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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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Is there an alternative to R squared to compare goodness of fits of different datasets? Slope makes them incomparable

I'm fitting the degradation of a signal. Some instruments degrade faster than others, so the slope varies a bit. This makes it difficult to compare how good the fits are relative to eachother. See ...
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Is conditional r-squared ever zero?

I am using multivariate auto regressive modeling (MAR) to assess a complex data set (MAR is a form of vector auto regressive modeling, VAR). The output of the MAR method is >1 response variables and >...
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Recommended references for R-squared and/or adjusted R-squared

I need some solid references that discuss the meaning and interpretation of R-squared and adjusted R-squared in linear regression. For example, I want to learn more about when a low adjusted R-squared ...
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Comparing the output and fit of an OLS and a Tobit model, and comparing Tobit models

I am trying to estimate a quite complicated model (many variables with different structures), with a limited dependent variable, which ranges from 0-100% with about 45% of the sample having an ...
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How to test the homoskedacity using GQ test, Interpret R2 with VIF, Calculate Adjusted R-squared [closed]

Can you please show me with some explanations how to test the homoskedacity using GQ test, calculate and interpret R2 with VIF for a model, Calculate Adjusted R-squared from the pictures from this ...
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What type of regression should be used in predicting Click Through Rate?

I'm looking for a model to predict CTR (click-through-rate) I have the following data: For each ad I know the number of impressions, clicks and some other attributes (which are mainly dummy variables)...
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R squared / deviance explained for elastic net glmnet

I am using R glmnet function for the elastic net for logistic regression with binary outcome and would like to calculate the R-square value. I am getting different results when I use the dev.ratio ...
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R^square for a pre-determined linear regression

I would like to produce the R^square goodness-of-fit statistics for a predictive model. I have the base data (10, 000 number of x-values) which are the true values given by an analytic/deterministic ...
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What does small R squared mean in linear regression [duplicate]

I'm applying linear regression on. problem and getting very small R squared, e.g. 0.087 and adjusted R squared 0.057. This is very small for R squared. What does this mean for my regression? Does it ...
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Computation of R-squared with lm() in R [duplicate]

Confusion on difference between the $R^2$ results from the lm() function in R and from the Equation $1-rss/sst$ (1) Ref: https://onlinecourses.science.psu....
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Does the $R^2$ depend on sample size?

It's well known that adding more regressors can only improve the $R^2$. What about the number of observations? Say you have a sample of size $N$, and you draw a random subsample of size $n < N$. ...
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Should I stack models or extract more features for a tiny, but hard gain in R2?

I heard that stacking models is only worth it doing it in a Kaggle competition as everyone is dealing with the same training data, and due to time limit, feature engineering only helps a little with ...
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What does “regression of predictor onto all of the other predictors” mean?

I encountered a lot of references that talk about R squared but I can't understand what the difference is between the R squared in regression of the response on the predictors and the R squared that ...
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R2 - contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y

I wish to look at the contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y. To summarize the contribution of the explanatory variables alone to the ...
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55 views

Why are conditional and marginal pseudo R^2 the same in this example?

Here is a reproducible example: The problem is that when I calculate Pseudo R^squared for the null model it gives 0.18 to conditional R^2, the variance explained by the random factor is not 0. However ...
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Pearson and R^2 Correlation between three variables

Get it from someone else but don't quite know how to answer. If $\rho_{X,Z}=0.4$, $\rho_{Y,Z}=0.3$, what is the range of $\rho_{X,Y}$? Here $\rho$ is the Pearson correlation coefficient. We run a ...
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2answers
34 views

How do I select right features

I am working on Boston Dataset in which the aim is to predict the MEDV which is median value of owner-occupied homes in $1000s. ...
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1answer
37 views

Mediation, low R^2

I am currently working on my model in which I would like to test mediation effects. In my model following applies Y-company attractiveness X-type of application (digital vs nondigital) and M-...
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Why is R squared zero when the best-fit line is horizontal?

Why is it so that the regression line is horizontal to the x-axis when r-squared = 0? I do understand that when r-squared = 1, estimated Y and actual Y are equal.
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Compute a measure of explained variance for hurdle models in R

I am working with a dataset df which comprises count data count and a number of categorical variables. ...
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Discussing R-squared of log-log model with a non-technical audience

I have been asked to report on the relationship between two right-skew financial variables using R-squared e.g. "market cap explain ?% of the variance in CEO compensation". The purpose of the ...
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1answer
58 views

Why is individual R-squared higher than overall R-squared?

I ran a ridge regression model on a set of data across 6 groups. As you can see, the overall R-squared is low. Because groups A and B make up the most of the data, I would think the overall R-...
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What statistics can I use to compare OLS to an ordered probit

I am trying to justify to the use of an ordered probit, my dependent variable is a survey response on a likert scale so is likely ordinal, but I wanted to provide a goodness of fit stat to back up my ...
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Calculating the Shared Variance from a Correlation Coefficient?

We often square coefficients like the R coefficient in simple/multiple linear regression or standardized factor loadings to get a percentage of variance accounted for by predictor variables. Can the ...
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OLS R-Squared Drops by 15% When Constant / Intercept is Removed?

