Questions tagged [r-squared]

The coefficient of determination, usually symbolized by $R^2$, is the proportion of the total response variance explained by a regression model. Can also be used for various pseudo R-squared proposed, for instance for logistic regression (and other models.)

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How can I calculate the R-squared of a simple linear regression only with sample size, the coefficients and its standards deviations?

I have the following estimated simple linear regression, which was estimated from a sample of 1217 individuals: $\hat{y}=1.77663 + 0.0910103x$ where $\hat{\beta_0} = 1.77663$ and standard deviation of ...
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R2 for mixed-effects Conway-Maxwell Poisson using package glmmTMB

After running a mixed-effects Conway-Maxwell Poisson model using glmmTMB, I've printed the results using sjPlot's tab_model() but I don't know what R2 calculation is being used. Is it Nakagawa's R2 ...
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How to show VIF

The variance of the $j$th element of the OLS estimator is given by $$\operatorname{Var}\left(\hat{\beta}_{j}\right)=\sigma^{2}\left(X_{j}^{T} M_{-j} X_{j}\right)^{-1}$$ where $X_j$ is the column of ...
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$R^2$ explanation to commercial people

We have a representative digital panel that measures digital media consumption of panelist and then project it for the total population via weighting. Recently I ran a multiple regression on panel ...
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Is it correct to say one 'estimates' or 'measures' r-squared?

I am writing a report and am unsure about whether is correct to say one 'measures' r-squared or whether one 'estimates' it. I know the two words have two different semantic meanings, probably related ...
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$p$-value and $R^2$ of a Power Regression Model

I'm trying to perform a power regression model to fit my data. I used this script to find the angular coefficient and exponent of my power regression. ...
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R-squared as sample size increases

How do I prove that $R^2=1-\frac{SSR/n}{SST/n}$ converges towards $\rho^2=1-\frac{\sigma^2_u}{\sigma^2_y}$ as $n \rightarrow\infty$, where $\sigma^2_u=\operatorname{Var}(u)$ and $\sigma^2_y=\...
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How does the meaning of R^2 come from squaring R?

I think more or less I understand what R and R^2 are, but I do not understand how R^2 comes from R. In a video I saw this explanation for R^2 : (VAR[mean] - VAR[line]) / VAR[mean]. From this formula I ...
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Total inconsistence between Pearson correlation in a correlation matrix vs Pearson test AND Rsquare smaller than Pearson [duplicate]

I have a very urgent issue that I need to solve this weekend. If I create a linear model between 2 variables and look for the R square with this code: ...
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Why can't we use sum of absolute residuals instead of R squared method in Linear regression [closed]

I am fairly new to statistics, so can somebody explain to me the given question in simple terminology. I read almost all answers on stack exchange but all I can say is they are too technical for me. A ...
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Conceptual/Math/brainteaser Question: Multiple Linear Regression

This is kind of a brainteaser and I'm struggling to solve it, any ideas on approaching this would be valued: I thought about using substitution of the different x and z into the third regression ...
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standard deviation of the model R2 in LOOCV in caret

I am performing a LOOCV linear model and I got the parameters R2 and RMSE, but I was wondering if there is a way to calculate the standard deviation of the model R2. I tried to do it in the same way I ...
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What is the relationship between a simple regression's $F$ value for $R^{2}$ and $t$ value for a slope?

I have a question that states: In a simple regression, if the $F$ value for $R^{2}$ is 4, then the $t$ value for the slope $b$ must be...? I'm having trouble understanding how to figure out the ...
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understanding R2 in probit

I try to create a model to predict football (socker) results with a performance variable. It doesn't really matter how this performance is calculated since any performance variable is an adequote ...
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Removing variables from a linear regression improves $R^2_{adj.}$

I am working on a linear regression model. The complete model with 11 variables in total has a quite low adjusted R-squared ($R^2_{adj.}$) of 0.11. 4 variables have a significant influence on the DV....
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How to adjust the standard error for a standardized beta after squaring the beta

