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1

The paper Estimation of the correlation coefficient using the Bayesian Approach and its applications for epidemiologic research provides posterior probability distributions for the linear correlation coefficient, from which you can easily compute the probability that the determination coefficient belongs to any set of interest as required (by numerical ...


3

For adjusted $R^2$ the answer is yes. $$R^2_{adj} = 1- \dfrac{n-1}{n-p}\dfrac{SSRes}{SSTotal}$$ (Some sources may write the denonominator of $R^2_{adj}$ as $n-p-1$. That assumes that $p$ does not consider the intercept term. In the book I used, the author assumes that $p$ does consider the intercept term.) If you do a regression on 100 observations and ...


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Here's an image where different R2 Scores are compared: The blue dots are the ground truth data. Each line has a different prediciton. As expected, note that the orange line has an R2 score very close to 1. Also note that the red fits very badly the dataset and has a negative score of -1.55. In case you are familiar with Python, feel free to play with the ...


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If you have the total sum of squares for the variable being predicted $$\mathrm{TSS}=\sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^2$$ and the residual sum of squares from the predictions from your model $$\mathrm{RSS}=\sum_{i=1}^{n}\left(y_{i}^{\,}-\hat{y}_i\right)^2$$ then you might say $$R^2 = 1-\frac{\mathrm{RSS}}{\mathrm{TSS}}$$ which makes sense as the ...


4

Yes, the linked STATA post answers your question in a single sentence: $R^2$ really has no statistical meaning in the context of 2SLS/IV. How can $R^2$ be negative? Wikipedia has a great visualization of $R^2$: On the left, we see the $\color{red}{\text{total sum of squares}}$, obtained by using the mean ($\bar{y}$) as a prediction: $${\text{total ...


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This is just the Pythagorean theorem!


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Use the observed values as there may be lag structure needed for GDP (X) that may be different than the lag structure need for air traffic passenger data (Y) . You can always subsequently express the change in passenger forecast as a percentage of the previous value as it relates to the change in GDP as it relates to the previous value of GDP . Finally to ...


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