Timeline for In bivariate linear regression is there a direct relationship between $n$, $r^2$ and coefficient error?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 6, 2013 at 12:37 | vote | accept | Sideshow Bob | ||
| Sep 6, 2013 at 11:52 | comment | added | Nick Cox | I can't see what you are doing wrong. If you can post your data, we can check. Otherwise see my answer. | |
| Sep 6, 2013 at 11:49 | answer | added | Nick Cox | timeline score: 3 | |
| Sep 6, 2013 at 11:29 | comment | added | Sideshow Bob | Just tried this - and it's not working for me - please see my edit | |
| Sep 6, 2013 at 11:28 | history | edited | Sideshow Bob | CC BY-SA 3.0 |
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| Sep 6, 2013 at 11:18 | comment | added | Nick Cox | No; as already pointed out correlation is $r$ and so $r^2$ is different in general (except for $r$ of 0 and 1). And no; the slope has nothing to do with significance. This should be easy to see in your favourite software. Standardise variables, do a regression, look at the correlation, look at the slope. Square the correlation. | |
| Sep 6, 2013 at 11:08 | comment | added | Sideshow Bob | Ok so you are saying it's not possible, with standardized data, to have large $\beta$ and small $r^2$, because they are both the same thing - a measure of effect size. $\sigma_\beta$ meanwhile tells me the significance. Thanks btw, learning a few things here :) | |
| Sep 6, 2013 at 10:53 | comment | added | Nick Cox | Your question is puzzling. If the predictor in bivariate regression has been standardised, then its coefficient equals the correlation: this is in essence an inevitable consequence. If not, then not in general. The way to think of this is in terms of units of measurement or dimensional analysis. A correlation, and hence its square, has no units, but a regression coefficient has units (units of y)/(units of x). Standardising washes out both units and leaves you with dimensionless numbers. | |
| Sep 6, 2013 at 10:47 | comment | added | Nick Cox | No; multivariate regression means a multiple response (target or outcome or dependent variable). Having multiple predictors (independent variables) does not itself make a regression multivariate. | |
| Sep 6, 2013 at 10:46 | history | edited | Sideshow Bob | CC BY-SA 3.0 |
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| Sep 6, 2013 at 10:45 | comment | added | Sideshow Bob | Yes. (My bad on $r^2$ but isn't multiple regression the same as multivariate regression?) | |
| Sep 6, 2013 at 10:35 | comment | added | Scortchi♦ | Do you mean "coefficient of determination" for "correlation", & "multiple regression" for "multivariate regression"? | |
| Sep 6, 2013 at 10:18 | history | asked | Sideshow Bob | CC BY-SA 3.0 |