Editing Talk:2701: Change in Slope

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I am an occasional data scientist, and I can confirm this is why we have monitor stands that tilt. [[Special:Contributions/172.71.94.50|172.71.94.50]] 16:33, 21 November 2022 (UTC)

The third e in "neeed" in the title text seems to be a typo
[[User:Victor|Victor]] ([[User talk:Victor|talk]]) 16:41, 21 November 2022 (UTC)
:I think Randall may have added it to represent that the speaker prolongs the "e" sound for emphasis, although that's usually done with 4-5 e's. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 16:53, 21 November 2022 (UTC)
::I had to double-check this, myself (presumed the 'Bot created the lage faithfully, but went straight to source to see if I needed to find a vandalism post to revert). May need a comment (to prevent hypercorrection, if not to note the implied emphisis) and certainly will if it turns out to be a typo and gets corrected (for which I'm sure a future checker will discover Randall's revisiting, but then worth a note to that effect). [[Special:Contributions/172.70.90.2|172.70.90.2]] 17:42, 21 November 2022 (UTC)
Bender Bot was one of the main characters in Futurama. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 16:54, 21 November 2022 (UTC)
:Just donning my unnecessary pedantry hat for a moment: his name is Bender Bending Rodriguez --[[User:192·168·0·1|192·168·0·1]] ([[User talk:192·168·0·1|talk]]) 23:02, 21 November 2022 (UTC)

A couple(?) of authors used the word(s) "(point of) inflection", which is {{w|Inflection point|not really suitable}} for a join between two straight segments. Was tempted to talk about "discontinuity", but that really only applies to the meta-slope (derivatives, to one degree or other) where it suddenly jumps (at a point), or the derivative's derivative has jumps (as it enters and leaves the smoothly linking curve). Hope it works well enough how I left it, though. [[Special:Contributions/162.158.142.176|162.158.142.176]] 21:28, 21 November 2022 (UTC)

For anyone curious, I used an image editor to turn the entire comic sideways and [https://cdn.discordapp.com/attachments/525939879805190154/1044395695525875712/xkcd_sideways.png it actually does seem to work,] to some degree anyway. [[User:SuperSupermario24|<span style="color: #b000ff;">SSM24</span>]] 23:37, 21 November 2022 (UTC)
:Added; thanks! [[Special:Contributions/172.71.158.230|172.71.158.230]] 00:14, 22 November 2022 (UTC)

: If you don't mind sharing: which program did you use? Did you tweak things like relative distance / camera FOV, to effectively select a specific point in the continuum that makes up the {{w|Dolly Zoom}} effect, and at the limit on one end results in {{w|orthographic projection}}? (Edit 10 minutes later: a better article to look at is {{w|Perspective distortion (photography)}}) Or did you just leave it at whatever the default is? Can you recreate the image with the two extremes, and share them? And lastly - can you upload the image (and potentially the new images) to the wiki directly, so they can be embedded in the page? Thanks! --[[User:NeatNit|NeatNit]] ([[User talk:NeatNit|talk]]) 17:21, 22 November 2022 (UTC)

This one shows the beauty of Explainxkcd: people reading the explanation are likely to learn accessible methods of substantial practical utility. [[Special:Contributions/162.158.166.173|162.158.166.173]] 00:38, 22 November 2022 (UTC)

Hey, if it works for picking out lumber at Lowe’s, why not for graphs, too? - MadMarie
:There was an old bit of explanation that related it to examining physical objects (for dent/bend-removal in metalwork, I think it was) that got wiped out by a later edit. Though I'm considering my own version, now generalised to cover your experience, as it seems quite relevant/analogous to me. [[Special:Contributions/172.70.90.2|172.70.90.2]] 14:37, 22 November 2022 (UTC)

Whoever wrote the 1st explanation needs to go touch grass and learn how real people talk, pissed me off so much I just effectively rewrote the whole thing from scratch [[Special:Contributions/172.71.202.46|172.71.202.46]] 06:34, 22 November 2022 (UTC)
:Intrigued, looking at the first explanation (give or take that person's initial small errors/omissions) I personally find it more to the point than what it has become. Not to say the complete rewrite was wrong, but it got it not that much closer to the mythical perfection. IMO. [[Special:Contributions/141.101.76.169|141.101.76.169]] 20:29, 22 November 2022 (UTC)

Going in a different direction than "this is silly" - if we ignore the "viewing point/parallax" issue, doing a change of basis like this is similar to linear methods like [SVD https://hadrienj.github.io/assets/images/ch12_svd/ch11_SVD_geometry.png] & [https://jakevdp.github.io/PythonDataScienceHandbook/figures/05.09-PCA-rotation.png PCA], and considering the graph as a mappingg in a "higher dimension" is similar to the "kernel trick" popularized by [https://i.ytimg.com/vi/wqSTBCguVyU/maxresdefault.jpg Support] [https://miro.medium.com/max/4800/1*gtF6KeL7b9zNHd7pXtC1Nw.png Vector] [https://dinhanhthi.com/img/post/ML/support-vector-machine/svm-3.jpg Machines] 11:31, 22 November 2022 (UTC)

== Raw Data ==

I love this cartoon. This is definitely something that was relevant in my work! 

At my old job I had some commercial or public-domain software for extracting the raw data behind a scatter plot. If anyone has something like that handy, I would love to see someone extract the data behind the graph on the left, so that we can:
   1. Apply the affine transformation which generates the image on the right with the tilted paper.
   2. Apply the statistical tests which Randall Munroe is alluding to.

