1725: Linear Regression

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Linear Regression
The 95% confidence interval suggests Rexthor's dog could also be a cat, or possibly a teapot.
Title text: The 95% confidence interval suggests Rexthor's dog could also be a cat, or possibly a teapot.

[edit] Explanation

Linear regression is a method for modeling the relationship between multiple variables. In the simplest case, it can be used for two variables wherein the model determines a "best-fit" line through a scatter plot of the datasets, together with a coefficient of determination, usually denoted r2 or R2. When only two variables are included in the regression, R2 is merely the square of the correlation between the two variables. R2 is a number between 0 and 1 that indicates how well one variable can be used to predict the value of another. A value of 1 means perfect correlation, while a value close to 0 indicates a weak relationship between the variables.

Constellations are patterns created by linking the apparent positions of stars. One could create fake constellations by connecting assorted points.

In this comic, a set of data has had linear regression and some form of statistical analysis applied to it, indicating that there is low correlation between the two. The data points are so widely scattered that (as noted in the comic) it is easier to connect the data points in a constellation-like pattern than it is to determine whether the correlation is negative or positive (without looking at the trendline, of course). Because of this, Randall suggests we should be suspicious of any conclusions drawn from this data.

The mention of a teapot may be a reference to Russell's teapot.

[edit] Transcript

Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.

[A two-panel comic with a caption underneath drawn in a combination of black and red. The two panels show an identical square of scattered black dots, with only the red additions being different. A black caption is written below, spanning both panels.]

[The left panel shows a slightly rising red line drawn through the middle of the panel, passing near a few dots but not obviously related to most of them]

R2=0.06

[The right panel shows many of the dots connected by red lines to form a stick figure of a man resembling the constellation Orion, with the hand on the reader's right raised and holding an object.]

Rexthor, the Dog-Bearer

[The caption below is black and applies to both panels.]

I don't trust linear regressions when it's harder to guess the direction of the correlation from the scatter plot than to find new constellations on it.


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Discussion

[edit] Teapot

It also seems likely that the teapot refers to the Utah Teapot (https://en.wikipedia.org/wiki/Utah_teapot). It was one of the first complex 3D objects defined for CGI rendering, and has seen countless uses since. Notably in the Pipes screensaver, and early SIGGRAPH papers where it was rendered along side the 5 platonic solids as if it belonged with them. Dkfenger (talk) 17:10, 26 August 2016 (UTC)

I'm not sure I follow. How do you reach that conclusion? Given that the concept of constellations (and thus stars) is clearly shown in the comic, it seems much more likely to me that he was referring to Russell's Teapot and not to a computer rendering (if there was any reference at all). The fact that that shape could abstractly resemble a teapot may be all that there is to it. :) KieferSkunk (talk) 18:06, 26 August 2016 (UTC)

I think that the teapot is a reference to the constellation Sagittarius. This seems most likely to me as the reference is to a constellation that looks like a teapot despite ostensibly being something else. Sagittarius is a constellation that is supposed to be an archer, but many people see it as a teapot instead. (http://www.space.com/30274-constellation-sagittarius-archer-dipper-teapot.html) Harperska (talk) 19:27, 26 August 2016 (UTC)

Based on what is an R^2 value of 0.06 significant??? I'm removing that. Djbrasier (talk) 20:59, 26 August 2016 (UTC)

Oops, misread it! I read "insignificant" as "significant". Djbrasier (talk) 21:00, 26 August 2016 (UTC)


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