I ran an Ordinary Least Squares model and found the constant / intercept is the more significant than all the other features. When constant is included, the R-squared is 45%, when I remove the ...
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Market modelling in R

Let's say I have data on SalesChannels(A-D), Weekstarts, Products(5 different ones), quantity sold, Price, promoperiod(true/false), Availability in Stores, and ad Spending in TV and Print and I want ...
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R2 drop in lasso: train vs test

I am using cross-validation to select best alpha(3-fold), and then applying it to test data. I am using sklearn's LassoCV. In-...
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1answer
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Difference between R-Squared and Adjusted R-Squared for one Predictor

I'm currently using R-Squared and adjusted R-Squared to determine goodness of fit of a linear model. Although I understand the difference between the two, I expect that for one predictor, both the R-...
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How to compare R-squared between two regression models derived from unequal sample sizes?

I estimated the variance in an outcome variable (y) that is explained by a predictor variable (x) after adjusting for the three covariates (c1, c2 and c3). I derived a full model (y~x+c1+c2) and a ...
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1answer
29 views

Calculate the correlation coefficient from the coefficient of determination

The question is how to calculate $r$ from $r^2$. Now, I know that its just as simple as taking a square root but is it as simple as that?
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Conditional and marginal R2 with mgcv

I am fitting a beta regression model with random effects using the mgcv pacakge in R. This package only provides an adjusted R-square. Is there any way to also get conditional and marginal R2 values ...
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1answer
45 views

How did R-square get its name? [duplicate]

How did R-square get its name? I understand how its calculated and interpreted, but I do not understand the r and square part of it.
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327 views

Multiple Regression, good P-value, but Low R2

I am trying to build a model in R to predict Conversion Rate. So, the model below: ...
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Is $R^2$ useless? [duplicate]

I stumbled on a discussion regarding the usefulness of $R^2$ as a metric. Where $R^2$ is defined as: $$ \frac{\sum (\hat{y} - \bar{\hat{y}})^2 } {\sum(y - \bar{y})^2 }.$$ The criticism is backed by ...
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What conclusion can I draw from this R square?

http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt The data records the average weight of the brain and body for a number of mammal species. There are 62 rows of data. I have a task to ...
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1answer
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High value of R-squared correlation on behavioral intention while very low value of R-squared correlation on actual use of mobile shopping app

I have been working on antecedents of mobile shopping with UTAUT-2 model combined with the constructs of trust and perceived risk. I am using a sample of international students for my study. I wanted ...
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Adding a predictor reduce R squared

Currently, I am doing Poisson models with N=16,000. My study requires me to find $R^2$ for each model (using 'rsq' package). When I add P12, the $R^2$ decreased as shown below. ...
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Should I lag explanatory variables in regression with apparently strong predictive relationship?

I'm no expert when it comes to statistics (learning though) and I am working on developing a multiple linear regression model in an attempt to forecast sales revenue. I feel like I may have developed ...
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Comparing log-transformed and non-log transformed models

Suppose I have the following two models fitted with constrained linear least squares: Model 1: $Y = \beta_1X_1 + \ldots + \beta_kX_k + \varepsilon$ Model 2: $\log_{10}(Y) = \beta_1\log_{10}(X_1) + \...
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pseudo R2 as xgboost objective function

I want to use a custom objective function with xgboost: 1 - (log(y) - log(p)) / (log(y) - log(q)) y = true value, p = my probabilities, q = some other base ...
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$R^2$ value and associated significance for each predictor in regression

I would like to measure the $R^2$ value for each of the predictors in my regression analysis. I understand that I can either use the $R^2$ change in a hierarchical regression, or I can square the ...
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1answer
37 views

Different formula of coefficient of determination (R-squared)

I saw the below equation given for "Coefficient of determination" in a paper and thought it must be a typo, then I saw it in another paper too. Would anyone know what this is and how it is different ...
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variable transformation

friends, I want to use regression for prediction purposes with a sample of over 20k. I have the following results for the OLS with adj R-squared of 0.64: my first question is: can I say that the ...
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2answers
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Alternative to using $R^2$ to assign data categories?

A background to my problem: I use survey data on firms, where I want to measure the relationship between a binary variable (perceived growth barriers) and firm size. However, I cannot treat "firm size"...
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4answers
178 views

Is R-squared truly an invalid metric for non-linear models?

I have read that R-squared is invalid for non-linear models, because the relationship that SSR + SSE = SSTotal no longer holds. Can somebody explain why this is true? SSR and SSE are just the ...
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Comparing overall and conditional models

Let's say I have two regression models with 5 variables, one that is for all observations, and one that only includes values when the temperature is higher than 75 degrees. As an example I have this: ...
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234 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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Find contribution of various features/input variables to the variance of the dependent variable / Attribute variance of dependent variable to features

I am working on this problem where I have 20 odd features (input variables) and two dependent variables. The objective is to find the variance structure of one of the dependent variables. More ...
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Adjusted R-squared for tree-based models

How can I use an evaluation metric like adjusted R-squared to evaluate tree-based models? It's not clear to me, since adjusted R-squared accounts for the number of predictors included in a given model,...
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2answers
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Plus/Minus Model accuracy from $R^2$

I completed a linear regression for a model I was working on, and obtained that the $R^2$ value was $R^2 = 0.801$. Can one assess a $\pm$ error from this value for future predictions? I.e., if I now ...