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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