, that OLS of statsmodels sometimes uses centered and uncentered model for the calculation of R^2. Other calculations like tvalues, params, etc use only uncentered model. I want to ...
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Is there such a thing as a too low R-squared when running multiple linear regression?

This is a very general question about R-squared or the coefficient of determination. I found a couple of threads on CV but none that answers my question in a straightforward way. In short, what is a ‘...
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Can a linear regression model's r-squared value exceed the sum of the r-squared values of its input variables? [duplicate]

Suppose the $R^2$ value of $x_1$ with $y$ is equal to $0.15$. The $R^2$ value of $x_2$ with $y$ is equal to $0.35$. Can there exist constants $a,b$ such that the variable $X=ax_1+bx_2$ has an $R^2>...
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Explained variance modelling a diff (Δ𝑦)

I have a question that I'm struggling with, and it's related with the explained variance of model that uses a "diff" as independent variable ($Δy$=$y_t$-$y_{t-1}$) with the following form: $...
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Would the real adjusted R-squared formula please step forward?

The following question, What is the adjusted R-squared formula in lm in R and how should it be interpreted?, presents different formulas for adjusted R$^2$, which were, Quote: Wherry’s formula: $1-(1-...
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Model selection between LMM and GLMM

I'm investigating how the variable "heading" affects reaction time (rt). Here is a subset dataset of 5 participants as an example: ...
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Logistic regression for insurance data with a lot of zeros

I have a dataset of insurance claims with a variable $Claim$ is a Binary random variable (i.e. $Claim = 1$ if there is a claim and $Claim = 0$ otherwise). About 95% of the observation has $Claim = 0$ ...
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Understanding the construction of $R^2_{os}$ with MSPE

Following Using $R^2$ to evaluate out-of-sample performance I try to calculate $R^2$ with MSPE. They defined $R^2$ as $R^2=1−MSPE/Var(y)$ Since I am dealing with nested models, I use the adjusted MSPE-...
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What is the value range of summary(lm) Multiple R^2?

I have the summary of a linear model in R: ...
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Bayesian r2 for negative binomial

I would like to calculate a R2 value for a Bayesian model with a negative binomial distribution. I have commands to calculate gaussian or binomial, but I was wondering if anyone knew of methods to ...
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How to Evaluate model's r-square after inverting from logarithmic

I stacked with question about inverting the r-square() model value after taking log1p(). My baseline LinearRegression model ...
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Significance for R squared change of individual variables in R

I have two regression models and I have computed the change in R squared for individual variables in R. with "getDeltaRsquare" ( see output below ). However, I want to see if these changes ...
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Change in the coefficient of determination (R2) when multiplying dependent variables by the independent one in linear regression

I have three independent variables {x_1,x_2,x_3} that I use to fit to a dependent variable y using an OLS regression. The coefficients of determination (R2) of the variables in relation to y are: R2(...
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Conceptual difference between R squared and variance score

I am looking to gain conceptual understanding of the difference between these terms. Note that I do know the formula for both. These have been presented clearly in: What is the difference between $R^2$...
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Comparing R^2 and Q^2 residuals

I am calculating the Residuals for a PCA algorithm. When I calculate them though the $Q^2$ residuals sometimes are larger than the $R^2$ residuals. My understanding of the $R^2$ and $Q^2$ relationship ...
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Why does changing quarter to months of time series change the R-squared value?

When I use plot the average value month on month Vs quarter on quarter, I get different R-squared value. What does this mean for my regression? Do I pick month / quarter based on a higher R-squared ...
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Sampling distribution of $R^2$

Given a sample from a population, and a model fit to that sample $y=f(x)+\epsilon$, what is the sampling distribution of $R^2$? (i.e.: scaled brier score). I could compute its variance easily enough, ...
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Hausman-style test for overfitting

In econometrics, the Hausman test evaluates the consistency of an estimator when compared to an alternative, less efficient estimator which is known to be consistent. Does a similar test exist for ...
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on the use of R squared as a measure of predictive accuracy for non-parametric models such as random forest

I am confused. I know there are a couple of similar questions about $R^2$ but I hope I get some opinions on this particular matter. I have trained a random forest and other nonparametric regression ...
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What's the difference between regressing $y$ on $x_1$ and $x_2$ rather than on their sum $z = x_1 + x_2$ or their difference $d = x_1 - x_2$?

I remember reading about this somewhere, but I cannot find the source anymore and I'm not sure what the benefit of doing it would be. Do the results of the regressions have anything in common (e.g. ...
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Help with adjusted r-square

What does it mean if my adjusted r-squared decreases between my bivariate and multivariate regression models? is this a bad or good thing?
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How can I interpret a model with good p-values and a bad R^2? [duplicate]

I performed a linear regression and I got a p-value < 0.05 but my R^2 is low (< 0.04). How can I interpret the results? The model is significant but there's not a good fit, what can I do to ...
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Using $R^2$ for RF

Can the $R^2$ measure be used to measure the performance of Random Forest model? My explanatory and dependent variables are linearly dependent.
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Is it reasonable to use marginal and conditional R2 as form of variance partitioning?

I have ~1000 rows 2 fixed effects and 3 random effects. I want to know if I can separate the "explained" variation of the fixed effects from the random effects. I want to show that If you ...
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Which $R^2$ plm outputs?

