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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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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36 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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17 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
44 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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5answers
302 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 ...
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1answer
64 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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75 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
51 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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12 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
90 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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28 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 ...
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1answer
108 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
57 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
77 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 ...
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1answer
41 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
173 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
101 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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82 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
69 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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41 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 ...
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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
111 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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32 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
477 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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36 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
2k 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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101 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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62 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 ...
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21 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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975 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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29 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
27 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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140 views

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
64 views

Variation explained in ordinal logistic regression models

I have made these three ordinal logistic regression models: ...
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1answer
99 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
38 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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81 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 ...
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70 views

Higher r-squared value on test data than training data?

I am trying to create a linear regression model. I split my data into training and testing data, and built a model. The R-squared value on the training data is 0.840. Then I ran the model on the ...
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219 views

Is R-squared value appropriate for comparing models?

I'm trying to identify the best model to predict the prices of automobiles, using the prices and features available on automobile classified advertisement sites. For this I used couple a of models ...
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1answer
214 views

Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?

I estimated a robust linear model in R with MM weights using the rlm() in the MASS package. `R`` does not provide an $R^2$ value ...
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2k views

Relationship between r-squared and correlation coefficient

Let's say I have two 1-dimensional arrays, $a_1$ and $a_2$. Each contains 100 data points. $a_1$ is the actual data, and $a_2$ is the model prediction. In this case, the $R^2$ value would be: $$ R^2 = ...
4
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89 views

comparing AIC and adjusted $R^2$

So, I have a homework assignment in which I'm being asked to compare the fit of two similar models by comparing their $R^2$ and AIC. Both models were run in R, one using the ...
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31 views

exact calculation of SD on R-squared

In R package "psychometrics" an estimate of SE of R squared of sersq <- sqrt((4*rsq*(1-rsq)^2*(n-k-1)^2)/((n^2-1)*(n+3))) with n sample size, and k number ...
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68 views

Relation between coefficient of determination, $R^2$, and significance in a regression

I have performed a simple regression of the following form: $y_t$ = $\beta_1x_{1,t}$ + $\beta_2x_{2,t}$ + $\beta_3x_{3,t}$ the $R^2$ turns out to be 38%. $\hat\beta_1$ = 0.7 (significant at the ...
3
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1answer
103 views

What is needed for a line to be an appropriate model for the data?

My answer key responds with a large $R^2$ and a residual plot with no pattern. The residual plot with no pattern makes sense. However, is having a large $R^2$ necessary? A linear model can be ...
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1answer
79 views

Do two different graphs with similar $R^2$ values show a connection between the data?

With my data (Y and X variables) I have $R^2$ = 0.3736. I used the data from an article that did the same type of experiment, and made a graph and found their $R^2$ = 0.3706. I know that the values ...
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95 views

Classification Tree Analysis - Assessment of tree explanatory power (R-square?) using the party package in R

I have produced a model using the ctree function in R, and want to know whether this tree is actually explaining my data well. I am trying to explain the presence ...
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1answer
136 views

Neural network with and without cross validation

I have been running ANN (Neural network) on my data set, until last week that I figured out I will get more robust model using Cross validation, So That's why I have started using ANN with the aid of ...
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1answer
150 views

Is $R^2$ valid in a nonlinear model?

The question is in the title. The coefficient of determination or $ R^2 \equiv 1 - \frac{ss_{res}}{ss_{tot}} $ is valid in a nonlinear model? Why?
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1answer
97 views

The larger $R^2$ the better? [duplicate]

I want to show that the variable $X$ is significant. In model 1, I use financial statements variables, other macroeconomic variables and $X$. Here, $X$ is siginificant at a 10% level and $R^2$ is ...