/sci/ - Science & Math

(part 2)

I figured out that Grapher can't compute the r squared value (likely since it can't make a regression) but instead gives med a chi squared. After some fiddling around, I found out that a chi squared value of zero is a perfect fit and anything above zero isn't. R squared goes from 0 to 1, so it's easy to wether or not something is a "good" fit, but with chi squared, there's no limit on how high the value can be.

I tried to do it in excel instead (where I know i can get a r squared value) but the equation for the exponential function is y=a*e^(b*x) instead of the one I know, y=b*a^x. So I would prefer to keep everything in grapher.

TL;DR:

What's the difference between regression and interpolation?

Why do I have to enter values to get the interpolation?

Is there a limit for chi squared? How does it compare to r squared in terms of telling wether or not something is a "good" fit.

I'll bump with science-related infographics btw.

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Some on /sci/ I know some of your guys know even the tiniest amount of this!!

>>5277142
Come on*

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Yeah, I have no idea why you're talking about interpolation.

What level course/class is this? Was your data generated from a function, or is it meant to be experimental and you just want the best fit?

>>5277155
I'm talking about interpolation because Grapher, the program I'm using to plot the data, can't do regression. I'm on second grade in a Danish equivalent of high school or college.

Pic related, it's my data.

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>>5277171
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>>5277181
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>>5277160

Shit. American, here. Does ; precede a decimal?

>>5277186

Here's data set 3:

>>5277186
Just to elaborate:

When talking about data plots, comma is used to seperate to seperate values and semi-colon is used to seperate two values where one of them has one or more decimals.

Personally I always use semi-colons to separate-

Bump

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>>5277200

Why would you make a rule about notation that CHANGES?

>>5277219
I didn't make the assignment. Imo it's stupid as well.

Love the info graphics! Keep em coming bro

>>5277229
I'm running out of good ones (aka the ones I understand or pretend to understand). I DL'd a torrent full of infographics (around 3,4 gigs) ranging from all kinds of topics.

Pic related, it's what the torrent contains.

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Here's the magnet link if some anons want it:

magnet:?xt=urn:btih:474e23740d44f2c13afc42d3ed17e6ed9889c486&dn=5200%2B+Infographics+Hi-Res&
tr=udp%3A%2F%2Ftracker.openbittorrent.com%3A80&tr=udp%3A%2F%2Ftracker.publicbt.com%3A80&tr=u
dp%3A%2F%2Ftracker.istole.it%3A6969&tr=udp%3A%2F%2Ftracker.ccc.de%3A80

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>that'

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I'm out soon.

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I'm out, see ya /sci/

>OP leaving his own thread

Ditt namn är för övrigt Philip Jakobsen.

Slow board.

<3

<span class="quote deadlink">>>5277370[/spoiler]

Herrejävlar vilken onödig grej att skriva.

>>5277373
Wat

>>5277112
Still there OP? I can help.

>>5277391
I'm here yes.

Okay OP I gotta go. I'll just say that interpolation is just getting predicted values from your regression equation.

You have to enter values because it's asking you what values for which you want to predict the response. For example, in your picture, if you have an x value of 2.5, the predicted y value will be just above 10^1. It's the intersection of the x value and the prediction line.

Also, the r-square gives you a value between 0 and 1 relating to goodness of fit (1 being perfect). Chi-square is very different, so don't let the similarity in naming throw you off.

The Chi-square test will ultimately give you a p-value. If the p-value is low (probably <0.05), you have a distribution that is different from your theoretical distribution.

I would recommend not using grapher since it looks horrible for this task.

>>5277440
Thanks anon, really appreciate it.

So I get singularity-related errors if I insert "wrong" values, right? Then why does it work with 1 and 2 for a and b respectively.

And all I really want to do is to back up my claim that data set 1 is the one that's exponential, because it make a straight line in a Lin-log graph paper, hence why I would like the r squared value. So the chi squared value is a not useable in my case then?

Also, p-value?

I'll revive this thread tomorrow (EU time).

Aaaaaand OP is back!!!

>>5278741
Bamp

Bump

Bamp

You're understanding interpolation wrong. Given a dataset, interpolation approximates a function by a polynomial of grade N that passes through every point. Instead of getting what you're supposed to get which is some smooth curves, you're going to get a rollercoaster for each data set.

What I'd guess the assignment want's you to do is look at the points of each set, do a simple "join the dots" and say if it looks like a line, an exponential, or a parabola.

If you really want to get the original function, you have to do least squares using a function base. So if you think it's an exponential you approximate it by a*e^x + b or similar using least squares and get the a and b that make the function pass closest tot he points you gave it, but you have to suppose what kind of function it is beforehand.

Also this may be a really shitty explanation but I'm tired.

>>5279132
Interpolation isn't limited to polynomial grade N. You can make your own like y=b*a^x

>>5279224
That's not interpolation.
I just explained it.

>>5279245
To me it seems like interpolation when judging from the program.

>>5279251
What you show in that software is not interpolation, it's approximation of a function using least square or similar. As you can see, the function you got doesn't quite pass through every point, but it's the one that minimizes the distance between those points to the function you chose.
In actual interpolation, the function you get does pass through every point you give it.
I don't care what the software developer decided to call it due to his lack (or the users?) of mathematical knowledge.

>>5279260
Alright, I think I understand it now. But why do I have to enter values? In the pic I choosed 1 and 2, because those were the first values where I didn't get the "reached a singularity"-error. When I increase the value of a, the line is rotated and the chi-squared value is increased.

My real question is, can I use the interpolation and the chi-squared value to back up my claim that data set 1 is the one with exponential growth, because of the straight line it makes in a lin-log graph paper.

>>5279268
As for the values, I don't know about the software, but I guess it just wants you to choose which data point you're going to use to approximate the function. The +- values are the error margin for the points.
As for the singularity error, I don't know. Maybe it actually is some sort of interpolation/squares hybdrid and you are giving it a non compatible system of data points (so, a function that would pass through 2 could never hit the 3rd one unless it's on the same function graph)
I don't really remember much about probability and statistics as to help you with the chi woes.

Can't you just plot this in a non logarithmic scale?

>>5279280
I could, but since I know a perfect exponential growth would make a straight line in a lin-log graph paper, I figured that I could make a simple regression and conclude, that the data set with the r squared value closest to 1 would be the one that's exponential.

But since Grapher can't do regression and gives me a chi squared value instead of r squared, I figured i had to understand how it works. The strange things is that in the manual written in half french half english, the interpolation function is described as regression. It's in no way a perfect program, but so far it's the best there is.

>>5279284
Why not just do it on paper? You only have 4 points.

>>5279285
I have to prove which of the 3 data sets posted eariler in this thread is linear, exponential and parabole-shaped.

Bump

Bamp

>>5279742
Post more infographs, The colour wheel was beyond awesome. I wonder why so many of the fields are empty. Do only muslims, westerners and japanese have a concept of Heaven for example?

>>5279920
Here ya go.