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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Which regression model to choose? [duplicate]

I have two models, one lm(y ~ x1 + x2 + 0) which gives me a close to 0.90 something $R^2$ and another model lm(y ~ x1 + x2) ...
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18 views

optim() for multi variable returns values on the boundary in R

I would like to use function optim() in R to minimise the target function. The two optimised parameters both have constrains. I have created a test sampel data. ...
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14 views

Excluding Outliers and Influential Observations ($R^2$ and AIC/BIC)

I am working on a cross-sectional data set relating mortgage payments to debt-income ratios. I have some extreme outliers and experimented with excluding them from the model (some 30 observations of a ...
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162 views

Is there an elegant/insightful way to understand this linear regression identity for multiple $R^2$?

In linear regression I have come across a delightful result that if we fit the model $$E[Y] = \beta_1 X_1 + \beta_2 X_2 + c,$$ then, if we standardize and centre the $Y$, $X_1$ and $X_2$ data, ...
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15 views

Measure of explained variance for Poisson GLM (log-link function)

I am looking for an appropriate measure of the "explained variance" of a Poisson GLM (using a log-link function). I have found a number of different resources (both on this site and elsewhere) that ...
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23 views

Regression variable conversion

There is a question that I cannot solve. They may be solved by variance and covariance but I couldn't. So I thought there should be another way to solve. Question: A researcher has a sample of 43 ...
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1answer
38 views

Good Literature about Problems with R squared

A question from a newbie. Recently, I was told that R squared or adjusted R squared can not used as a criteria to select a good regression model (model selection) due to, for example, overfitting . I ...
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40 views

Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$

I am interested in the geometric meaning of the multiple correlation $R$ and coefficient of determination $R^2$ in the regression $y_i = \beta_1 + \beta_2 x_{2,i} + \dots + \beta_k x_{k,i} + ...
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1answer
39 views

R-squared for elastic net

How is the R-squared calculated for an elastic net? How about LASSO? Should be different from OLS, or not? Edit: The main problem is as follows: We have all kinds of fruits like $f_1, f_2, ..., fn$ ...
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31 views

R-squared adj. in multiple linear regression of 75% = high correlation?

I have a response column and a column of categorical predictors (around 25 categories) and I get with minitab linear regression analysis a R-sqr adjusted of 75%. ...
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23 views

How do we calculate the $R^2$ statistic for a mixed model with one random intercept only?

I have read in previous posts that for mixed models with random intercepts only, the statistic for $R^2$ is $$R^2 = \frac{\text{V of intercept only model} − \text{V of full model}}{\text{V of ...
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8 views

Why is the R-Square of PROC CALIS a period

I am running PROC CALIS on some data and everything seems to work correctly, except the R-Square table has a . (period) for the R-Square of one of the measured dependent variables. Why would this be? ...
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20 views

Test of between groups difference in r-squared value in linear regression

Running a linear regression with one continuous IV (sleep) and one categorical IV (gender). Have run a split-file analysis and there appears to be a difference between genders in r-squared. How would ...
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0answers
28 views

$R^2$ (coefficient of determination) and linearity in multiple linear regression

For simple linear regression (SLR), in order for $R^2$ (the coefficient of determination) to be a meaningful measure, it must be true that $X$ and $Y$ are linearly correlated. Specifically, $R^2=r^2$, ...
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1answer
32 views

Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum?

Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum? Is there an easy mathematical explanation to this as $r^2$ is squared and don't add ...
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18 views

Model Averaging

Good Afternoon, I am working on model averaging of data collected about bird species and habitat vegetation. I have been using the MuMIn package in R and have taken a subset of all possible models ...
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1answer
78 views

Assessing strength of instrument

I want to use a risk score (RS) as an instrument for an exposure on a clinical outcome. However, I wont have access to data on the outcome for some time, and wish to examine whether this risk score ...
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20 views

Distinguishing between different notions of $R^2$

What is the distinction between $R^2_{pop}$ – the population R-squared $R^2_{out}$ – the out-of-sample R-squared $R^2_{c.v.}$ – the squared population cross-validity coefficient ? These ...
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1answer
39 views

Regression model for ordinal dependent variable and catogrical independent variables

If I'm using R, which regression model should I use for my dataset? (I need to get the R-squared value.) I have 1 dependent variable and 6 independent variables as follows: 1 dependent variable: ...
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0answers
40 views

Small $R^2$ Despite Clear Difference in Totals Between Groups

I have a very large set of products (1000+), each one contributing a certain amount to total revenue. Product profit for purposes here can be negative. I decided to use a binary indicator variable ...
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69 views

Relative weights in regression analysis in SPSS: Matrix-approach vs. factor and regression

I am trying to perfome a relative weight analysis as described by Johnson (2000). I have 13 predictors to a more general indicator. Initially, I started by: running a principal component analysis ...
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39 views

Compare $R^2$ statistical significance in multivariate multiple regression

I have a multivariate multiple regression model with 3 dependent variables and the same 5 covariates. I used manova and mvreg in ...
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2answers
47 views

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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44 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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48 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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27 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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147 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
34 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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54 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
52 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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142 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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248 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
196 views

Calculating $R^2$ in mixed models using Nakagawa & Schielzeth's (2013) R2glmm method

I have been reading about calculating $R^2$ 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
152 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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24 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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24 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 ...
2
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0answers
184 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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22 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
161 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 ...
7
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4answers
470 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
583 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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108 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
77 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 ...
0
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1answer
40 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
137 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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65 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
637 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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3answers
157 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
196 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
56 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 ...