How to manually find R^2 value between a sinusoidal plot on a scatter plot

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wine&bread17

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May 1, 2022
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Hey guys,

I want to model a function based on a scatter plot that looks like cos (x) and I have a few questions. First of all, should I not take into consideration the outliers, which I would calculate just using the interquartile range? For a bit of context, I'm looking at the concentration of air pollutants across 2 years, so I have 24 values for the graph. Also, of course I have seen ways to model it just by looking at the min, max etc. and coming up with a function, but for regression are there more complicated ways by which I can approach this probem?
 
wine&bread17 said:
Hey guys,

I want to model a function based on a scatter plot that looks like cos (x) and I have a few questions. First of all, should I not take into consideration the outliers, which I would calculate just using the interquartile range? For a bit of context, I'm looking at the concentration of air pollutants across 2 years, so I have 24 values for the graph. Also, of course I have seen ways to model it just by looking at the min, max etc. and coming up with a function, but for regression are there more complicated ways by which I can approach this probem?
Click to expand...
You are trying to model this on a single cosine curve? How much do you understand about the method of least squares regression?

-Dan
 
topsquark said:
You are trying to model this on a single cosine curve? How much do you understand about the method of least squares regression?

-Dan
Click to expand...
Since Fourier transform is unitary doing least square regression is equivalent to extracting first components from the Fourier transform of the data.
 
blamocur said:
Since Fourier transform is unitary doing least square regression is equivalent to extracting first components from the Fourier transform of the data.
Click to expand...
Yes, exactly. But a Fourier analysis will provide a series of sine and cosine terms. It sounded to me like the OP wanted to fit the data to a single cosine curve. That's why I was asking.

-Dan
 
Thanks for the suggestions! And to answer your question, I know the basics of least square regression, but only for linear plots. My current level of mathematics is just IB Maths SL (a.k.a highschool).

Yes, I want to fit the data for 24 months onto a single cos plot.

Hello!!

Can someone help me? I have a scatter plot for 2 years (monthly data for 24 months, hence 24 values), which looks period. I plotted a cos(x) graph and I saw that the calculator can also do a sinusoidal regression for you, also giving you the r^2 value. Does anyone know how I can calculate the r^2 value manually? It's for a maths project. Thank you in advance!
 
wine&bread17 said:
Hello!!

Can someone help me? I have a scatter plot for 2 years (monthly data for 24 months, hence 24 values), which looks period. I plotted a cos(x) graph and I saw that the calculator can also do a sinusoidal regression for you, also giving you the r^2 value. Does anyone know how I can calculate the r^2 value manually? It's for a maths project. Thank you in advance!
Click to expand...
Do a Google search with

calculate R-square manually​

as key-words.
 
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