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.)
1,169 questions
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Why can a model with higher MSE still have a higher R² than another model
Two mdoels trained on different training datasets (related but not exactly the same) and tested on the exact same datasets, the model that has higher MSE, still has a higher R², is that possible?
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Is a low R² for Beta-binomial regression an issue?
I am studying a large dataset of animals subjected to 2 treatments. I aim to assess the impact of treatment on mortality rate. For each observation, I have the number of individuals dead or alive ...
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R-squared for glmmTMB with beta distribution and variance-covariance matrix as random effect
I'm performing a multi-species analysis on in which each data point relates to a species (n = 19). My response variable is a proportion and so I'm using a beta distribution with logit link. I've ...
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Correcting $R^{2}$ of a sample linear regression, knowing the size of the population
Given a linear model of the type:
\begin{equation} \tag{Eq. 1}
y=ax + c + \epsilon
\end{equation}
I take a sample of size $N_{s}$ from a finite population of size $N_{f}$ and take the values of the ...
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Expected value of Partial $R^2$ in linear models
In linear regression
$$
Y = \beta \cdot X + N(0,\sigma^2)
$$
partial $R^2$ quantifies how much additional variance in the response variable $Y$ is explained by a predictor $X_j$, given that the other ...
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why can't I use the R squared to compare two linear regressions I if apply the log transform?
Yes the regressions have the same number of coefficients. The difference is just that one uses log(Y) instead of Y. The only ...
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Why does empirical partial R² deviate significantly from theoretical values [closed]
I'm examining the accuracy of empirical estimates of partial R² in linear models, particularly when compared with their theoretical values (under multivariate normality). I expected them to converge ...
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Any news on Tjur's $R^2$ for ordinal regression?
There is an over 10-years-old answer which cites a weakness of Tjur's coefficient of determination:
Another potential complaint is that the Tjur R2 cannot be easily
generalized to ordinal or nominal ...
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R-squared in a multiple regression with nested slopes
Consider a multi-linear regression:
\begin{equation} \tag{Eq. 1}
Y=(a + b)X + (a + 6b)Z + \epsilon
\end{equation}
you can see that the slopes of variables $X$ and $Z$ are related by the term $a$. I ...
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Why is the sum of partial R2s in a multiple regression greater than the R2 of the overall model? [duplicate]
in a multiple linear regression, why can the sum of the partial R-squares of the variables in the model be greater than the R2 of the overall model? I would intuitively expect that the sum of all ...
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Does adjusted $R^2$ have a lower bound? Assume the usual OLS linear model with an intercept
Let's fit a linear model (with an intercept) using ordinary least squares, with more observations that parameters (including the intercept). In such a situation, $
R^2=1-\left(\frac{
\overset{n}{\...
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Coefficient of determination ($R^2$) for complex-valued models
For a model $f:\mathbb{R}\rightarrow\mathbb{R}$, the coefficient of determination is unambiguously defined by:
$$
R^2=1-\frac{\text{Unexplained variance}}{\text{Total variance}}=1-\frac{\sum_{k=1}^n\...
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How can $R^2<0$ happen when the Pearson correlation is high or even perfect?
Say I have two sensors with measurements $\{
x_i
\}_{i=1}^n
$ and $\{y_i\}_{i=1}^n$ that have a high Pearson correlation, perhaps even perfect correlation by reporting the values in different units (...
- 72.9k
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Why is R² not equal to the square of Pearson's correlation coefficient (r²) in my multivariate regression model?
I'm working on calibrating air quality sensor data using a multivariate regression model (Lasso), with predictors like raw PM2.5, humidity, and temperature. After fitting the model, I compared:
...
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How do I find the variance explained by a fixed effect in a MCMCglmm threshold model?
I have run a threshold model using MCMCglmm (binary response variable) and obtained the proportion of variance explained by the random effects, but how do I do this for my fixed effect?
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