# Help Math Nerds: Pls Help

Discussion in 'Technical Discussion' started by Devon, Mar 31, 2024.

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1. ### Devon

I'm a loser, baby, so why don't you kill me? Tech Member
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Okay, so, I am stumped with a thing here. I have these sets of points, and I'm wondering how I would go about deriving some kind of formula from it.

Here are the points I have plotted:
• (120, 3.0452)
• (136, 3.0500)
• (156, 3.0556)
• (172, 3.0588)
• (200, 3.0632)
• (228, 3.0664)
• (256, 3.0692)
• (276, 3.0704)
• (300, 3.0720)
• (328, 3.0740)
• (352, 3.0752)
• (372, 3.0756)
• (392, 3.0764)
• (412, 3.0768)
• (428, 3.0776)
• (452, 3.0780)
• (476, 3.0788)
• (508, 3.0792)
• The X range is meant to be [0, 508].
• y = 0 when x = 0.
• It has a logarithmic shape to it, so perhaps some form of log() or maybe a square root is involved.
• It doesn't really have to go through those points exactly (the means I got these points had a margin of error), but it should still follow then closely.
Any pointers? I expect the whole thing to look similar to this, maybe:

Last edited: Mar 31, 2024
2. ### President Zippy

Zombies rule Belgium! Member
You're probably familiar with linear regression, but there are also methods for finding a best-fit polynomial curve (polynomial regression), and also a logistic curve (logarithmic function):

https://online.stat.psu.edu/stat462/node/207/

Here is a similar page for polynomial curves, should you ever need one:

https://online.stat.psu.edu/stat462/node/158/

EDIT: Google spreadsheets does not have a function for doing logistic regression, but Excel does. If you calculate the regression on your dataset, you will get an equation of the form:

y = a*ln(x) + b​

Where a and b are constants.

Alternatively, your logistic regression could use the common log (log in base 10) instead of the natural log (log in base e), it doesn't matter which one you choose. Constant (a) will change, but constant (b) will remain the same.

In fact, if you have a y value for x=1, that value is b. Note that for the log function in any base (ln, log10, log2):

log(1) = 0​

Last edited: Mar 31, 2024
3. ### Devon

I'm a loser, baby, so why don't you kill me? Tech Member
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