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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31 views

Why could pseudo $R$-squared (pseudo $R^2$) increase when I remove variables?

I have a multinomial logistic regression with $11$ independent variables. When I remove variables, the pseudo $R$-squared increases. Isn't this not supposed to happen? Why could this be happening?
8
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1answer
203 views

Can standardized $\beta$ coefficients in linear regression be used to estimate the $R^2$?

I am trying to interpret the results of an article, where they applied multiple regression to predict various outcomes. However the $\beta$'s (standardized B coefficients defined as $\beta_{x_1} = B_{...
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33 views

How should one select amongst competing mixed models in a model selection paradigm?

I suspect two biological functions trade off (i.e. as one goes up, the other goes down). Trade-offs are often non-linear, but there has not been a ton of work to suggest which family of curves tends ...
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23 views

Low coefficient of determination and low p-value

What should we think of a regression model that has a low coefficient of determination (e.g. $R^2 = 0.01$) and simultaneously a low p-value ($p<0.01$)? That in reality there is a non-random but ...
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0answers
23 views

likelihood ratio test (mixed model, nlme in R) not significant, but big R²?

I am carrying out linear mixed models with only one factor as predictor. I start with a likelihood ratio test (LRT) to see if adding the factor (to the null model consisting of the random effect ...
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1answer
36 views

How to show that a model is not over-fitted?

This might have a very simple answer, but I am doing an analysis of a financial series and have decided to use regression in order to predict a particular revenue given a set of input variables. ...
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0answers
11 views

R2 low for difference-in-difference panel data with fixed effects

I performed a difference-in-difference with panel data and firm + time fixed effects. I have 2 questions regarding the very low (almost 0) $R^2$: When only ...
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27 views

Interaction term: no R² change

I use hierarchical regression to test whether or not an independent variable moderates the relation between another independent variable and the dependent variable as follows: model 1: control ...
19
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1answer
163 views

Is there such a thing as an adjusted $R^2$ for a quantile regression model?

Having included an quantile regression model in a paper, the reviewers want me to include adjusted $R^2$ in the paper. I have calculated the pseudo-$R^2$s (from Koenker and Machado's 1999 JASA paper) ...
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1answer
28 views

Choosing best fit regression model from root MSE and adjusted R squared

I run regression model and wanted to choose the best fit model among 3 regression models. ...
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12 views

Variance explained by indirect effect in repeated-measures mediation analysis

I ran a mediation analysis with a repeated-measures categorical predictor on a continuous DV. As described by Judd, Kenny and McClelland (2001) I first built two contrasts (the categorical predictor ...
0
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1answer
36 views

What is an acceptable R squared range for cross sectional data linear regressions?

May I know an acceptable R squared range for a cross sectional data analysis using linear regression? I think the requirement for this is lower than time series or panel data but would like to know ...
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13 views

Is there any possibility to calculate adj. r-squared for geeglm (GEE, geepack) in R?

I using geepack package in R fo generalized estimating equation model. Is it possoble co calculate a marginal r2 for a geemodel in R software? Thank you for answers
3
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0answers
30 views

Is it possible to calculate a pseudo-R squared for a binomial GLMM with a cauchit link?

I'm modeling some repeated-measures presence-absence data using a binomial GLMM in lme4. I've been using the method suggested by Nakagawa and Schielzeth (2013) to calculate a marginal and conditional ...
0
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1answer
37 views

Can we find the coefficient of determination, $R^2$, from an estimated regression equation?

Assume we have a regression equation where $\hat y = 15 + 25.5 x_1 - 5 x_2 + 6 x_3$ Using these beta values, how would you go about finding a coefficient of determination?
3
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34 views

R squared and higher order polynomial regression

The plot below shows the saturation of a road against the impact on journey time (normalized to free flow journey time). The blue (BPR function) curve presents a standardized model used in the field ...
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0answers
11 views

Relative contribution of variables in explaining the dependent variable in a logistic model

we are using a logistic regression and I want to know the relative contribution of each explanatory variable in explaining the dependent variable. that is basically rank the variables according to ...
1
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1answer
29 views

What measure should I use to compare two sets of calculations?

