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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

#### fivefeet8

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Bgnome said:
linear regression is often used in math analysis and statistics as well from what i recall
Yeah it is. Any graphing calculator and do it nowadays. But to do it manually, you need to use calculus to derive the set of equations to find the curve. What's more is that you then need to find the standard deviation of the measure points from the curve. This requires more calculus to derive another set of equations to find that. It's a bit tedious at times.

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