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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How to calculate PRESS and $R^2_{predicted}$ in Stata automatically [migrated]

So I have two models and I want to calculate these statistics. Is there any package to calculate them in Stata? PRESS statistic (wiki) And, if I am not mistaken. $$ R^2_{predicted} = 1 - ...
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Assesing the explanatory power of predictors, interactions and combination of terms

I have a model with 5 basic predictors and all interactions between the predictors themselves. Something like (I'm simplifying here, in reality I have many more variables): ...
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77 views

Is there any difference between $r^2$ and $R^2$?

The correlation coefficient is usually written with a capital $R$ but sometimes not. I wonder if there really is a difference between $r^2$ and $R^2$? Can $r$ mean something other than a correlation ...
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1answer
25 views

Why does adding more terms into a linear model always increase the r-squared value?

Many statistics textbooks state that adding more terms into a linear model always reduces the sum of squares and in turn increases the r-squared value. This has led to the use of the adjusted ...
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1answer
37 views

Do you think I should apply a transformation to my independent variables?

I have done a simple linear regression on my two standardized independent variables and standardized dpendent variable. In the residual plot there is a distinct quadratic pattern left after the two ...
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54 views

What if a transformed variable yields more normal and less heteroskedastic residuals but lower $R^2$?

I am trying to decide whether to use a square root transformed dependent variable in multiple linear regression. Transforming $y$ leads to more normally distributed residuals and also to less ...
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1answer
284 views

Interesting derivation of R squared

Years ago I found this identity through experimentation playing with data and transformations. After explaining it to my statistics professor he came in the next class with a one-page proof using ...
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2answers
297 views

What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?

What is the distribution of the coefficient of determination, or R squared, $R^2$, in linear univariate multiple regression under the null hypothesis $H_0:\beta=0$? How does it depend on the number ...
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1answer
54 views

What measure of effect size in ANOVA has mode at zero under the null (unlike $\eta^2$ that does not)?

I encountered a weird effect when computing eta squared in ANOVA. Here is a short simulation to demonstrate it. I simulate $k$ groups with $n=10$ each, with all values drawn from standard normal ...
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1answer
64 views

Model uncertainty (model averaging) and R-Squared (R2)

Is it possible to calculate r-squared for an "average model"? Lets say I have 4 different response variables that I want to model to a set (or subset) of 4 independent variables. I'd then like to ...
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1answer
75 views

Partitioning explained variance to fixed effects by comparing r squared (R2) between linear mixed models

Lets say I have 2 linear mixed models. One is simply a subset of the other. The first contains terms for 2 fixed effects and a random intercept. One of the fixed effects, "x1" I know, a priori, ...
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1answer
83 views

A way to compute significance of R-squared change across models in a path model, or specifically lavaan?

I have a straightforward path model with a single endogenous variable and multiple observed predictors - in other words, a regression. (I'm doing it as a path model to be able to easily test ...
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28 views

McFadden's Pseudo R² - Comparability across different datasets

Several authors in applied research papers claim that McFadden's Pseudo R² cannot be used for comparing models that are based on different datasets. I have searched some ...
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30 views

Why is it possible that the White test and the special case of the White test can give different values of $R^2$

In the textbook I am using (Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge, 5e), it is implied that the $R^2$ from the regression of residual-squared on all independent ...
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1answer
40 views

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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32 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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23 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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2answers
198 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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34 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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25 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
44 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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1answer
121 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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66 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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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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31 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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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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62 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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34 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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33 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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26 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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107 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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21 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
45 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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41 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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215 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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41 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
57 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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65 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
93 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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43 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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152 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
35 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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81 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
63 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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38 views

$R^2$ equals square of correlation between observed and fitted responses [duplicate]

I'm having a hard time proving that $R^2$ is equal to the square of the sample correlation between $Y$ and $\hat{Y}$. Every book I search tells me that's very easy, like verbeek. They just state that ...
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1answer
258 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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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
362 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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267 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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29 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.