Timeline for Why is the correlation coefficient the slope of the regression line?
Current License: CC BY-SA 3.0
11 events
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| Mar 5, 2020 at 2:06 | review | Suggested edits | |||
| Mar 5, 2020 at 15:43 | |||||
| Nov 10, 2018 at 13:42 | comment | added | Parthiban Rajendran | I have illustrated what Mr@whuber says here, but have my own question ( I ask for mathematical derivation from regression to correlation via covairance). Can you kindly check | |
| Nov 3, 2017 at 16:39 | comment | added | Adam B | The op said he didn't want mathematical derivations. | |
| Nov 3, 2017 at 16:24 | comment | added | Adam B | Yes but these are just "rotating" the model. You'll get the same overall result. The numbers you get like the intercept will be respective of x rather than y but all the model-level statistics will be the exact same. And the overall conclusion "are x and y related?" Will be identical. | |
| Nov 3, 2017 at 16:21 | comment | added | whuber♦ | They are totally different models statistically: one minimizes residuals of $Y$ and the other minimizes residuals of $X$! You seem to be caught up in a circular chain of claims. It's time to actually prove some of them... . | |
| Nov 3, 2017 at 16:20 | comment | added | Adam B | X against y and y against x are mathematically identical models. You'll get the same p value and the regression coefficients are the inverse of one another. | |
| Nov 3, 2017 at 16:16 | comment | added | whuber♦ | This answer seems to overlook the basic question: a correlation coefficient is a symmetric function of paired variables. It definitely is not intended to compute a "line of best fit," which--because "best fitting" treats the variables asymmetrically--it obviously is not doing. Indeed, there are two distinct "lines of best fit": the linear regression of $Y$ against $X$ and the linear regression of $X$ against $Y$. | |
| Nov 3, 2017 at 16:01 | comment | added | Adam B | @D.W. added some more explanation to my answer. Hope that helps. | |
| Nov 3, 2017 at 16:01 | history | edited | Adam B | CC BY-SA 3.0 |
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| Nov 3, 2017 at 15:33 | comment | added | D.W. | Thanks for taking the time to answer! "It just so happens that [they] are mathematically equivalent" - Yeah. I'm trying to get some intuition for why this is true. I'm hoping for something more than "the math just turns out that way". If the slope of the linear regression line is large, why should that tend to indicate a larger correlation coefficient, or vice versa? "a correlation coefficient calculates the line of best fit between two variables" - Perhaps a different way to answer would be to provide some intuition for why the formula for the correlation coefficient does this. Any ideas? | |
| Nov 3, 2017 at 7:54 | history | answered | Adam B | CC BY-SA 3.0 |