In linear regression, the coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by the regression model.

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Regression produces a high coefficient of determination, but also a high MSE

I've ran several regression models on a dataset (the SEER cancer dataset). I'm trying to use regression to calculate how many months a cancer patient can expect to live. Each record consists of around ...
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13 views

How can I get the pseudo-R squared by using censreg (tobit regression)?

I was using VGAM for tobit regression but when I entered new dataset which had more than 50000 records, it got errors like this: ...
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1answer
24 views

Why does the adjusted r-squared of this model improve with addition of a statistically insignificant variable?

I stumbled on this while doing MLR, and was curious as to why this happens. The adjusted R-squared is (if I understand correctly) supposed to be a way of comparing the predictive quality of models ...
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12 views

VECM “goodness of fit” in R

I'm using ca.jo in R to perform the Johansen test on a given dataset. I obtain my VECM coefficients, cointegration rank, etc. However, it does not seem to give any notion of "strength of ...
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1answer
140 views

Why do we need $R^2$?

In linear regression, the $R^2$ value is the square of the correlation between predicted values and observed values. But why do we need the $R^2$ value? Why not just use the correlation coefficient? ...
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1answer
33 views

How to show whether the average coefficients of determination from one regression technique are better than another across many objects?

I have 50,000 objects on which I have performed two different types of regression. Using cross validation, I obtained the average $R^2$ score from each model on each of the objects. So now I have a ...
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20 views

Pseudo R-Squared for gls function in Stata

I'm doing bachelor thesis finding "impact of Working Capital Management on profitability". This is the first time i deal with software like stata and many things really made me confused. After do ...
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1answer
31 views

Multlinear regression: analysis of residual of transformed response and predictor variables

In the first step of modeling a regression equation I came up with the following model: $T_c = 26.73 + 0.042{\rm Sc} + 0.247{\rm Lc} - 14.709{\rm Lf} + 1.41{\rm Lu} - 0.214{\rm Fc} + 0.041{\rm Ad} - ...
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1answer
48 views

Fit measures for GMM Arellano-Bond estimator in R

A colleague and I have been working with difference GMM, i.e. the Arellano-Bond estimator, in R. Our option has been to use the pgmm command from the plm package. However, now I am struggling to test ...
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5answers
221 views

Does $r$-squared have a $p$-value?

I seem to have confused myself trying to understand if a $r$-squared value also has a $p$-value. As I understand it, in linear correlation with a set of data points $r$ can have a value ranging from ...
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1answer
57 views

Calcualting R2 in mixed models useing Nakagawa & Schielzeth's (2013) R2glmm method.

I have been reading about calculating R2 values in mixed models and after reading the R-sig FAQ, other posts on this forum (I would link a few but I don't have enough reputation) and several other ...
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1answer
45 views

Does it make sense to calculate Q2 and R2 values on PLS-DA models?

Since PLS-DA is a computational technique which deals with outcomes expressed as a categorical variable (e.g. "Yellow","Brown","Black","Green") I cannot understand how it is possible to calculate Q2 ...
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0answers
18 views

Does R square of Cox Regression tells the same thing as Linear Regression R square?

My R square from cox regression is about 0.02, Does it tell me that model is doing really bad? I used coxph in R.
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0answers
18 views

McFadden's Pseudo-R2 is very high

I was running a logistic regression and to measure the relationship between two variables (Categorical). I used the MacFadden's pseudo R-squared as a measure. I found that certain variables show an ...
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0answers
61 views

Low explained variance in Random Forest (R randomForest)

I am using randomForest in R for regression, I have many categorical predictors (all of them have the same 3 categories (0,1,2)) and I want to see which of them can predict the response (continuous). ...
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1answer
20 views

How is the coefficient of determination in ANCOVA computed?