I have a standardized beta from a regression, which is equivalent to a correlation. I also have it's standard error (SE). I want to plot the R2 (explained variance) with an error bar, and to get the ...
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Explained variance score vs $R^2$ score

I came across explained variance score and $R^2$ score in scikit learn docs. Docs defines exaplained variance score as: $\text{explained variance} (y,\hat{y})=1-\frac{Var\{y-\bar{y}\}}{Var\{y\}}$ ...
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Understanding regression model with and without intercepts

I was going through this answer which gives total sum of squares as $TSS=\sum_i(Y_i-\hat{Y}_i)^2+\sum_i(\hat{Y}_i-\bar{Y})^2+2\sum_i(Y_i-\hat{Y}_i)(\hat{Y}_i-\bar{Y})$ It then says: In a model with ...
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Can it be shown analytically that the sum of squared semipartial correlations is bounded by r-squared?

Two related questions: I have read in different texts that the sum of squared semipartial correlations is "typically" less than $R^2$, except when supressor variables, or rather a supression ...
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Unrealistically High R squared value of 1 (and low RMSE of zero) [closed]

I am working on a regression problem of load prediction (where I try to estimate next hour consumption using previuous consumption values). At first I had relatively poor perfromance, however when I ...
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Panel regression vs. average of time-series regression

I have an unbalanced panel of cross-sections (i=1,2,..,5 and j=1,2,...,10) and time-series (t=1,2,...,120). For each j, I would like to see how much variation of Y variable is explained by X variable ...
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Why is $R^2$ in linear regression estimated from resubstitution?

In linear regression, the coefficient of determination $R^2$ is a normalized measure for prediction accuracy. In machine learning, performance measures are not computed by estimating the performance ...
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Do we maximize explained sum of squares with OLS?

I know that with OLS we minimize the sum of squared residuals but does that imply that we maximize SSE? From the following r-squared formula $$ R^2 = \frac{SSE}{SST} = 1- \frac{SSR}{SST}$$ and the ...
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Why can't the uncentered $R^2$ be negative?

In vectorized OLS, let $\mathbf{y}$ and $\hat{\mathbf{y}}$ be the observations and predictions, and define the residuals as $\mathbf{e} = \mathbf{y} - \hat{\mathbf{y}}$. Then the uncentered $R^2$ is $$...
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Stationary R squared

I am looking for information on the stationary R square value from an ARMA model. Are there any references for it? I haven't been able to find much of anything. How is it calculated? How does it &...
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Does it make any sense to use R^2 as a measurment [closed]

I was wondering whether it makes any sense to use R-squared for the graph/model. I think it is not since it does not clearly explain a linear relation.
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For linear regression, if the theoretical coefficients and the variance of the error is known, is the theoretical R squared value, F statistic known?

For linear regression, suppose we know the true, theoretical coefficients of the predictors (say, for a simulation) and the standard deviation of the error term (sigma). For instance, suppose we know ...
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R-squared with benchmark set to zero

I am using this paper as a reference for my master's thesis and I am trying to reproduce their results. As a performance evaluation they use modified $R^2=1-\frac{\sum{(i,t)}\in_{test}(r_{i, t+1}-\hat{...
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Finding the coefficient of determination from a regression line?

Suppose you are given the following estimated model from a sample of size 1217: $\hat{y} = 1.177663 + 0.0910103x$ and the standard errors of the coefficients are $0.0865446$ and $0.0065643$ ...
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Multiple regression in SEM when the covariance between predictors is fixed to zero

I did a multiple regression with $x_1$ and $x_2$ predicting $y$, and found that I could recreate in SEM software (lavaan or AMOS) the same results I got doing things the regular way in R with the <...
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Definition of partial R-squared?

I'm trying to understand the definition of Partial R-squared values in the context of a regression model. Does anyone have a layman's definition or an intuitive example that might help me better ...
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How to interpret variance explained and r-squared outcome from a multiple regression model in R?

