Linked Questions
13 questions linked to/from Relationship between $R^2$ and correlation coefficient
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Relationship between R2 and correlation coefficient [duplicate]
in simple linear regression
R-squared is equal to the squared correlation coefficient between the actual y and the predicted y (i.e. š¯‘¦ hat )
how to prove this relationship?
Thanks!
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What do r (Pearson correlation coefficient) and R^2 stand for? [duplicate]
As far as I understood, R squared explains how much the variation in Y is explained by its linear association with X. And it's used as an indicator for goodness of fit of a linear model.
Then when ...
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How is this simplified pearson coefficient derived? [duplicate]
I came across a variation of the Pearson coefficient as seen here:
$$r=\left[1-\left(\frac{\sum_{i=1}^n (x_{ti}-x_{pi})^2}{\sum_{i=1}^n x^2_{ti}}\right)\right]^{1/2}\,,$$
where $x_{ti}$ is a target ...
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Do correlation or coefficient of determination relate to the percentage of values that fall along a regression line?
Correlation, $r$, is a measure of linear association between two variables. Coefficient of determination, $r^2$, is a measure of how much of the variability in one variable can be "explained by" ...
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Why is the correlation coefficient always smaller than $1$ and bigger than $-1$?
I kind of see that the covariance is similar to the product of the standard deviations but I can't figure out how. My problem is that I don't understand how does this formula tells us how strong the ...
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Thousands of features and only 70 samples
I am working on a regression problem where I have around 5-10 thousand features and have only 65 samples. I am training my algorithm on 55 samples and testing on 10 samples. I am using both Pearson ...
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Why does $r^2$ between two variables represent proportion of shared variance?
Firstly, I appreciate that discussions about $r^2$ generally provoke explanations about $R^2$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing ...
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Why do some statistics symbols have a "squared", e.g. Variance $\sigma^2$, "R squared" $R^2$ or heritability $H^2$
I sometimes encounter symbols in statistics whose symbol carries a "squared". In other areas, like for example mechanics, you give the quantity you are interested in a normal letter and then define ...
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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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Using correlation for "explained variation"
I present using dummy data for an example, see below for R code to replicate data.
Imagine that I have collected data on how much mail 500 people receive. In my survey there are 250 men and 250 ...
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Coefficient of determination relationship?
$R^2 = \frac{SSREG}{SSTOT}$ or $R^2 = 1-\frac{SSRES}{SSTOT}$
If $X$ is the predictor random variable for science SAT
and $Y$ is the predictor random variable science GPA
given by equation $$\hat Y =...
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How to distinguish two versions of R-squared calculated on test set?
I've come across two ways that people calculate R-squared on a test set:
Calculate the square of the correlation between predictions and actual values (in practice, I've seen people do this in R by ...
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