Given the following ANCOVA model: $Y_{ij}=\mu+\alpha_i+\beta X_{ij}+\epsilon_{ij}$, $e_{ij}\sim N(0,\sigma^2)$ i.i.d., $\alpha_1=0$, $i=1,..., m$, $j=1,..., n$ Given I have already computed ...
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1answer
83 views

The 'best' model selected with AICc have lower $R^2$ -square than the full/global model

I have used the R lme function (nlme package) to construct linear mixed models, with a single random effect (as a random intercept) and a varIdent variance structure on a fixed effect (that is a ...
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4answers
356 views

Is using deciles to find correlation a statistically valid approach?

I have a sample of 1,449 data points that are not correlated (r-squared 0.006). When analyzing the data, I discovered that by splitting the independent variable values into positive and negative ...
2
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1answer
199 views

R square test in matlab

I did the code for my $R^{2}$ (R square) test in MATLAB but it is not working accordingly. I want to test the Weibull distribution against my raw data, hence I want to do an $R^{2}$ (R square) test. ...
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0answers
88 views

Why does $r^2$ between two variables represent proportion of shared variance?

Firstly, I appreciate that discussions about $r^2$ generally provoke explanations about $R^2$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing ...
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1answer
61 views

$R^2$ correspondence for nonlinear time series

Is there a statistical measure for nonlinear time series data that is comparable to $R^2$ value in linear regression (giving an idea of how well the fit is)? The data is not monotonic, so I cannot ...
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1answer
25 views

Can specific residuals be compared in multigroup analysis using Lavaan in R?

Is there a way to statistically compare r-squared across 2 groups using nested models in multigroup analysis? I know how to use lavaan to test various other parameters across groups (e.g. regression ...
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1answer
114 views

Possible to calculate AIC from $r^2$, $\sigma$ and/or p-value for $r^2$

As per the heading, is it possible to add AIC to some previously computed models based on the stats I have (which include $r^2$, its p-value, $\sigma$ for each variable individually)? They are all ...
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42 views

R-squared of a vector error correction model

I hope somebody can help me with this. I estimated vector error correction model (and Johansen's cointegration test) and my R-squared is only 23%. Does R-squared tell me my model is bad in this case ...
2
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1answer
259 views

What is the problem with using R-squared in time series models?

I have read that using R-squared for time series is not appropriate because in a time series context (I know that there are other contexts) R-squared is no longer unique. Why is this? I tried to look ...
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1answer
85 views

Selecting the best model using cross-validation on coefficient of determination and/or mean squared error

Sorry if this question is oft repeated. Let's say I'm doing regression and I want to know whether I should use Linear Regression or Random Forests. I do 10-fold cross validation on each model to ...
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1answer
114 views

R-squared to compare forecasting techniques

Is it appropriate when forecasting to use $R^2$ as the measure of how well exponential smoothing fits a data set for the purpose of time-series forecasting? I understand that it is appropriate for ...
2
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1answer
48 views

Changes in R-squared

I was reading online, and I found that If the Variance of X increases then the value of R-squared increases If the Variance of the residuals increases then the value of R-squared decreases Can ...
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1answer
261 views

How can I test heteroskedasticity in a Tobit model with Stata 12?

I want to test heteroskedasticity in a Tobit model with Stata 12. But I don't know how to do that. When I used an OLS model, I tested heteroskedasticity and autocorrelation, and didn't find much, but ...
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1answer
164 views

In multiple regression r is positive but the coefficients are negative

I have run a multiple linear regression with 4 IVs. Three of the IVs are constructs and the fourth is gender. All IVs have statistically significant correlations with the DV. All three construct IVs ...
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0answers
95 views

Is the F test for R² in (multiple) Regression one- or two-tailed?

I have been wondering about the F test that is provided by many statistical packages along with the standard regression output. As I understand it, F can be computed by $$ F_{df_{reg},df_{res}} = ...
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1answer
85 views

Does the actual coverage of a 95% CI on $R^2$ get closer to nominal coverage with larger sample size?

