The coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by a regression model.

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Transformation of data with zero and R squared

I have a conceptual concern about data tranformation and R^2. Often we transform data to respect the assumption of the linear model. Therefore, we can use multiple type of transformation such as log ...
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Why would the full model have a higher R-squared than reduced model? [duplicate]

After doing an F-test, I concluded that the reduced model is the preferred model. But why does the full model have a higher R-squared value than the reduced model?
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24 views

Reasonable R² for a Machine Learning Problem [closed]

I got a R² of 3.6 in a competition of Machine Learning which were not disclosed meanings of variables. I am using XGBoost method. Is this number unacceptable for this type of problem or may have ...
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8 views

how to calculate the variance contribution of individual coordinates for multidimensional scaling analysis

I have searched the CrossValidated and stak Overflow and found the following related threads, Standard method for calculating contribution of individual variable to outcome Non-metric Stress in 3 ...
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16 views

Calculating within, between or overall R-square in R [migrated]

I'm migrating from Stata to R (plm package) in order to do panel model econometrics. In Stata, panel models such as random effects usually report the within, ...
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23 views

Same coefficients for fixed effect, random effect and OLS with panel data

I have a panel data on nonperforming loans from 1990q1 till 2014q4 with 30 banks. I would like to estimate both fixed effect and random effect model with gdp growth, unemployment, exchange rate, and ...
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24 views

ARMAX / ARIMA models: Effect Size and R-squared

Is there an easy way in Stata to get the percentage of the variance explained by an ARMAX/ARIMA model (similarly to the adjusted R-squared in multiple linear regression)? Moreover, working with ...
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1answer
36 views

Variable selection for multiple regression from large number of predictors

I have 20 response variables $Y = (Y_1, \dots, Y_{20})$, and 1600 predictor variables $X = (X_1, \dots, Y_{1600})$. There are 128 observations. I wanted to know which pairs of $X$ can best predict ...
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1answer
49 views

Implementing logistic regression (R)

I am implementing a logistic regression on a 250 x 20 dataset (250 observations of 20 variables) with a dichotomous response. In this proces I have encoutered some different problems, namely: 1. ...
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11 views

Can't figure out how to calculate R squared with the information I'm given?

I know the formula for R squared is SSR/SST. However, I've been asked to construct the R squared for a multiple regression, given the following information: - the coefficients of the regressors and ...
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1answer
128 views

Computing cross-validated $R^2$ from mean cross-validation error

I am currently using cv.glmnet in R. I would like to compute both a training $R^2$ and a cross-validated $R^2$. R gives mean cross-validated error and for the ...
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3answers
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Is a high $R^2$ ever useless?

In stats we're doing linear regressions, the very beginnings of them. In general, we know that the higher the $R^2$ the better, but is there ever a scenario where a high $R^2$ would be a useless ...
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20 views

R-squared after using robust standard errors

I am performing a analysis on panel data in which I have to take account of serial correlation and heteroscedasticity. Therefore, I am using robust standard errors. However, the software (R) does not ...
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1answer
39 views

Proof: Adding additional regressor and the influence on the adjusted R^2

I'm looking at the influence of an additional regressor in an OLS-model and on the adjusted $\bar{R}^2$. What I have to proove is that $\bar{R}^2$ rises if and only if the square of the respective ...
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0answers
7 views

How to see the adjR-square in Lasso Regression?

After doing lasso, the final parameters are only 6, but I have 200 covariates originally, is it too literally? And how to see the correspond adj R-square in Lasso Regression? By the way, I also tried ...
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61 views

How to interpret poor $R^2$ score but good RMSE value?

I split my data into training set and test set and am running linear regression on it. I am using Python's "scikit" library and I am getting an $R^2$ score of 0.31 and an RMSE value of 0.037. The ...
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1answer
29 views

R-squared or adjusted R-squared to use when comparing nested models?

I have a model with predictor variables x1, x2, and x3. I have another model with predictor variable x1. My understanding is that when you have multiple predictors, you use adjusted R-squared, but ...
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1answer
114 views

Is it possible to calculate R-squared on a total least squares regression?

I am using the Deming function provided by Terry T. on this archived r-help thread. I am comparing two methods, so I have data that look like this: ...
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15 views

Studying independent variable strength with R^2 values

I have a dataframe in R and wish to assess the degree to which each of my independent variables impacts the dependent variable during mixed models analysis. To do so, I've built a mixed model using ...
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2answers
57 views

How to calculate pseudo R2 when using logistic regression on aggregated data files?

I encountered a strange phenomenon when calculating pseudo R2 for logistic models when using aggregated files: the results are simply too good to be true. An example (but as far as I can see, every ...
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2answers
141 views

What does negative R-squared mean?

Let's say I have some data, and then I fit the data with a model (a non-linear regression). Then I calculate the R-squared ($R^2$). When R-squared is negative, what does that mean? Does that mean my ...
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1answer
40 views

R² of ANCOVA mostly driven by covariate

Based on data from a scenario-based experiment, I am running a 2x2x2 ANCOVA with one continous covariate (sample size=320). Without including the covariate, the ANOVA model and two of the main effects ...
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13 views

Relationship between R^2 and sum of squared errors in non-linear models

I'm reading from different sources (whuber's answer on R^2, another source) that when using R^2 one needs to be careful with regard to interpretation - both in linear and non-linear models. In ...
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39 views

R-squared and omitted variable bias

Suppose you have the model: $$ y_i=\alpha+\beta X_i + u_i $$ where $u_i = e_i + Z_i$ and ${\rm Cov}(X_i, Z_i) \ne 0$. Therefore, we know that $E[u_i|X_i] \ne 0$. Is the $R^2$ biased as well?
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136 views

Expected value of $R^2$, the coefficient of determination, under the null hypothesis

I am curious about the statement made at the bottom of the first page in this text regarding the $R^2_\mathrm{adjusted}$ adjustment $$R^2_\mathrm{adjusted} ...
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32 views

Goodness-of-fit metrics for linear regression

My software reports something like ...
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1answer
20 views

McFadden's R2 > 1?

