https://www.explainxkcd.com/wiki/index.php?action=history&feed=atom&title=1725%3A_Linear_Regression 2026-05-22T16:34:31Z Revision history for this page on the wiki MediaWiki 1.30.0 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=375821&oldid=prev 2025-04-30T18:25:41Z

<p>added <a href="/wiki/index.php/Category:Comics_with_red_annotations" title="Category:Comics with red annotations">Category:Comics with red annotations</a> using <a href="http://commons.wikimedia.org/wiki/Help:Gadget-HotCat" class="extiw" title="commons:Help:Gadget-HotCat">HotCat</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 18:25, 30 April 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Animals]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Animals]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Dogs]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Dogs]]</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Comics with red annotations]]</ins></div></td></tr> </table>

FaviFake https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=337659&oldid=prev 2024-03-18T23:54:19Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 23:54, 18 March 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Line 16:</td> <td colspan="2" class="diff-lineno">Line 16:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-<del class="diffchange diffchange-inline">derivef </del>constellation names have both a proper name and an epithet (for example, &quot;Orion, the Hunter&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs &lt;i&gt;Tyrannosaurus rex&lt;/i&gt;), adds to the humor.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-<ins class="diffchange diffchange-inline">derived </ins>constellation names have both a proper name and an epithet (for example, &quot;Orion, the Hunter&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs &lt;i&gt;Tyrannosaurus rex&lt;/i&gt;), adds to the humor.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td></tr> </table>

172.71.158.34 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=336630&oldid=prev 2024-03-05T13:47:49Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 13:47, 5 March 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</td> <td colspan="2" class="diff-lineno">Line 10:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A constellation is pattern created by linking the apparent positions of stars as seen in the sky from Earth. (Astronomers, in technical contexts, usually refer to these as {{w|Asterism_(astronomy)|asterisms}}, reserving &quot;{{w|Constellation_(astronomy)|constellations}}&quot; for the 88 regions into which the sky is divided, each named for the most prominent asterism it contains, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers.) Different civilizations have recognized different constellations, and one could create their own constellations by connecting assorted points, the way Randall connected points in his plot to make &quot;Rexthor.&quot;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A constellation is <ins class="diffchange diffchange-inline">a </ins>pattern created by linking the apparent positions of stars as seen in the sky from Earth. (Astronomers, in technical contexts, usually refer to these as {{w|Asterism_(astronomy)|asterisms}}, reserving &quot;{{w|Constellation_(astronomy)|constellations}}&quot; for the 88 regions into which the sky is divided, each named for the most prominent asterism it contains, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers.) Different civilizations have recognized different constellations, and one could create their own constellations by connecting assorted points, the way Randall connected points in his plot to make &quot;Rexthor.&quot;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr> </table>

172.70.115.132 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=314106&oldid=prev 2023-05-25T00:38:27Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 00:38, 25 May 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Line 16:</td> <td colspan="2" class="diff-lineno">Line 16:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-derivef constellation names have both a proper name and an epithet (for example, &quot;Orion, the Hunter&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs <del class="diffchange diffchange-inline">*</del>Tyrannosaurus rex<del class="diffchange diffchange-inline">*</del>), adds to the humor.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-derivef constellation names have both a proper name and an epithet (for example, &quot;Orion, the Hunter&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs <ins class="diffchange diffchange-inline">&lt;i&gt;</ins>Tyrannosaurus rex<ins class="diffchange diffchange-inline">&lt;/i&gt;</ins>), adds to the humor.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td></tr> </table>

172.71.26.254 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=314105&oldid=prev 2023-05-25T00:37:30Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 00:37, 25 May 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Line 16:</td> <td colspan="2" class="diff-lineno">Line 16:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-derivef constellation names have both a proper name and an epithet (for example, &quot;Orion, the <del class="diffchange diffchange-inline">hunter</del>&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs <del class="diffchange diffchange-inline">T-</del>rex), adds to the humor.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; spoofs the fact that numerous Greek-derivef constellation names have both a proper name and an epithet (for example, &quot;Orion, the <ins class="diffchange diffchange-inline">Hunter</ins>&quot;). The fact that &quot;Rex&quot; is an archetypal dog name (but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs <ins class="diffchange diffchange-inline">*Tyrannosaurus </ins>rex<ins class="diffchange diffchange-inline">*</ins>), adds to the humor.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td></tr> </table>

