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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Is the F test for R² in (multiple) Regression one- or two-tailed?

I have been wondering about the F test that is provided by many statistical packages along with the standard regression output. As I understand it, F can be computed by $$ F_{df_{reg},df_{res}} = ...
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2answers
30 views

Does the actual coverage of a 95% CI on $R^2$ get closer to nominal coverage with larger sample size?

If the answer is "it depends", what does it depend on? Does convergence depend on the ratio of predictor variables to sample size, or the size of $R^2$, or something else? I am mainly interested in ...
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10 views

Use of R-squared and Slope for determining time-stabilized Data

Can I determine cutoffs for the values of R-squared and its slope that are not arbitrary? Can I do anything to improve my method? Exposition: I work with a type-2 superconducting magnet for the ...
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8 views

Multiple Regression - Extreme F-statistic and R-square on 1 - too good to be true?

I have used a psychometric survey of 10 items which measure risk perception. I have taken the mean scores of these 10 items from a sample of 355 respondents who rated six hazards via the 10 ...
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1answer
36 views

Is it worth reporting small fixed-effect $R^2$ (marginal $R^2$), large model $R^2$ (conditional $R^2$)?

In a mixed model analysis (lme4 + lmerTest for R), I want to analyse the effect of 3 predictors, say A, B and ...
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25 views

$R^2$ in multivariate regression

I'm trying to determine how the population $R^2$ value is defined in the multivariate regression model where we have $Y_i = \mu_y + B^\prime(X_i - \mu_x) + err$ Where $Y_i \in \mathbb{R}^q$ and ...
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2answers
144 views

What happens to adjusted R squared as sample size increases?

What effect does sample size have on adjusted R squared values?
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25 views

Is the R-squared for this model respectable?

I have a model where the political position (left-right) of the coalition in power, among other things, explains stock returns. All data is monthly. See the results below. The question is, would you ...
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1answer
58 views

What's the difference between multiple R and R squared?

In linear regression, we often get multiple R and R squared. What are the differences between them?
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28 views

one-way MANOVA effect size interpretation

I'm having problem understanding effect sizes in one-way MANOVA model. In my case, I'm having a 13 variables which I used for clustering and then the produced ...
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49 views

Generalized $R^2$ for average model

I have some power-law data sets coming from an Ecology study. Some of them seem to be best modeled using linear regression after log-transformation of the data, but other data sets seem to be best ...
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16 views

Pseudo-$R^2$ in spatial regressions and Kelejian-Robinson test in R

I am currently trying to find out if there is a way to calculate a pseudo $R^2$ value from the output of maximum likelihood estimation of the spatial error model, and maximum likelihood estimation of ...
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944 views

Pitfalls to avoid when transforming data?

I achieved a strong linear relationship between my $X$ and $Y$ variable after doubly transforming the response. The model was $Y\sim X$ but I transformed it to $\sqrt{\frac{Y}{X}}\sim \sqrt{X}$ ...
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18 views

How to interpret marginal R squared?

i have obtained a marginal R squared value of 0.01599143 after fitting a tweedie model to my data set. Is this value too low? How can i interpret this?Thanks
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1answer
24 views

Is it possible to have an F-test with a $p<.05$ even if there is an $R^2<.1$ for a least squares analysis in JMP?

I've been working with JMP, and I have found that often I get a significant p value but a relatively small r. Is this supposed to happen?
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2answers
96 views

Comparing interaction effects using different variables. Possible?

I want to compare which are the "most important" interaction effects (in a data driven way, I realize that it is has downsides). I realize that for substantial researchers this does not make sense, ...
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1answer
35 views

Variation explained in ordinal logistic regression models

I have made these three ordinal logistic regression models: ...
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1answer
85 views

Is there any way the adjusted $R^2$ might decrease by adding predictors?

Let's consider a multiple linear regression formula: $ \hat{y} = \beta_0 + \beta_1 \hat{x}_1 + \beta_2 \hat{x}_2 $ (1) which produces adjusted $R^2 = r_1$. Now I want to add to one predictor to ...
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1answer
32 views

$R^2$ relative to a noiseless function

I am interested in computing the $R^2$ between a set of points $D_f = \{ (x,y)\} $ where $y = f(x)$ and a set of points $D' = \{(x',y') \}$ obtained adding noise to $D_f$. I don't think I can use: $$ ...
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36 views

Calculating McFadden's pseudo-$R^2$ in glmnet?

How do you calculate the McFadden's pseudo-$R^2$ using the cv.glmnet object from the glmnet package? The deviance.glmnet ...
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45 views

Higher r-squared value on test data than training data?

I am trying to create a linear regression model. I split my data into training and testing data, and built a model. The R-squared value on the training data is 0.840. Then I ran the model on the ...
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137 views

Is R-squared value appropriate for comparing models?

I'm trying to identify the best model to predict the prices of automobiles, using the prices and features available on automobile classified advertisement sites. For this I used couple a of models ...
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1answer
95 views

Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?

I estimated a robust linear model in R with MM weights using the rlm() in the MASS package. `R`` does not provide an $R^2$ value ...
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3answers
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Relationship between r-squared and correlation coefficient

Let's say I have two 1-dimensional arrays, $a_1$ and $a_2$. Each contains 100 data points. $a_1$ is the actual data, and $a_2$ is the model prediction. In this case, the $R^2$ value would be: $$ R^2 = ...
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comparing AIC and adjusted $R^2$

So, I have a homework assignment in which I'm being asked to compare the fit of two similar models by comparing their $R^2$ and AIC. Both models were run in R, one using the ...
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28 views

exact calculation of SD on R-squared

In R package "psychometrics" an estimate of SE of R squared of sersq <- sqrt((4*rsq*(1-rsq)^2*(n-k-1)^2)/((n^2-1)*(n+3))) with n sample size, and k number ...
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62 views

Relation between coefficient of determination, $R^2$, and significance in a regression

I have performed a simple regression of the following form: $y_t$ = $\beta_1x_{1,t}$ + $\beta_2x_{2,t}$ + $\beta_3x_{3,t}$ the $R^2$ turns out to be 38%. $\hat\beta_1$ = 0.7 (significant at the ...
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1answer
94 views

What is needed for a line to be an appropriate model for the data?

