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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.

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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.

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

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.

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[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)

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Oh, I see it now. These equations can take several forms, and the one that I posted was the only one I could remember yesterdayfivefeet8 said:

[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)

But I recognize the one you posted too... I should have thought about it before :emb:

It's called a linear regression, and it uses the least squares method to find the curve that best fits the measured data.Viper_Viper said:

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what level of math is it? college level?

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It's only pre Calculus level, but it's used in many Physics experiments.ArchIBaLD said:what level of math is it? college level?

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

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

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