I calculated a McFadden's R2 = 1.94094. Repeatedly. What have I done wrong? Is it inappropriate to use McFadden's R2 for conditional maximum likelihood?
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2answers
30 views

How to compare predictive results of MARS and OLS with each other?

I fitted a MARS model and an OLS model to my data. The main goal is prediction. How can I compare the result and decide which is better? Since I don't have much records I did not split the data in ...
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28 views

To what extent are the different versions of $R^2$ comparable, with and without an intercept

I have been trying to fit some data with a linear regression. I don't have any theoretical assumptions on the regression, and from what I know both an intercept or no intercept can be plausible ...
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28 views

Coefficient of Determination (R-Squared) definition in Matlab [duplicate]

First of all, I have to say that my knowledge of statistics is very basic. I was trying to fit data with a linear regression in Matlab, and I came across the problem of $R^2$ definition. I am using ...
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30 views

Comparing R-squared across regression equations with a dependent sample

I was able to find information on how to compare R-squared values across regression equations with independent samples by creating confidence intervals around the estimates. However, the sample used ...
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49 views

Gelman & Hill ARM textbook, Question 3.2, R-squared

I'm reading Gelman and Hill 'Data Analysis using linear regression and multilevel/hierarchical models'. I have a problem with exercise 2 in chapter 3. Suppose that, for a certain population, we ...
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68 views

R-squared larger than one

I have 10 response variables and used 10 weighted elastic net models to find which of the 31 predictors that I have in my system can better explain my responses. I obtain an R-squared for my models ...
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15 views

What is the relationship between R-squared and MS(Res)?

My textbook (Applied Regression Analysis: A Research Tool by Rawlings, Pantula, and Dickey) asks me to "Show algebraically the relationship between R-squared and MS(Res)", but I don't even know what ...
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19 views

Correlation between explained variable and residuals (cross section regression)

My regression has a low R square, meaning a big portion of the variability of the dependent is not explained by the independent variables. Because of this, I have correlation between my dependent ...
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57 views

Convergence error in r.squaredGLMM() but not glmer() fit

I am fitting binomial generalized linear mixed effects models with 2-8 fixed continuous variables and one random effect with 8 levels. The data set has about 700 points. I am using package lme4, ...
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1answer
88 views

Formula for 95% confidence interval for $R^2$

I googled and searched on stats.stackexchange but I cannot find the formula to calculate a 95% confidence interval for an $R^2$ value for a linear regression. Can anyone provide it? Even better, ...
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15 views

How to know if the r squared value is good enough or not [duplicate]

In a linear model, after calculating root mean squared error and r squared, what do I do? How do I know if the values are good enough or not? Is there a table with threshold values for these metrics ...
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61 views

Using the RSQ function in excel for multiple regression

The RSQ function for calculating R-Squared in excel shows arguments as known Xs and known Ys. However if you provide modeled Y (Y-hat) and actual Y for a multiple regression, the result is the same as ...
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64 views

How do you calculate the standard error of $R^2$

I would like to confirm something. I know that $R^2$ (in a linear regression) can be found by taking the square of Pearson's $r$. The standard error of Pearson's $r$ is calculated using the ...
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2answers
58 views

Explanatory power of a Decision Tree

With Multiple Regression, the R-Squared gives the researcher an estimate of the explanatory power of the regression equation. What is the equivalent for Decision Trees?
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1answer
268 views

Ridge regression in R with p values and goodness of fit

Doing ridge regression in R I have discovered linearRidge in the ridge package - which fits a model, reports coefficients and ...
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1answer
29 views

Three Different Regression Results… Why is one so weak compared to the other two?

I have a data set I'm working with, it's roughly 450K rows of data. I'm breaking the data out from a certain column, and that column has three results. After that, I ran a regression analysis for each ...
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2answers
87 views

$R^2$ increases when removing predictors

I have a multiple regression model with many predictors (admittedly more than I want: 21). When I remove one of the predictors (leaving me with 20) my R squared increases a bit. Should this happen? Is ...
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2answers
134 views

Should we report R-squared or adjusted R-squared in non-linear regression?

I am running a non-linear regression for a dose response with the equation: $$Y = \frac{c}{1 + \big(\frac x g\big)^b}$$ When reporting my results for publication, do I report the R-squared or ...
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1answer
44 views

Are R-squared and F the same for variables in Multiple Regression in R

I ran a multiple regression analysis and got significant results for lFreq, Len variables, and interaction lFreq x Len. Now I need to report these results and I am a bit confused whether F(7, 924) = ...
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21 views

Why the weighted least square $R^2$ from R summary doesn't match my manual calculation [duplicate]

I have a weighted least square model and I wanted to calculate $R^2$ manually, but my results don't match the R summary. Why is that? ...
2
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1answer
100 views

Regression Analysis: R squared and p-value

I would like to know if the coefficient of an independent variable is still relevant if the R-squared is low (assuming the p-value for the independent variable is less than 0.05). For example, ...
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30 views

What value of (adjusted) McFadden R square or other pesudo R square means good fitting

I got adjusted MaFadden R square for logistic regression: 0.918772 , 0.6135568 , 0.3407252 respectively, which value is good? I just heard the value between 0.2 and 0.4 is good for McFadden R square. ...
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1answer
36 views

Calculating R-Squared with logged data

I have created an example in R to illustrate the problem: ...