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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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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76 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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35 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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28 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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16 views

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

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? ...
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52 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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21 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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20 views

Calculating R-Squared with logged data

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

Multiple R squared drops when I cluster dataset

I ran a linear regression with two independent variables on a dataset and got an R squared of approximately 40%. I then divided the dataset into two clusters and ran the linear regression on each of ...
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12 views

Combining r-square from clusters

I have a dataset which is split into multiple clusters first - say two clusters, $C1$, and $C2$ with $n1$ and $n2$ data points. I fit a regression model per cluster. For our example, let them be $M1$ ...
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45 views

Interpretation of R-squared when using FGLS

Context: I am analyzing time series and cross-sectional data using Stata's xtpcse command which corrects for autocorrelation in panel data using a Prais–Winsten ...
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85 views

Problem with R-Squared value

I have a problem to determine my R-Squared value. I do a polynomial regression: fit3 <- lm(value ~ date + I(date^2)+ I(date^3),data=training) I have a R-Squared value (0.9416) when I do ...
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58 views

Difference between RSQ function in Excel and Regression in the Excel Data Analysis Add-in?

When I use the RSQ function between one x variable and y variable, the resulting $R^2$ differs from the $R^2$ values given by running regression analysis from excel's Data Analysis. For example, ...
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15 views

How to Calculate F distribution given R squared? [duplicate]

After some research, I find that the relationship between $R^2$ and the F distribution is as follows: $$ R^2 = 1 - (1 + F \cdot \frac{p-1}{n-p})^{-1} $$ But I am not sure what the $p$ and $n$ values ...
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2answers
78 views

Better Quantitative Measure of Predictor “Relevance” than p-values?

I have a regression of the general form: $$ Y = \alpha + \beta_{1}*X_{1} + \beta_{2}*X_{2} +\beta_{3}*X_{3} + ... + \epsilon $$ Let's assume the following constraints: k=14; all X's are ...
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42 views

How to compare explained variances of nested multivariate multiple regression models?

I have two groups of continuous* variables - let's call them MF (5 variables) and OR (2 variables), plus some demographics. It has been previously found that the MF are associated with one of the OR ...
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43 views

Interpretation of random-effects GLS regression (multilevel model, 2 levels, strictly hierarchical)

There are several values in this analysis that I wonder how to interpret, and whether they can be used to calculate some sort of effect size. Contextual information: level 1 trials in a test - level ...
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44 views

Coefficient of Determination with Multiple Dependent Variables

I have X | Y1 | Y2 data, that I fit with some model. The model produces two values for one independent variable, where one is compared with the Y1 values, and the ...
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37 views

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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74 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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63 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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27 views

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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49 views

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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87 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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109 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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246 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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41 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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24 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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41 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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17 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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1answer
87 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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22 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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38 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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1answer
64 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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120 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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1answer
88 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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29 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
29 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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1answer
207 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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49 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 ...
2
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1answer
127 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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37 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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44 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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1answer
37 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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57 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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20 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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68 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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17 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 ...