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#### fivefeet8

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What is the derived equation to estimate uncertainy on data points and curve fitting? I know it's :

uncertainy^2 = 1/(n-p)*SUM(of N from i = 1) E^2. What is E^2?

Where n = the number of data points and p = the number of fit parameters in a linear equation. y = mx + b.

#### Boltzmann

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I'm not sure whether I got your question right, since it's late here and I'm asleep (it was my birthday yesterday, I got quite a few drinks and too little sleep - my mind is not exactly sharp today).

I'm not familiar with the term E^2, though, but since the equation you posted is remarkably similar to the equation for finding uncertainties in the y-intercept, I'll assume that it IS the same equation. In this case, it would take the form of the equation below.

Where m is the slope of the line (calculated in the usual way), and b is the y-intercept (same as for m).

Please excuse me if I got this wrong. Just say it here and I'll look at it more closely tomorrow at work.

EDIT: For some reason the attached file is not showing up...
EDIT 2: Nevermind, managed to do it another way, and it's even better.

#### fivefeet8

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Thanks.. That was the answer, but in a different form. The form I was looking for was:

[y_i - f(x_i)]^2

Where f(x) is a linear equation with the form:

y = mx + b

And y_i is the measured y-value. So it's essentially:

(measured value - expected value)

#### Viper_Viper

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Just a random question, what type of calculus/physics is that? Next year I will be taking AP Physics BC and AP Calculus BC in my Highschool.

#### Boltzmann

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fivefeet8 said:
Thanks.. That was the answer, but in a different form. The form I was looking for was:

[y_i - f(x_i)]^2

Where f(x) is a linear equation with the form:

y = mx + b

And y_i is the measured y-value. So it's essentially:

(measured value - expected value)
Oh, I see it now. These equations can take several forms, and the one that I posted was the only one I could remember yesterday But I recognize the one you posted too... I should have thought about it before :emb:

Viper_Viper said:
Just a random question, what type of calculus/physics is that? Next year I will be taking AP Physics BC and AP Calculus BC in my Highschool.
It's called a linear regression, and it uses the least squares method to find the curve that best fits the measured data.

#### ArchIBaLD

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what level of math is it? college level?

#### Bgnome

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linear regression is often used in math analysis and statistics as well from what i recall