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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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
19 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
35 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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10 views

Relationship between Prediction Interval width and R-squared [closed]

I am trying to fit a multiple regression model that will be used for prediction. I have three variables, y (response), x1, and x2. If I fit this model with both predictors I get the following ...
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50 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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17 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
29 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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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 ...
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1answer
39 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 ...
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0answers
30 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
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2answers
95 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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57 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
46 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 ...
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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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28 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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29 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
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1answer
182 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 ...
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0answers
26 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
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1answer
33 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
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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 ...
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35 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
196 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 ...
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52 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 ...
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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
23 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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38 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
57 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 ...
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59 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 ...
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0answers
47 views

Why is my R-squared so low when the relative absolute error is not that bad?

I feel this may be a slightly dumb question but I'm trying to predict the price of a good and I'm obtaining low r-square values (approx. 0.20) but, in my case, acceptable absolute relative error ...
0
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1answer
75 views

R-squared and F-stat in dummy variables regression vs panel FE model

When estimating a Fixed Effects model on panel data and an equivalent dummy variables regression, the coefficient estimates and associated SEs are identical. However, the R-squared and F-statistic are ...
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1answer
48 views

Why not using the R squared to measure forecast accuracy?

Why in literature usually the common accuracy measures like MAD, MSE, RMSE, MAPE ... are used. Why not using the R squared (coefficient of determination)? I was thinking about the difference: By ...
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25 views

RMSE vs R Squared literature

I have found many related answers and explanations, but not one that involves literature. I have a model and I have used cross validation. Some models have really high R and adjusted R squared values, ...
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29 views

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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0answers
26 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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0answers
58 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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0answers
35 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
56 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
58 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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12 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 ...
6
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1answer
162 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
1k views

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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30 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 ...
3
votes
1answer
63 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
11 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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89 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
64 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
283 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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30 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
151 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 ...