My answer key responds with a large $R^2$ and a residual plot with no pattern. The residual plot with no pattern makes sense. However, is having a large $R^2$ necessary? A linear model can be ...
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31 views

Do 2 different graphs with similar r^2 values show a connection between the data?

In my previous question, Does my data show quadratic regression in a calibration curve? I wanted to see if my data showed quadratic regression. I have realized that I can't really do that, so I'm ...
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59 views

Classification Tree Analysis - Assessment of tree explanatory power (R-square?) using the party package in R

I have produced a model using the ctree function in R, and want to know whether this tree is actually explaining my data well. I am trying to explain the presence ...
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1answer
101 views

Neural network with and without cross validation

I have been running ANN (Neural network) on my data set, until last week that I figured out I will get more robust model using Cross validation, So That's why I have started using ANN with the aid of ...
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1answer
140 views

Is $R^2$ valid in a nonlinear model?

The question is in the title. The coefficient of determination or $ R^2 \equiv 1 - \frac{ss_{res}}{ss_{tot}} $ is valid in a nonlinear model? Why?
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1answer
85 views

The larger $R^2$ the better? [duplicate]

I want to show that the variable $X$ is significant. In model 1, I use financial statements variables, other macroeconomic variables and $X$. Here, $X$ is siginificant at a 10% level and $R^2$ is ...
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91 views

Measure the goodness-of-fit in boosted regression tree

What is the apropriate statistic to measure the goodness-of-fit in Boosted Regression Tree (or Gradient Boosting Regression) with continuous response? How can I calculate the coefficient of ...
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28 views

How to calculate Beta and coefficient of determination ($R^2$) from unstandardized coefficients in OLS regression? [duplicate]

I have a table in which the multiple linear regression results is provided. If I have unstandardized coefficients and standard error for each independent variable, is it possible to calculate ...
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1answer
179 views

R-squared from rolling regression in Stata 12 [closed]

I am aiming to do a rolling regression in Stata, and I simply want to obtain the R-squared. I am aiming to keep it simple, I am not writing a whole program but if this is necessary, I am open for such ...
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1answer
80 views

Comparing models with different number of predictors

Given that the overall F-test of a multiple regression model has an F distribution, which depends on the number of predictors in the model, I understand why you cannot compare the F-statistics from ...
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1answer
178 views

Multiple Linear Regression Models Comparison Based on R-squared And Residual Errors

am currently working on a problem where I have to calibrate weather parameters at a ground location using Satellite data available (1979-2012) over rectangular grid points and surface observatory data ...
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360 views

Is adjusted R-squared appropriate to compare models with different response variables?

I heard that adjusted R-squared from two model are comparable only if two models use the same response variables. So if the response variable in one model is Y and the other one is log(Y), then I ...
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1answer
165 views

Understanding over-fitting

I am trying to understand over-fitting. I am using a regression tree method in Matlab. The given sample size is 500, which I divide into a training set of 400 and a test set of 100. I create the model ...
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1answer
256 views

R-squared vs. t-test confusion

I am using regression tree for this educational exercise. I have 500 observation points of independent variables $X$ and dependent variable $Y$. I use 400 points to generate my model and keep 100 ...
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2answers
206 views

Dealing with good performance on training and validation data, but very bad performance on testing data

I have a regression problem with 5-6k variables. I divide my data into 3 non-overlapping sets: training, validation, and testing. I train using only the training set, and generate a lot of different ...
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407 views

Selecting PCA components which separate groups

I frequently used to diagnose my multivariate data using PCA (omics data with hundreds of thousands of variables and dozens or hundreds of samples). The data often come from experiments with several ...
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1answer
92 views

Confidence interval on R-squared

I know that it is possible when you realize a multiple linear regression to calculate the confidence interval on the R-squared and on the adjusted R-squared. Does somebody know how to do it with R?
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1answer
172 views

Adjusted R squared on a holdout set

The formula for adjusted $R^2$ is: $$ 1 - \frac{(n-1)}{(n-p-1)}(1-R^2) $$ where $r^2$ is the coefficient of determination, $n$ is the number of points, and $p$ is the number of parameters the model ...
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1answer
112 views

Is it true that adjusted-$R^2$ not a measure of fit? Why or why not?

Previously I've read that adjusted-$R^2$ is not a measure of fit. Recently, though, I wanted to substantiate that piece of knowledge by understanding the reason why but I couldn't find any substantive ...
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Can adjusted-$R^2$ compare models across different samples?

I was reading this journal article about the decrease in the relevance of the income statement: Basically what the author does is this: (1) For each year, he takes that year's (say, 2010) income ...
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1answer
134 views

Coefficient of determination ($R^2$) and sample size

Is there any relationship between $R^2$ and sample size - does the $R^2$ increase with sample size? And does the adjusted $R^2$?
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30 views

Goodness of fit for complex-valued data

I have some experimental data, $f_{exp}(y_j)$ for $j = 1,\ldots,N$, that (after some post-processing) has a complex value. I have a model for these measurements, $f_{model}(y_j)$. In some cases the ...
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51 views

R-squared for user-defined prediction algorithms

I've been working on a machine learning project for a while and I've come up with an algorithm that does what I want it to do (predict some values). I wondered if it is possible to calculate R-squared ...