We have three kinds of $R^2$ when considering panel regression (overall, within and between). Programs like stata return all 3 r-squared whereas plm in R returns only one. My question is : For sure ...
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R-squared fot multivariate regression

I have an output of recalibrated VARX model, which means for each 500 points of my data set I have trained a model and predicted the next month values using that ...
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How to prove the equivalence of partial correlation and coefficient of partial determination?

I am taking a regression course. I do not know how to prove these formulae are equivalent. $$ R_{Y1|2}^2 = \frac{SSE(X_2) - SSE(X_1, X_2)}{SSE(X_2)} $$ $$ R_{Y1|2}^2 = \frac{(r_{Y,X_1} - r_{Y,X_2}r_{...
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Is there a relation between the p-values of coefficients and the R2 in an OLS regression?

I have a very simple question. I know that the R-squared is the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. I ...
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What algoritm is used by Statistica 13 for factor analysis method “Communalities=multiple R2”?

What algoritm is used by Statistica 13 for factor analysis method "Communalities=multiple R2"? I'm trying to reproduce in Python the explanatory factor analysis done with the Statistica's &...
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Explanation of R^2 with partition of variance

In the context of multiple linear regression, I'm looking for an explanation of $R^2$ with as few concepts as possible. I came up with the following: Explanation Data is modeled as $y = \hat{y} + \...
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Negative adjusted R-square when using PLM fixed effect model, but not when using LM model with dummy variables

I am analysing panel data model across 20 years and 55 counties. I want to perform fixed effect panel data regression. I started using lm using dummy variables and ...
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What in God's name is r^2? [duplicate]

Call it what you like—coefficient of determination, goodness of fit—I'm lost. I'm an AP Statistics student, and our class is on Unit 3, which delves into least squares regression linear models. To ...
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Interpretation of unreasonably high R-squared [closed]

High CrossValidated community, I need your "brains" to explain a result related to my model(s). I have some data that contain physical quantities $y$ measured at specific points (e.g. ...
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How to evaluate a regression model with multiple results?

I created a neural network for time series forecasting. My experiments involve comparing the effects the different regularizers have on the model. I used cross-validation and measured my model's ...
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Extract all R2 values from LMM

In order to analyse which factors have greater weight in the proportion of incidence (number of infected individuals against total individuals), the interaction of all factors (habitat, site and ...
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What does it mean to have 'R^2 larger than chance' (from sklearn docs)

See the following: From : https://scikit-learn.org/stable/modules/permutation_importance.html The part I'm unsure about is: Its validation performance, measured via the score, is significantly ...
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Why do we not get an R squared value for the intercept only term? [duplicate]

When I try to fit an intercept only model in R, why do I need get an R squared? I can see from the formula of the adjusted R squared that this would be 0, but this isn't shown either.
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Why do I have a negative R squared if my model has an intercept?

Don't know what else to say, I am running a first difference panel IV model and getting a negative R squared. I imagine it has something to do with instrumental variables but can't figure out what. I ...
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How to deal with predictors which are not significant, although r-squared is significant?

I did factor analysis and found three factors. To examine if which factors significantly affected a certain dependent variable, I added all three factors to a regression model. The correlation ...
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Range of $R^2$ of the model with two predictors given the $R^2$s of univariate models of each predictor

We have a dependent variable $Y$ and two predictors $X_1,X_2$. Given a fixed dataset, $R^2$ of the model $Y$~$X_1=t_1$ and $R^2$ of the model $Y$~$X_2=t_2$. What is the range of $R^2$ of the model $Y$~...
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If adjusted R-squared is zero, can individual coefficients have meaningful interpretation in multiple regression?

It can happen that adjust R-squared metric in multiple regression is zero (or very close to zero), but individual coefficients are statistically significant. Under these circumstances, can I still ...
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$R^2$ can be written as sum of correlation coefficients

I am dealing with the following problem with multiple linear regression. Assume $Y_i = \beta_1 X_{1i} + \beta_2X_{2i} + u_i$ in the linear regression model. Suppose $\sum_{i=1}^{n} X_{1i}X_{2i} = 0$, ...
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R2 on out-sample data set

The conventional definition of $R^2$ is: $R^2 = 1-SSE/SST$, where SSE denotes sum of squared errors and SST is total sum of squares ($n\times variance$, n being number of sample points in train set). ...
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Is there a reason to use MSE over R^2 for scaled data?

It seems that in the case of a scaled dependent variable (mean subtracted, divided by SD), the relationship between R^2 and MSE becomes: R^2 = 1 - MSE (http://brenocon.com/rsquared_is_mse_rescaled.pdf)...
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Nakagawa's R2: what does it tell practice?

I am having a hard time figuring what Nakagawa's R² really "means". I understand that in simple linear regressions, R² indicates the amount of variance in the dependent variable explained by ...
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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 $R^2$?
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I have a very high $R^2 (0.96)$ for my ARDL time series model, is this problematic?

All my variables are stationary, so cointigration can't be the problem. I have included one lag of the dependent variable and 5 explanatory variables. When I remove the explanatory variables, the R^2 ...
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Which Standard Deviation do I use when calculating the R squared of a Holdout Sample?

When I am calculating the accuracy of my regression model on my holdout sample, which standard deviation do I use? Currently, I am using this formula: R squared = 1 - (sum(holdout - predicted)^2) / ((...

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