Timeline for Effect of switching response and explanatory variable in simple linear regression
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2015 at 20:11 | vote | accept | Greg Aponte | ||
| Mar 13, 2015 at 20:12 | |||||
| Jan 8, 2012 at 12:55 | comment | added | Elvis | @cardinal Many thanks for all these comments, I hope to have time in the next few weeks to go into all this in depth | |
| Jan 8, 2012 at 12:22 | comment | added | chl | @cardinal I should have been more careful when reading the Wikipedia entry... For future reference, here is a picture taken from Biostatistical Design and Analysis Using R, by M. Logan (Wiley, 2010; Fig. 8.4, p. 174), which summarizes the different approaches, much like Elvis's nice illustrations. | |
| Jan 4, 2012 at 13:43 | comment | added | cardinal | @chl: (+1) Yes, I believe you are right and the Wikipedia page on total least squares lists several other names for the same procedure, not all of which I am familiar with. It appears to go back to at least R. Frisch, Statistical confluence analysis by means of complete regression systems, Universitetets Økonomiske Instituut, 1934 where it was called diagonal regression. | |
| Jan 4, 2012 at 10:32 | comment | added | chl | @cardinal Very interesting comments! (+1) I believe major axis (minimizing perpendicular distances between reg. line and all the points, à la PCA) or reduced major axis regression, or type II regression as exemplified in the lmodel2 R package by P Legendre, are also relevant here since those techniques are used when it's hard to tell what role (response or predictor) plays each variable or when we want to account for measurement errors. | |
| Jan 3, 2012 at 23:41 | comment | added | cardinal | (cont.) (2) Viewed this way, it is easy to see that this "least rectangles regression" is equivalent to a form of orthogonal (or total) least squares and, thus, (3) A special case of Deming regression on the centered, rescaled vectors taking $\delta = 1$. Orthogonal least squares can be considered as "least-circles regression". | |
| Jan 3, 2012 at 23:39 | comment | added | cardinal | Some notes: (1) Unless I am mistaken, it seems that the "least rectangles regression" is equivalent to the solution obtained from taking the first principal component on the matrix $\mathbf X = (\mathbf y, \mathbf x)$ after centering and rescaling to have unit variance and then backsubstituting. (cont.) | |
| Jan 3, 2012 at 22:03 | comment | added | Elvis | @whuber I think all statisticians love pictures, at least all applied statisticians :) Thank for the direction to this post, your answer is pretty cool I’ve never thought of that. I wonder if I would dare to use it in teaching, my students might be a little unsettled by this kind of argumentation. | |
| Jan 3, 2012 at 21:52 | comment | added | whuber♦ | +1 I love pictures. I never heard of "least rectangles regression," but it is strongly reminiscent of another post which (at least visually) connects it with the correlation coefficient. | |
| Jan 3, 2012 at 21:48 | history | edited | Elvis | CC BY-SA 3.0 |
+ least rectangles
|
| Jan 3, 2012 at 21:03 | history | answered | Elvis | CC BY-SA 3.0 |