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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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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30 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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11 views

NAs returned when applying r.squaredGLMM [closed]

I wish to calculate conditional and marginal R2 values for a linear mixed model. However, R keeps returning 'NAs' for each (no warning message). I have tried a number of model variations and the same ...
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11 views

How to do forward stepwise regression using adjusted R^2 in R [closed]

As I understand, stepwise regression in R uses AIC by default. How can I do forward stepwise regression in R, using "significant improvement in adjusted R squared" as my criterion for adding ...
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34 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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11 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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20 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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44 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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37 views

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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1answer
53 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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31 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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27 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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28 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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41 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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19 views

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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59 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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15 views

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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1answer
42 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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103 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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307 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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66 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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14 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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30 views

Nagelkerke $R^2$ interpretation

I used logistic regression and found that my model fits well: ...
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56 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
47 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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103 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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207 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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20 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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49 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
60 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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39 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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18 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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66 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
40 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 ...
2
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1answer
56 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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27 views

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
40 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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42 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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1answer
37 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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77 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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80 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
636 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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1answer
101 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
54 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
46 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
64 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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344 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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336 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 ...