I am running a regression model in R and I want to interpret the variance explained percentage, as well as, R-squared value. ...
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When and why should R squared be used instead of adjusted R squared?

The title says it all. In what situation R squared (non adjusted) is more useful and should be used instead of the adjusted one? Why?
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How to quantify and sum up the effect of each record of two time series on their correlation?

Let's say I have two one-day time series data. Each has 24 points (24 hours). ...
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Simple linear regression: R2 not equal to squared Pearson coefficient

The R2 of a simple linear regression model is the squared Pearson correlation coefficient (r) between the observations and the fitted values. Isn't the above in contradiction with the fact that the ...
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How to calculate the R Squared given limited information?

I am attempting to solve the following problem from my Statistics class: WALC=β_0 + β_1 TOTEXP + β_2 AGE + β_3 EDUC + β_4 SIZE + e. Suppose RSS=2032.73 and SD(WALC)=12.4537. N = 45. What is R Squared?...
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what does variation in X mean, linear regression and r squared

I was reading a document about the coefficient of determination and saw that r^2 shows how much of the variation in y is represented by the variation in x. What I couldn't understand was the part ...
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Nagelkerke pseudo R^2 interpretation in spatial regression

Could anyone explain to me the interpretation of Nagelkerke pseudo R^2 in spatial regression models? Definitions say it is computed using some conditonal probability, but I didn't quite get what they ...
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OLS- relation between R-squared an t-stat

I read here and in a comment by "Jeff" to the first answer here that $R^2= \frac{t^2}{t^2+df} $ I presume this is valid for simple linear regression only (with only one x variable, so not ...
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When can we not drop an independent variable that has a high VIF?

In a linear regression context, and we observe that some independent variable can be approximately written as a linear combination of a set of other independent variables (e.g., with $R^2 > 0.95 \...
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Given a predictor that explains 10% of the variance in an outcome, how accurate can my prediction be for a person with a known score on the predictor?

Sorry if this is really elementary stuff, but I'm a stats noob trying to wrap my head around this. Intuitively, I'm imagining that a model with this information alone would be able to accurately ...
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Different ways to calculate Rsquared after Regression with complex survey data in R

I'm struggling to find out the differences or the "right way" to calculate R² after regression with complex survey data in R. My data includes missings and though I know this is not really ...
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Do estimates of effect size vary as a function of sample size?

Imagine 50 studies of the same phenomenon with 100 participants, vs. 50 studies with 200 participants. Would we expect greater variation in estimates of effect size with a smaller number of ...
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How to construct (simulate) data that will have a given coefficient of determination?

I want to produce random sample bivariate data that will have a given coefficient of determination and a given linear regression model. In particular, I want to understand how it should be constructed,...
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What does $R^2$ tell and what is the “strength of the relationship” between two variables?

I was reading this answer by @whuber where it is discussed about the meaning and uses of $R^2$. I’m having some trouble understanding what the “strength of the relationship” between two variables ...
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In a regression model, how to interpret a IC 95% for R-squared with negative values but with a significant effect of a predictor?

Imagine a regression with 3 predictors and one dependent variable with a sample size over 400. Only one predictor has a positive significant effect, p value equals to .02 aprox. R-squared is low (less ...
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Question regarding explained variation of individual regressors

If you regressed a dependent variable on multiple independent variables, would it be possible to figure out how much each regressor is explaining the variance of the dependent variable? Or can you ...
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What is the difference between correlation and explained variance?

Is there any meaningful difference between these two statements? X is highly correlated with Y X explains a lot of the variation of Y
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Linear regression R-squared vs slope

If you look at basic resources on R-squared, such as https://en.wikipedia.org/wiki/Coefficient_of_determination, they all tend to say the same thing: That it is a measure "about the goodness of ...
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If given the coefficeints, standard errors and r^2, how can I determine overall significance of an OLS model?

Basically the title. Say I am given coefficients 1,2,3 and standard errors .1, .02, .01 respectively and an R^2 value of 0.35. How would I go about testing the overall significance of the model?

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