Timeline for Relation between regression coefficient and correlation coefficient
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2019 at 14:50 | comment | added | whuber♦ | This answer is good, but the final formula is incorrect because $\sqrt{R^2}=|R| \ge 0$ whereas the correlation can be negative. | |
| Jul 28, 2017 at 1:45 | comment | added | Yannis Vassiliadis | So how is what I wrote not correct? The sign of the correlation and the sign of the coefficient match. | |
| Jul 28, 2017 at 1:42 | comment | added | Michael R. Chernick | This is not correct. The correlation is proportional to the slope and if the slope is negative so is the corrrealtion. | |
| Jul 27, 2017 at 23:19 | comment | added | Yannis Vassiliadis | It is not independent. Say you regress $y$ on $x_1$ and $x_2$, and you get significant coefficients $\hat{\beta_1}$ and $\hat{\beta_2}$. Now repeat by omitting $x_2$. Now you have $\hat{\beta_1'}$, which is equal to $\hat{\beta_1}$ plus some bias. The bias is proportional to the correlation between $x_1$ and $x_2$, so the coefficient is not independent of the other variables (to be more precise, the variables are not independent of each other). In any case, none of these are applicable in a simple linear regression setting, was asked in the original question. | |
| Jul 27, 2017 at 23:09 | vote | accept | user2728024 | ||
| Jul 27, 2017 at 23:06 | comment | added | user2728024 | But the coefficient for a variable should be independent of the other variables, since its the change in outcome with a unit increase in the value of that particular variable. Please correct me if I am wrong. | |
| Jul 27, 2017 at 23:03 | history | edited | Yannis Vassiliadis | CC BY-SA 3.0 |
added 45 characters in body
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| Jul 27, 2017 at 23:03 | vote | accept | user2728024 | ||
| Jul 27, 2017 at 23:09 | |||||
| Jul 27, 2017 at 23:02 | comment | added | Yannis Vassiliadis | When you said simple linear regression, I assumed you meant with only one independent variable. In that case, it should always match. If it's multiple independent variables, then no, it really doesn't have to match. A correlation is a measure of the linear relationship between 2 variables, while a multiple regression is a measure of the linear relationship between $y$ and multiple $x$s. | |
| Jul 27, 2017 at 22:56 | comment | added | user2728024 | If it's not matching, then what could be the reason? Can collinearity couse the issue? | |
| Jul 27, 2017 at 22:42 | history | answered | Yannis Vassiliadis | CC BY-SA 3.0 |