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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Marginal and Conditional $R^2$ for GLMM

I am trying to calculate $R^2$ (variance explained) for a set of data using GLMM's, and . Here's some dummy data. ...
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xtreg, re in STATA, which R2 to report? [duplicate]

After estimating the data using xtreg, re, I notice there're 3 different measures of R-squared, within, between, and overall R-2, so my question is, can I just report the overall R2 in this case since ...
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When is r$^2$ not equal to $R^2$?

This blog post has a nice description of when the square of the Pearson correlation coefficient, r, is equal to the coefficient of determination, $R^2$. Specifically, states that they will be the same ...
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What is the logic behind low coefficient of determination? Does low $R^2$ really matter in an exploratory study? [duplicate]

In my study, I have got $R^2$ of only 33% in my regression model, with one dependent variable and two independent variables. So, I would like to ask for your opinions if such a low $R^2$ really ...
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28 views

How to show the Contribution of Independent variables in terms of percentage in Multiple regression?

I would like to show the independent variables (IV) contribution in percentage. For example, Regression equation is ...
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101 views

If $X$ is one of several variables that sum to $Y$, is the $R^2$ between $X$ and $Y$ a useful value?

One assumption for regression analysis is that $X$ and $Y$ are not intertwined. However when I think about it It seems to me that it makes sense. Here is an example. If we have a test with 3 sections ...
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288 views

Choice between different robust regressions in R

I'm writing a program for evaluating real estates and I don't really understand the differences between some robust regression models, that's why I don't know which one to choose. I tried ...
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62 views

When AIC and Adjusted $R^2$ lead to different conclusions

I hope it's okay to ask theoretically driven R questions here. R has given me the following results from my 'tournament of models'. All models are entirely distinct except from 3 basic control ...
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7 views

Distribution-specific variance component to use with R-squared for ordinal logistic GLMM

I think this should be straightforward, though I cannot find an answer after digging around a lot within work by Nakagawa et al. on $R^2$ values for GLMMs. My question is similar to that posed before ...
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27 views

Nagelkerke $R^2$ interpretation

I used logistic regression and found that my model fits well: ...
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2answers
55 views

Comparing 2 regression models

I have 2 continuous outcome (independent) variables, A and B, and 1 dependent variable (biomarker) that are all very correlated. I would like compare the outcome variables in relation to the biomarker ...
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1answer
35 views

How Residuals of Instrumental Variables Estimation are calculated and why you can have a negative R-squared?

I would like to understand, precisely, why you can have a negative $R^2$ with a 2SLS estimation, such as you have in commands like ivreg2 in Stata. There is ...
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77 views

Why report r-squared in Instrumental Variables Estimation?

I mean the the R-squared calculated such as in $R^2=1-\frac{RSS}{TSS}$ when you use the $RSS$ from the original structural model and not recalculation that you should do in order to do an F test. With ...
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1answer
199 views

How to determine the sign of R underlying R-squared?

So we know that: $$ R^{2}=\frac{SSR}{SSTO} $$ If we want to know the value of $R$, how do we know what the proper sign is?
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1answer
18 views

Relation between R2 and the covariate correlation matrix (multidimensional case)

Following the post : Relation between $R^2$ and the covariate correlation matrix Does it exist a formula for N>3 when N is the number of covariates ? Many thanks
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1answer
42 views

Relation between $R^2$ and the covariate correlation matrix

I'm quite new to Statistics and I'm facing a problem. Is there any relation between $R^2$ and the correlation matrix of the covariates? A short example is (case with 2 covariates) : A7 ~ A1 + A2 ...
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1answer
33 views

Adjusted R-squared: number of terms or independent variables?

When applying a multiple linear regression, does the adjusted R-squared value depend on the number of independent variables in the model or the number of terms? Specifically, I'm concerned that adding ...
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35 views

Explanation of the formula for calculating adjusted R squared of linear model

The classcial formula for calculating the adjusted $R^2$ of a linear model is as follows: $$R^2_{adj} = 1 - ((n-1)/(n-p-1)) \times (1-R^2)$$ where $n$ is the sample size and $p$ is the number of ...
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17 views

ANOVA: Why residuals are uncorrelated with group means?

If I want to compare group means $\bar Y_1, \bar Y_2, \dots, \bar Y_L$ of a numeric variable $Y$ across the $L$ levels $x_1, \dots, x_L$ of a categorical variable $X$ in terms of R-squared, then I can ...
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63 views

Large sample with low R² and high RMSE; or Small aggregated sample with high R² and low RMSE?

I have 45 independent variables and 50 (US) state controls. I have a sample of about 100,000 county-level observations. With this sample, I run my regression (observations weighted by population) and ...
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1answer
37 views

Goodness of fit between actual values and non-linear model

I was wanting to get a goodness of fit similar to R^2 for a model I'm evaluating. The output of the model is one of 8 numbers based on environmental characteristics. This is not a linear model, so ...
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1answer
42 views

Which one to compromise between MAPE and Adj R square in multiple regression

I'm trying to forecast sales of a product based on the other variables like Competitor sales, Fuel Price and CPI (Consumer Price Index). The below given output (based on 1 to 44 months) gives me the ...
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log transformation decreased model fit?

I just wondered why logged income (independent variable) decreased my model fit for OLS regression. My income distribution is skewed to the right and I am trying to transform the data. I separately ...
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1answer
35 views

comparing $R^2$ across two data sets

I have a set of covariates that characterize the type of experience a worker has (industry experience, general management experience, etc), and I am regressing compensation on these measures of ...
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33 views

Comparing R2 between Different Samples

Good Evening All, I'm looking to directly compare the variance explained by the same regression model (same IVs, DV) between two different samples. The way I'm conceptualizing it is like Fisher's ...
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29 views

Exponential equation fitting

I have two variables: y= head (0.5,0.10,0.15,0.25,0.34) and x= instar (1, 2, 3, 4,5). How fitting my data on exponential growth in R? I need p-value fitting, F (is possible?), R^2 and degree freedom. ...
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63 views

Show that $\sqrt{ESS} \leq \sqrt{ESS_{A}}+\sqrt{ESS_{\bar{A}}}$ where ESS=Explained sum of squares

Suppose we have a dependent variable $Y$ with mean zero and set of regressors which we divide into two sets, $A$ and $\bar{A}$. Let $ESS$ denote the explained sum of squares (ESS) from regressing $Y$ ...
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62 views

Comparing two R square. Are they statistically different?

What is a correct way to compare two $R^2$? I have dependent variable $Y$ and $X_1, X_2, X_3, X_4.$ I run two regression models, namely with $X_1$, $X_2$ and $X_3$, $X_4$. Both $R^2$ values are close. ...
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29 views

r linear regression mistakenly giving me r2 value of 1 [duplicate]

I'm using R to create a linear regression model from survey data about public sentiment for a new technology. I am encountering a problem where the addition of a new explanatory variable raises the ...
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1answer
632 views

Regressions. Why a and b explains more than a+b?

So I have sample of 1987 observations. I'm checking how accounting measures can explain stock returns. If I do a regression of stock returns on CFO (cash flow) and Accruals, I get $R^2= 0.075$. But if ...
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31 views

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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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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45 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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41 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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1answer
59 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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321 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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326 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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69 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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178 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
178 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
112 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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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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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
49 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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39 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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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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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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86 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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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
46 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 ...