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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Change in r squared due to clustering in multiple linear regression

Puny undergraduate stats student here. I am examining the effect of two regressors on a predictor. OLS on the raw data (approx 200k cases) yields next to no correlation in the following models: ...
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64 views

Offset in a Poisson GLM (R)

I am trying to model disease counts (d) by using population (p) as offset to control for exposure. In R, I found two possible ways to go: ...
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61 views

Does it make sense to compute adjusted $r^2$ with test set?

I have divided my time series into training and testing set. I would like to know if makes sense to compute the adjusted $r^2$ with the testing set or just on the training stage.
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What does “explained variation” mean in reference to R-squared?

I have been trying to get my head around $R^2$ in a bit more details instead of just seeing it as a number. So far I have looked at the process in the following manner: If I knew very little about ...
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relation between $R^2$ of simple regression and multiple regression

A very basic question concerning the $R^2$ of OLS regressions run OLS regression y ~ x1, we have an $R^2$, say 0.3 run OLS regression y ~ x2, we have another $R^2$, say 0.4 now we run a regression y ...
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Use adjusted R-squared to select between regression models

I use the same sample to run two regressions. Both regressions have the same dependent and independent variables except in one regression the dependent variable and one of the independent variables ...
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73 views

Should partial $R^2$ add up to total $R^2$ in multiple regression?

Following is a model created from mtcars dataset: ...
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61 views

R-squared as criterion to choose between linear and non-linear regression

I am working in some regression models to forecast opinions based on general demographic characteristics, and I'm not sure how to choose between linear regression and curve estimation (I'm using SPSS ...
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146 views

How should I interpret the generalized squared multiple correlation?

I am testing this model in SPSS AMOS. The value of .23 above the top right corner of timedrs is the squared multiple correlation for that variable. I also ran the same analysis as two multi-step ...
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37 views

Help explain the “redundancy” of canonical correlation

I am reading a material about canonical correlation and it introduces a concept named "redundancy". I have been puzzled for one day but still could not get a understanding. The following is a screen ...
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21 views

What is canonical r squared?

I know r-squared is the the percent of variance explained by a model. I am currently reading materials about canonical correlation and found a new concept "canonical r squared". The material does not ...
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25 views

For a one-tailed test using OLS regression in SPSS, is it appropriate to divide the change statistics p-values in half?

I am running a series of moderation regression models in SPSS and entering the models in using blocking (e.g., controls in block 1, controls and IVs in block 2, controls, IVs and moderator in block ...
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13 views

ANCOVA model with non-significant variables performs better?

I'm running an ANCOVA test with 2 dichotomus and 1 ordinal variable as fixed factors and 2 continuous variables as covariates. I was advised to remove any non significant factors because with them ...
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50 views

GridSearchCV Regression vs Linear Regression vs Stats.model OLS

I am trying to build multiple linear regression model with 3 different method and I am getting different results for each one. I think that I have to get the same results but ...
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21 views

R-Squared in a non-linear model [duplicate]

I am running a dynamic demand model (a non-linear model) in SAS. My model includes three equations which should be solved simultaneously. I am applying a Iterated Seemingly Unrelated Equation (ITSUR) ...
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33 views

R-squared value when using offset — how is it calculated?

I have a linear model with a test score variable as a dependent variable and a vector of covariates. I have an offset variable in the model. So the formula is= $$\text{score}_i = B_0 + B_xX_x + ...
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20 views

On finding the $R^2$ value [duplicate]

If the $R^2$ value of a regression of $X$ on $Y$ is say $0.65$ then can we find the $R^2$ value of the regression of $Y$ on $X$ from this information alone? If Yes then How?
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47 views

Why does the amplitude, bandwidth and position of Gaussian change when data changes from positive to negative

I'm trying to fit a single Gaussian to some values in Matlab. When the values are positive, the model fits without any issues. However, when these values become negative, the r squared value changes, ...
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60 views

High R-squared although many insignificant coefficients

I just did a regression based on the gravity model where I try to identify the most important factors that determine the trade flows. In total I have 18 variables and 363 observations. In fact I would ...
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59 views

LOOCV $R^2$ higher than regular $R^2$ in RF

I am working with RF and the caret package, and I am having a confusion because sometimes the LOOCV $R^2$ is higher than the regular $R^2$. Is it right? How can I interpret this? Here an example ...
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24 views

Can there be a situation where one regression model gives lower RMSE than the other but also lower R-squared?

Consider the following scenario where you use the same data X (the same number of predictors p, same number of observations ...
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1answer
24 views

Determine confidence in a CART model with factor (2 levels) response variable (using rpart)

I use the package rpartto model a classification/regression tree. I have the variables $x,y,s$ where $x$ is in $\{-1,1\}$, y is continuous in $[0,1]$ and $s$ is a ...
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83 views

Is Predicted R-squared a Valid Method for Rejecting Additional Explanatory Variables in a Model?

I'm building a model to understand the important drivers from a set of possible drivers for a time series of data. In my case the possible drivers are other time series. Like most statistical models ...
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Why not just use log for regression if it improves r-squared?

theoretical question here: Say I have a model, $y = \beta_0 + \beta_1 x + u$ and it gives an $R^2$ of 0.02 Suppose, I re-estimate the model with $y = \beta_0 + \beta_1\log(x) + u$ which gives an ...
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79 views

Negative $R^2$ at random regression forest [duplicate]

I am currently writing my master's thesis about random forests and just started to work with the R software. When I am running my model the output looks like this: ...
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35 views

What impact does a higher $R^2$ have on the precision of the CI?

I attended a seminar today at which the presenter mentioned that a higher $R^2$ would, all other things being equal, produce a narrower confidence interval. Is that true, and if so then why? Google ...
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38 views

Comparing r^2 values?

Short version: I have two values of r^2, one a control group (.713) and one for an experimental (.527), and I would like to quantitatively compare the difference in how well/poorly the points in each ...
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34 views

Transformation of explanatory variable

I have tried to transform one of my explanatory variables, which is research and development budget per firm per year, to a logarithmic variable. The p-value of the variable before and after the ...
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47 views

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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63 views

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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94 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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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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339 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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77 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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18 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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42 views

Nagelkerke $R^2$ interpretation

I used logistic regression and found that my model fits well: ...
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75 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
76 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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170 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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223 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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26 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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58 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
87 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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48 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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21 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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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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49 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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110 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 ...