Timeline for Why do the widths of confidence & prediction intervals change across a regression line - shouldn't it be the same with i.i.d?
Current License: CC BY-SA 4.0
13 events
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Nov 3, 2023 at 17:33 | comment | added | feetwet | Great old answer here | |
Feb 3, 2023 at 18:27 | comment | added | rubikscube09 | You are missing the fact that the slope and intercept you're plotting are estimate from data. If you knew the exact value of the slope, then you'd indeed have two parallel lines as your confidence intervals. | |
Feb 3, 2023 at 10:01 | vote | accept | TheFriendlyAsker | ||
Feb 3, 2023 at 9:20 | answer | added | Luca Citi | timeline score: 5 | |
Feb 3, 2023 at 0:39 | comment | added | whuber♦ | A graphical analysis like the one I present at stats.stackexchange.com/a/354256/919 for a more complicated situation will give you immediate intuition: when you slide a line around the scatterplot among the positions that make it a plausible fit, you will see it tends to rotate around a central point (the point of averages) and move up and down just a little bit. The resulting envelope is a pair of hyperbolas. Obtaining a pair of parallel lines, as you seem to intuit, could occur only when the errors are all perfectly positively correlated. | |
Feb 3, 2023 at 0:36 | history | became hot network question | |||
Feb 2, 2023 at 21:00 | history | tweeted | twitter.com/StackStats/status/1621252130915979265 | ||
Feb 2, 2023 at 19:35 | answer | added | Lukas Lohse | timeline score: 11 | |
Feb 2, 2023 at 18:29 | answer | added | Harvey Motulsky | timeline score: 13 | |
Feb 2, 2023 at 17:20 | comment | added | TheFriendlyAsker | Sort of, I'm asking if the distribution obtained from sliding a small segment along x_1 -- centred around the best fit line -- has the same distribution? By "around the best fit line", that is too say that if we were to plot the distributions of the residuals around that black line for both x_1 = a and x_1 = b, then we would see that the blue and yellow conditional pdfs are the same. Sorry I know I'm explaining this poorly | |
Feb 2, 2023 at 16:55 | history | edited | TheFriendlyAsker | CC BY-SA 4.0 |
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Feb 2, 2023 at 16:37 | answer | added | Alexis | timeline score: 4 | |
Feb 2, 2023 at 16:33 | history | asked | TheFriendlyAsker | CC BY-SA 4.0 |