172.71.26.254 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=314104&oldid=prev 2023-05-25T00:36:35Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 00:36, 25 May 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Line 16:</td> <td colspan="2" class="diff-lineno">Line 16:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; <del class="diffchange diffchange-inline">could be </del>a <del class="diffchange diffchange-inline">spoof on {{w|Thor}}</del>, <del class="diffchange diffchange-inline">a Norse god who wields a hammer</del>. <del class="diffchange diffchange-inline">By replacing his hammer with a dog and adding </del>&quot;Rex&quot; <del class="diffchange diffchange-inline">(</del>an archetypal dog name<del class="diffchange diffchange-inline">, </del>but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs T-rex), <del class="diffchange diffchange-inline">Randall may have created a comical, dog-bearing version of Thor</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; <ins class="diffchange diffchange-inline">spoofs the fact that numerous Greek-derivef constellation names have both </ins>a <ins class="diffchange diffchange-inline">proper name and an epithet (for example, &quot;Orion</ins>, <ins class="diffchange diffchange-inline">the hunter&quot;)</ins>. <ins class="diffchange diffchange-inline">The fact that </ins>&quot;Rex&quot; <ins class="diffchange diffchange-inline">is </ins>an archetypal dog name <ins class="diffchange diffchange-inline">(</ins>but also meaning {{w|Rex (title)|king}} as in king of the dinosaurs T-rex), <ins class="diffchange diffchange-inline">adds to the humor</ins>.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</div></td></tr> </table>

172.71.27.2 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=314102&oldid=prev 2023-05-25T00:32:20Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 00:32, 25 May 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</td> <td colspan="2" class="diff-lineno">Line 10:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A <del class="diffchange diffchange-inline">{{w|</del>constellation<del class="diffchange diffchange-inline">}} is the region of sky containing an {{w|Asterism_(astronomy)|asterism}}; an asterism </del>is <del class="diffchange diffchange-inline">a </del>pattern created by linking the apparent positions of stars as seen in the sky from Earth. <del class="diffchange diffchange-inline">Strictly speaking</del>, <del class="diffchange diffchange-inline">Randall's </del>&quot;<del class="diffchange diffchange-inline">Rexthor</del>&quot; is <del class="diffchange diffchange-inline">an </del>asterism, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers. Different civilizations have recognized different constellations <del class="diffchange diffchange-inline">(the modern IAU, for example, lists 88 &quot;official&quot; constellations)</del>, and one could create their own constellations by connecting assorted points.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A constellation is pattern created by linking the apparent positions of stars as seen in the sky from Earth. <ins class="diffchange diffchange-inline">(Astronomers, in technical contexts, usually refer to these as {{w|Asterism_(astronomy)|asterisms}}</ins>, <ins class="diffchange diffchange-inline">reserving </ins>&quot;<ins class="diffchange diffchange-inline">{{w|Constellation_(astronomy)|constellations}}</ins>&quot; <ins class="diffchange diffchange-inline">for the 88 regions into which the sky </ins>is <ins class="diffchange diffchange-inline">divided, each named for the most prominent </ins>asterism <ins class="diffchange diffchange-inline">it contains</ins>, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers.<ins class="diffchange diffchange-inline">) </ins>Different civilizations have recognized different constellations, and one could create their own constellations by connecting assorted points<ins class="diffchange diffchange-inline">, the way Randall connected points in his plot to make &quot;Rexthor</ins>.<ins class="diffchange diffchange-inline">&quot;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr> </table>

172.71.26.254 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=269872&oldid=prev 2022-05-16T23:29:03Z

<p>Reverted edits by <a href="/wiki/index.php/Special:Contributions/The_author_of_xkcd" title="Special:Contributions/The author of xkcd">The author of xkcd</a> (<a href="/wiki/index.php?title=User_talk:The_author_of_xkcd&amp;action=edit&amp;redlink=1" class="new" title="User talk:The author of xkcd (page does not exist)">talk</a>) to last revision by <a href="/wiki/index.php/User:Jacky720" title="User:Jacky720">Jacky720</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 23:29, 16 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{comic</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| number&#160; &#160; = 1725</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| date&#160; &#160; &#160; = August 26, 2016</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| title&#160; &#160; = Linear Regression</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| image&#160; &#160; = linear_regression.png</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| titletext = The 95% confidence interval suggests Rexthor's dog could also be a cat, or possibly a teapot.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">}}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Explanation==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">A {{w|constellation}} is the region of sky containing an {{w|Asterism_(astronomy)|asterism}}; an asterism is a pattern created by linking the apparent positions of stars as seen in the sky from Earth. Strictly speaking, Randall's &quot;Rexthor&quot; is an asterism, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers. Different civilizations have recognized different constellations (the modern IAU, for example, lists 88 &quot;official&quot; constellations), and one could create their own constellations by connecting assorted points.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">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.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; could be a spoof on {{w|Thor}}, a Norse god who wields a hammer. By replacing his hammer with a dog and adding &quot;Rex&quot; (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.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The teapot may be a reference to {{w|Russell's_teapot|Russell's teapot}}, or possibly to the {{w|Sagittarius_(constellation)#Visualizations|&quot;teapot&quot; asterism in the constellation Sagittarius.}} Alternatively it is just because the &quot;dog&quot; 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 suggestions are just another example on how humans see patterns also where there are none to find, like those of {{w|pareidolia}} mentioned in [[1551: Pluto]].</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Transcript==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[Two square panels show identical sets of scattered black dots, with only the red additions being different.]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[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. A red text is below the dots:]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:&lt;span style=&quot;color:red&quot;&gt;R&lt;sup&gt;2&lt;/sup&gt;=0.06&lt;/span&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[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. A red text is below the dots:]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:&lt;span style=&quot;color:red&quot;&gt;Rexthor, the Dog-Bearer&lt;/span&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[A caption is below and spanning both panels:] </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">: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.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{comic discussion}}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Comics with color]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Scatter plots]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Math]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Statistics]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Astronomy]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Animals]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Dogs]]</ins></div></td></tr> </table>