Assume I have two sets of calculations produced by two different simulators. There is no way to precisely measure actual values for these calculations, so I'm defaulting to the assumption that one of ...
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0answers
23 views

How to implement SMC in Python as it in R? [closed]

Is there any function in Python similar to Squared Multiple Correlation (SMC) in R? What if I want to implement SMC in Python? Is the only way to do it just rewriting SMC into Python line by line? ...
3
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1answer
30 views

Determinie how well sales correlate with weather

I work with for a retail company. A recurring problem in our meetings is that our mid-level managers usually blame weather for the sales development. I want to find out if this is right or wrong. My ...
0
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0answers
17 views

What is the formulaic relationship between R2 and correlation coefficients between different units in a balanced panel data set?

I am trying to understand the relationship between R2 and correlation coefficients between different units in the underlying data. Specifically, I have a balanced panel data set, with N different ...
0
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1answer
22 views

Calculating R-squared from item-factor loadings

If I have run a Confirmatory Factor Analysis and have all of the standardized loadings of each item onto its respective variable, how would I calculate the R-squared for each item? Is it simply the ...
4
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2answers
77 views

Regression: What is the utility of R squared compared to RMSE?

Suppose I'm doing regression with training, validation, and test sets. I can find RMSE and R squared (R^2, the coefficient of determination) from the output of my software (such as R's lm() function). ...
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1answer
45 views

Is least square dummy variable model better than random effects model?

I have a panel dataset with one dependent and twelve independent variables. There are 50 individuals with data for 100 days. Theoretically, most of them should be significant. First, I checked for ...
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2answers
44 views

How to summarize R-squared of several regressions, one per subject

I will explain my question, I have made a study and I have 10 regression (one for each subject). I have a significance for each regression, but in some subjects the value of R-squared is 0.5 and in ...
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55 views

Why the focus on variance reduction for $R^2$?

It seems to odd to me that we measure the explanatory power of a regression model in "percent of variance explained", or $R^2 = cor(\hat{y},y)^2 = r^2$ even though we all know that variance is just an ...
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19 views

Variance explained $R^2$ by separate fixed effects (and interactions)

I am currently assessing the effect of five environmental variables (A, B, C...) on a trait (Y). I would like to estimate how much variance in Y each environmental variable explains. Previously I had ...
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2answers
38 views

How to get Cox & Snell, Nagelkerke R-Square in R logistic regression output?

I'm new to R (used to work with SPSS), and looking for a function that will output the Cox & Snell and Nagelkerke R-Square measures of logistic regression. In SPSS they are displayed as part of ...
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0answers
14 views

Getting different r-square values whe constraining the models to be equal (Testing invariance in structural model)

I compared the chi-square value from the model with all parameters allowed to be unequal across groups (e.g., parameters are set free) to the chi-square from the model where paths at time-point 1 and ...
3
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1answer
41 views

Error term in multiple regression model

I am trying to run a multiple regression model to see the effect of field characteristics such as soil texture, slope and hydraulic conductivity on drainage density. My samples are agricultural ...
0
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0answers
31 views

Model fitting: relative importance of SE of regression coefficient vs adj. R squared when estimating accurate coefficient is only objective

My objective is to infer the magnitude of a particular coefficient ($β_5$ in the equation below) as accurately as possible. I'm trying to decide between two models: the first which has a lower SE (....
3
votes
2answers
99 views

Why is $SST=SSE + SSR$? (One variable linear regression)

Note: $SST$ = Sum of Squares Total, $SSE$ = Sum of Squared Errors, and $SSR$ = Regression Sum of Squares. The equation in the title is often written as: $$\sum_{i=1}^n (y_i-\bar y)^2=\sum_{i=1}^n (...
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2answers
59 views

Why does $R^2$ grow when more predictor variables are added to a model?

