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Revision as of 12:19, 18 December 2013

Welcome to the explain xkcd wiki!
We have an explanation for all 1 xkcd comics, and only 20 (1%) are incomplete. Help us finish them!

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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.

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. Different civilizations have recognized different constellations (the modern IAU, for example, lists 88 "official" constellations), and one could create their own 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.

"Rexthor the Dog bearer" seems to be a spoof on Thor, a Norse god who wields a hammer. By replacing his hammer with a dog and adding "Rex" (an archetypal dog name), Randall creates a comical, dog-bearing version of Thor.

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

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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