:Knock yourself out:
{{cot|Digitized data courtesy https://apps.automeris.io/wpd/}}
<pre>
0.000000, 0.015366
0.001887, 0.000000
0.002830, 0.041488
0.024528, 0.060695
0.033019, 0.014597
0.038679, 0.009988
0.044340, 0.072220
0.047170, 0.055317
0.050000, 0.072220
0.064858, 0.092964
0.070215, 0.117001
0.088207, 0.088354
0.091037, 0.122928
0.091037, 0.109099
0.100943, 0.140215
0.103773, 0.165338
0.106603, 0.178246
0.128891, 0.171331
0.147641, 0.196685
0.146226, 0.187465
0.162264, 0.215124
0.180188, 0.264910
0.182452, 0.218812
0.202830, 0.275052
0.204245, 0.261222
0.208490, 0.272747
0.217923, 0.293491
0.227358, 0.267369
0.230322, 0.234880
0.241744, 0.311930
0.256603, 0.344199
0.262263, 0.338930
0.299056, 0.376467
0.308254, 0.420261
0.313206, 0.417956
0.336791, 0.456371
0.344338, 0.433322
0.355659, 0.456371
0.367923, 0.496323
0.374055, 0.503237
0.388206, 0.503237
0.389621, 0.514762
0.409433, 0.533201
0.412263, 0.525518
0.415093, 0.540884
0.432074, 0.555328
0.446225, 0.599275
0.443395, 0.588519
0.449526, 0.537811
0.449055, 0.588519
0.468866, 0.609263
0.487263, 0.627702
0.490093, 0.636922
0.516979, 0.670727
0.523448, 0.697179
0.519809, 0.662276
0.548111, 0.697618
0.551413, 0.740642
0.550941, 0.689935
0.565092, 0.726813
0.572168, 0.724508
0.576413, 0.772911
0.582073, 0.772911
0.582073, 0.763691
0.601177, 0.785588
0.604714, 0.791350
0.625335, 0.775545
0.643394, 0.817473
0.664620, 0.855119
0.688812, 0.871693
0.688003, 0.821643
0.710374, 0.925035
0.707544, 0.806716
0.715091, 0.888156
0.717921, 0.880473
0.724148, 0.976665
0.749054, 0.927010
0.757544, 0.961913
0.763204, 0.959608
0.783016, 0.983426
0.781601, 0.971133
0.797166, 1.028756
0.802827, 1.031060
0.805657, 0.999560
0.821223, 0.966523
0.822638, 0.957304
0.842449, 1.038744
0.843864, 1.028756
0.859431, 1.049500
0.865091, 1.058719
0.876411, 1.077159
0.882072, 1.086378
0.889147, 1.077159
0.901883, 1.024914
0.904714, 1.017231
0.908605, 1.100208
0.913204, 1.107122
0.936553, 1.130171
0.937261, 1.116342
0.967447, 1.159370
0.969806, 1.205310
0.978301, 1.104817
0.983956, 1.101525
1.000000, 1.167820
</pre>
{{cob}}
:104 points. [[Special:Contributions/172.71.154.39|172.71.154.39]] 19:17, 22 November 2022 (UTC)
::: I only count 69 distinct dots, although a handful look like they might be merged pairs. What's up with that? [[Special:Contributions/172.70.210.48|172.70.210.48]] 04:54, 26 November 2022 (UTC)

:: Can someone please check my work https://colab.research.google.com/drive/1c_7Qj3S1VXtL-AckfSfHCd4ofGYYDYH5 and tell me if I'm doing it right? I'm pretty sure I don't really know what I'm doing. I kind of cargo cult-coded the Savitzky-Golay filter stuff linked from the explanation and have zero understanding of what's actually going on. [[Special:Contributions/172.70.211.126|172.70.211.126]] 21:58, 22 November 2022 (UTC)

:: Here's how Randall seems to be suggesting to do it, based on the light gray figures: [superceded] -- Can someone please help fix the residuals on the second plot? [[Special:Contributions/172.71.154.158|172.71.154.158]] 01:18, 23 November 2022 (UTC)
::: I fixed the residuals and added an inset confidence interval comparisons for the two slopes, split by both their maximum difference and by the maximum sum of the r<sup>2</sup> values: https://colab.research.google.com/drive/1apKDIN5FE32mtGiQew5cE6wK6m6eM_Fr It's not clear from the gray text which method Randall is suggesting. [[Special:Contributions/172.70.211.126|172.70.211.126]] 22:07, 24 November 2022 (UTC)
:::: I added this to the end of the Colab notebook:

 # Later in the Explainxkcd explanation, a "Significance of the Difference between Two Slopes Calculator"
 # at https://www.danielsoper.com/statcalc/calculator.aspx?id=103 is recommended, so ... we get:
 
 # split by maximum slope difference:  (as shown in green and red)
 #   t-Value:               5.52246856
 #   Degrees of freedom:  100
 #   Probability:           0.00000027 (significant as < 0.05)
 
 # split by maximum sum of r²s:
 #   t-Value:               6.25478825
 #   Degrees of freedom:  100
 #   Probability:           0.00000001 (also very significant)
 
 # So, while the latter might technically be  about 27 times more likely, both represent undoutably
 # different linear fits. Perhaps someone can ask Randall which he was suggesting, if indeed either?

:::: What's the most reliable way to ask Randall this? Twitter? Email? Google Chat? [[Special:Contributions/172.71.158.91|172.71.158.91]] 23:08, 24 November 2022 (UTC)
::::: Why don't you generate a series of mildly noisy datasets of two slightly different but random lines each and see which method gets closest to the generating parameters? Also, please put more blank lines in your code, and consider right-aligning the comments. [[Special:Contributions/172.70.211.146|172.70.211.146]] 01:56, 26 November 2022 (UTC)

What's funny is people are doing a lot of statistics and computer magic when you can just tilt your screen like the comic says and get the same effect :P {{unsigned ip|172.70.54.52|16:14, 25 November 2022}}
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