Editing 1725: Linear Regression
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{{w|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 "{{w|least squares|best-fit}}" line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''<sup>2</sup> or ''R''<sup>2</sup>. When only two variables are included in the regression, ''R''<sup>2</sup> is merely the square of the correlation between the two variables. ''R''<sup>2</sup> 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. | {{w|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 "{{w|least squares|best-fit}}" line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''<sup>2</sup> or ''R''<sup>2</sup>. When only two variables are included in the regression, ''R''<sup>2</sup> is merely the square of the correlation between the two variables. ''R''<sup>2</sup> 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. | ||
− | + | {{w|Asterism_(astronomy)|Asterism}}s are patterns created by linking the apparent positions of stars as seen in the sky from Earth. Strictly, "Rexthor" is an asterism, as a {{w|constellation}} is the region of sky containing the asterism, although "constellation" is used informally in place of "asterism" by even seasoned astronomers. 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. | 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" could be a spoof on {{w|Thor}}, a Norse god who wields a hammer. | |
+ | By replacing his hammer with a dog and adding "Rex" (an archetypal dog name, but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs T-rex), Randall may have created a comical, dog-bearing version of Thor. But could also also just be the dog-king. | ||
− | The | + | The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that the probability of the real value (the estimated population parameter) to lie inside the range is at least 95%. The confidence interval is a standard method to provide evaluation of the estimation error in statistics. On the right panel the resulting estimate seems to be a drawing, so the 95% confidence interval would be a set of all drawings derived from the sample such that the probability of the right drawing to be among them is at least 95%. According to the title text among these drawings you can find a cat and a teapot as well, so we can't be 95% confident that a dog exists in the data. |
− | + | The teapot may be a reference to {{w|Russell's_teapot|Russell's teapot}}, or possibly to the {{w|Sagittarius_(constellation)#Visualizations|"teapot" asterism in the constellation Sagittarius.}} Alternatively is is just because the "dog" actually looks more like a teapot than a dog, and Randall noticed this and added it in the title text. In the latter case the two first suggestion is just another example on how humans see patterns also where there are none to find, like those of {{w|pareidolia}} mentioned in [[1551: Pluto]]. | |
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− | The teapot may be a reference to {{w|Russell's_teapot|Russell's teapot}}, or possibly to the {{w|Sagittarius_(constellation)#Visualizations|"teapot" asterism in the constellation Sagittarius.}} Alternatively | ||
==Transcript== | ==Transcript== | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Scatter plots]] | [[Category:Scatter plots]] | ||
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[[Category:Astronomy]] | [[Category:Astronomy]] | ||
[[Category:Animals]] | [[Category:Animals]] | ||
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