If the answer is "it depends", what does it depend on? Does convergence depend on the ratio of predictor variables to sample size, or the size of $R^2$, or something else? I am mainly interested in ...
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0answers
48 views

Use of R-squared and Slope for determining time-stabilized Data

Can I determine cutoffs for the values of R-squared and its slope that are not arbitrary? Can I do anything to improve my method? Exposition: I work with a type-2 superconducting magnet for the ...
2
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0answers
18 views

Multiple Regression - Extreme F-statistic and R-square on 1 - too good to be true?

I have used a psychometric survey of 10 items which measure risk perception. I have taken the mean scores of these 10 items from a sample of 355 respondents who rated six hazards via the 10 ...
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1answer
147 views

Is it worth reporting small fixed-effect $R^2$ (marginal $R^2$), large model $R^2$ (conditional $R^2$)?

In a mixed model analysis (lme4 + lmerTest for R), I want to analyse the effect of 3 predictors, say A, B and ...
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0answers
38 views

$R^2$ in multivariate regression

I'm trying to determine how the population $R^2$ value is defined in the multivariate regression model where we have $Y_i = \mu_y + B^\prime(X_i - \mu_x) + err$ Where $Y_i \in \mathbb{R}^q$ and ...
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2answers
715 views

What happens to adjusted R squared as sample size increases?

What effect does sample size have on adjusted R squared values?
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37 views

Is the R-squared for this model respectable?

I have a model where the political position (left-right) of the coalition in power, among other things, explains stock returns. All data is monthly. See the results below. The question is, would you ...
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1answer
4k views

What's the difference between multiple R and R squared?

In linear regression, we often get multiple R and R squared. What are the differences between them?
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128 views

one-way MANOVA effect size interpretation

I'm having problem understanding effect sizes in one-way MANOVA model. In my case, I'm having a 13 variables which I used for clustering and then the produced ...
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0answers
66 views

Generalized $R^2$ for average model

I have some power-law data sets coming from an Ecology study. Some of them seem to be best modeled using linear regression after log-transformation of the data, but other data sets seem to be best ...
0
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0answers
27 views

Pseudo-$R^2$ in spatial regressions and Kelejian-Robinson test in R

I am currently trying to find out if there is a way to calculate a pseudo $R^2$ value from the output of maximum likelihood estimation of the spatial error model, and maximum likelihood estimation of ...
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4answers
979 views

Pitfalls to avoid when transforming data?

I achieved a strong linear relationship between my $X$ and $Y$ variable after doubly transforming the response. The model was $Y\sim X$ but I transformed it to $\sqrt{\frac{Y}{X}}\sim \sqrt{X}$ ...
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0answers
32 views

How to interpret marginal R squared?

i have obtained a marginal R squared value of 0.01599143 after fitting a tweedie model to my data set. Is this value too low? How can i interpret this?Thanks
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1answer
28 views

Is it possible to have an F-test with a $p<.05$ even if there is an $R^2<.1$ for a least squares analysis in JMP?

I've been working with JMP, and I have found that often I get a significant p value but a relatively small r. Is this supposed to happen?
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2answers
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Comparing interaction effects using different variables. Possible?

I want to compare which are the "most important" interaction effects (in a data driven way, I realize that it is has downsides). I realize that for substantial researchers this does not make sense, ...
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1answer
83 views

Variation explained in ordinal logistic regression models

I have made these three ordinal logistic regression models: ...
2
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1answer
101 views

Is there any way the adjusted $R^2$ might decrease by adding predictors?

Let's consider a multiple linear regression formula: $ \hat{y} = \beta_0 + \beta_1 \hat{x}_1 + \beta_2 \hat{x}_2 $ (1) which produces adjusted $R^2 = r_1$. Now I want to add to one predictor to ...
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1answer
39 views

$R^2$ relative to a noiseless function

I am interested in computing the $R^2$ between a set of points $D_f = \{ (x,y)\} $ where $y = f(x)$ and a set of points $D' = \{(x',y') \}$ obtained adding noise to $D_f$. I don't think I can use: $$ ...
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94 views

Calculating McFadden's pseudo-$R^2$ in glmnet?

How do you calculate the McFadden's pseudo-$R^2$ using the cv.glmnet object from the glmnet package? The deviance.glmnet ...