I do understand that $ R^2 = \frac{\text{SSR}}{\text{SST}}= 1- \frac{SSE}{SST}$, however, I don't understand what changes when more predictor variables are added and how $R^2$ is affected accordingly. ...
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0answers
58 views

Lasso Regression - model predictions are not correct. low r-squared

I am attempting to use Lasso to choose the best variables from a set of 20. I have managed to construct a model using LassoCV, however when using the test data to compare the predicted returns to the ...
0
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0answers
11 views

Is one value the linear combination of four others?

The textbook asserts that, "AFQT" is a linear combination of four other given components, [“Word, “paragraph”, “math” and “arithmetic”]” and asks us to test this proposition in JMP. I ran a linear ...
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0answers
34 views

Statistical method to combine/summarize multiple R squared values

I have a set of measurements using two different methods. I Have 6 samples that I have measurements for using both methods. I am trying to demonstrate how comparable the measurements are from the ...
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0answers
16 views

Relationship between weighted $r^2$, and $r^2$ of transformed data

When regressing heteroscedastic data, recommended practice is to either transform the data to remove heteroscedasticity weight the data to compensate So let's say we have some data $ y = x + \...
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0answers
41 views

Pseudo-r-squared glmer.nb

I am running a negative binomial generalised linear mixed model - glmer.nb()from the {lmer} package - to investigate the extent to which elevation (elev) can predict changes in the density of ...
2
votes
1answer
341 views

Difference between selecting features based on “F regression” and based on $R^2$ values?

Is comparing features using F-regression the same as correlating features with the label individually and observing the $R^2$ value? I have often seen my ...
0
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0answers
28 views

Calculating a large number of R-squared statistics in R

I have a very large number of R-squared statistics to collect, basically I'm collecting a monthly R-squared series for a period of around 25 years for a large number of variables where I'm interested ...
3
votes
1answer
34 views

Is there any way that adjusted R squared would be greater than R squared?

Is there any way that adjusted $R^2$ would be greater than $R^2$? Including cases of extreme values of n and p and negative values of $R^2$.
3
votes
1answer
47 views

Distinguishing between what makes up R-squared

I am interested in the relationship between religiosity and religious distrust (would you dislike having as neighbours people of different religions). One of my main goals is to make the role of each ...
0
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0answers
42 views

Coefficient of determination in ARIMA model vs linear regression

In an ARIMA model, $R^2$ can be computed from squared correlation between fitted and actual values. My question is, is this $R^2$ the same as the $R^2$ in linear regression?
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3answers
198 views

If two traits have known correlation, can you predict probability they'll “align” for a random pair?

Suppose you have two traits that are correlated in a given population, like a person's BMI and their blood pressure. And let's say I want to estimate the probability that in a randomly-selected pair ...
0
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0answers
66 views

Holdout ${R}^{2}$ calculation

I am considering a simple linear regression model for a short time series consisting of yearly data over 16 years. I am to keep the 16th year as a holdout. Considering the calculation of ${ R }^{ 2 }...
0
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0answers
15 views

Multiple regression: forcing y-intercept=0 improves R^2, is this correct/possible? [duplicate]

I have been running multiple regressions in Excel successfully (using the Data Analysis Toolpak) but when I run the same regressions and force the y-intercept through 0, the R^2 values are very ...
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1answer
32 views

Coefficient of determination

I'm taking an online intro class on statistics and right now we are covering a topic on relationship between quantitative variables. One of the subtopics is coefficient of determination. Here is an ...
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0answers
39 views

Low MSE, but negative $R^2$

I'm training some neural nets on my data and I get a satisfying MSE (compared to the variable scale I'm working with) and an anomalously negative $R^2$ value. What does the negative $R^2$ mean in this ...
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1answer
64 views

Calculating R^2: two different results depending on method

So I've fitted a linear trend to my data and calculated R^2 in two different ways (in Matlab), one is using corrcoef and the other is "by hand". These return ...
0
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0answers
93 views

How to get R squared/goodness of fit for Tobit model in R?

I'm quite new to R, so maybe the answer to my question is quite easy but in hours of checking google and communities like this I didn't find a solution. I do a tobit regression to analyse censored ...