# Tag Info

### Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$

If there is a constant term in the model then $\mathbf{1_n}$ lies in the column space of $\mathbf{X}$ (as does $\bar{Y}\mathbf{1_n}$, which will come in useful later). The fitted $\mathbf{\hat{Y}}$ is ...
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### What does negative R-squared mean?

$R^2$ can be negative, it just means that: The model fits your data very badly You did not set an intercept To the people saying that $R^2$ is between 0 and 1, this is not the case. While a negative ...
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### Is a high $R^2$ ever useless?

Yes. The criteria for evaluating a statistical model depend on the specific problem at hand and aren't some mechanical function of $R^2$ or statistical significance (though they matter). The relevant ...
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### R-squared is equal to 81% means what?

As a matter of fact, this last explanation is the best one: r-squared is the percentage of variation in 'Y' that is accounted for by its regression on 'X' Yes, it is quite abstract. Let's try to ...
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### What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?

For the specific hypothesis (that all regressor coefficients are zero, not including the constant term, which is not examined in this test) and under normality, we know (see eg Maddala 2001, p. 155, ...
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### Showing machine learning results are statistically irrelevant

You answered yourself: I made two additional models (mean and last sample) which often match or beat the RMSE of the RF and ANN models published in the paper. The mean model just takes the mean of ...
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### Relationship between $R^2$ and correlation coefficient

One way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$....
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### Is there any difference between $r^2$ and $R^2$?

Notation on this matter seems to vary a little. $R$ is used in the context of multiple correlation and is called the "multiple correlation coefficient". It is the correlation between the ...
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### What is the mathematical relationship between R2 and MSE?

Yes, allow me to elaborate. Recall that for some outcome $y_i \in \mathbb{R}, \forall i=1,2,..,n$ we define MSE and $\textrm{R}^2$ as \textrm{MSE}(y, \hat{y} ) = \frac{1}{n} \sum_{i=1}...

### What does it mean for a linear regression to be statistically significant but has very low r squared?

It means that you can explain a small portion of the variance in the data. For instance, you can establish that a college degree impacts salaries, but at the same time it's just a small factor. There ...
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### Why does statsmodels.api.OLS over-report the r-squared value?

This is not technically an error in statsmodels, rather it is because statsmodels.OLS does not add the intercept/constant term ...
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### R square in mixed model with random effects

The R package MuMIn also now has a function for calculating Nakagawa and Schielzeth's r-squared for mixed models. That is the function r.squaredGLMM() and you ...
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### Linear regression what does the F statistic, R squared and residual standard error tell us?

The best way to understand these terms is to do a regression calculation by hand. I wrote two closely related answers (here and here), however they may not fully help you understanding your particular ...
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