Timeline for Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2021 at 13:49 | comment | added | ttnphns | This is a great answer +1. Just to in form a reader that similar pictures can be found in stats.stackexchange.com/a/124892/3277 | |
| Apr 12, 2021 at 3:38 | comment | added | Silverfish | @anonuser01 You'd get the same effect if you include an independent variable whose value for each observation is 2, or $\pi$. Either way, the vector $\mathbf{1}_n$ lies in the column space of the design matrix. Note that if you did then include an intercept term as well, you get perfect multicollinearity since there's a linear dependence between the intercept column and variable-that-just-so-happens-to-be-constant column of the design matrix. | |
| Jul 10, 2020 at 22:45 | comment | added | 24n8 | So, I have a question. Here, you stated explicitly that $\boldsymbol{1}_n$ is due to the intercept term. But what if, say, we remove the intercept, and by some coincidence, we have such that all samples's p-th feature is 1. In that case, you would have the $\boldsymbol{1}_n$ in the column space. It seems this analysis would still hold even thought here is no intercept term? | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
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| Apr 6, 2016 at 20:13 | comment | added | ttnphns | +1. Note that the figure of your answer, with "column space X", Y, Ypred as vectors etc. is what is known in multivariate statistics as "(reduced) subject space representation" (see, with further links where I've used it). | |
| Dec 25, 2014 at 15:13 | comment | added | amoeba | +1 Very nice write-up and figure. I am surprised that it only has my single lonely upvote. | |
| Dec 25, 2014 at 1:39 | history | edited | Silverfish | CC BY-SA 3.0 |
fill some details in
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| Dec 23, 2014 at 14:06 | history | answered | Silverfish | CC BY-SA 3.0 |