Davidy22 https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=269559&oldid=prev 2022-05-16T22:57:13Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 22:57, 16 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{comic</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| number&#160; &#160; = 1725</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| date&#160; &#160; &#160; = August 26, 2016</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| title&#160; &#160; = Linear Regression</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| image&#160; &#160; = linear_regression.png</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| titletext = The 95% confidence interval suggests Rexthor's dog could also be a cat, or possibly a teapot.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">}}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Explanation==</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{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 &quot;{{w|least squares|best-fit}}&quot; line through a {{w|scatter plot}} of the datasets, together with a {{w|coefficient of determination}}, usually denoted ''r''&lt;sup&gt;2&lt;/sup&gt; or ''R''&lt;sup&gt;2&lt;/sup&gt;. When only two variables are included in the regression, ''R''&lt;sup&gt;2&lt;/sup&gt; is merely the square of the correlation between the two variables. ''R''&lt;sup&gt;2&lt;/sup&gt; 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.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">A {{w|constellation}} is the region of sky containing an {{w|Asterism_(astronomy)|asterism}}; an asterism is a pattern created by linking the apparent positions of stars as seen in the sky from Earth. Strictly speaking, Randall's &quot;Rexthor&quot; is an asterism, although &quot;constellation&quot; is used informally in place of &quot;asterism&quot; by even seasoned astronomers. Different civilizations have recognized different constellations (the modern IAU, for example, lists 88 &quot;official&quot; constellations), and one could create their own constellations by connecting assorted points.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">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.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">The comic is somewhat misleading, since the data in the graph actually has an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.02, only a third of what Randall claims.&#160; An example of published research with an ''R''&lt;sup&gt;2&lt;/sup&gt; of 0.06 where the association in the graph is noticeable (if not strong) can be found [http://www.i-jmr.org/2012/1/e1/ here] (figure 2 has ''r'' = 0.25 which corresponds to ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06). In addition, it is hard to see the association in the comic's graph because relatively few points are plotted. In a data set with 1000 observations and ''R''&lt;sup&gt;2&lt;/sup&gt; = 0.06, any association between the two variables would be quite clear.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">The lines connecting the stars in this &quot;constellation&quot; create a crude illustration of a person with an outstretched arm holding up a dog, which could be a reference to the film {{w|Life is Beautiful}} where a waiter carries a dog on his tray without realizing. The name &quot;Rexthor the Dog Bearer&quot; could be a spoof on {{w|Thor}}, a Norse god who wields a hammer. By replacing his hammer with a dog and adding &quot;Rex&quot; (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.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">The 95% {{w|confidence interval}} in statistics is such a range of an estimate, that it is expected to contain the real value (the estimated population parameter) 95% of the time. 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 drawings, expected to contain the correct drawing in 95% of samples where it is calculated. According to the title text, the interval in this particular sample also includes a cat and a teapot, so we can only make extremely vague statements in order to maintain 95% confidence.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">The teapot may be a reference to {{w|Russell's_teapot|Russell's teapot}}, or possibly to the {{w|Sagittarius_(constellation)#Visualizations|&quot;teapot&quot; asterism in the constellation Sagittarius.}} Alternatively it is just because the &quot;dog&quot; 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 suggestions are just another example on how humans see patterns also where there are none to find, like those of {{w|pareidolia}} mentioned in [[1551: Pluto]].</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Transcript==</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[Two square panels show identical sets of scattered black dots, with only the red additions being different.]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[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. A red text is below the dots:]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:&lt;span style=&quot;color:red&quot;&gt;R&lt;sup&gt;2&lt;/sup&gt;=0.06&lt;/span&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[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. A red text is below the dots:]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:&lt;span style=&quot;color:red&quot;&gt;Rexthor, the Dog-Bearer&lt;/span&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[A caption is below and spanning both panels:] </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">: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.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{comic discussion}}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Comics with color]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Scatter plots]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Math]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Statistics]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Astronomy]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Animals]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Dogs]]</del></div></td><td colspan="2">&#160;</td></tr> </table>

The author of xkcd https://www.explainxkcd.com/wiki/index.php?title=1725:_Linear_Regression&diff=262762&oldid=prev 2022-05-04T23:49:22Z

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Jacky720