Estimating Standard Deviation by Using Curve Fitting Toolbox
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I am using Curve Fitting Toolbox to fit a 10 points data. Here's the result.
Linear model Poly1:
f(x) = p1*x + p2
Coefficients (with 95% confidence bounds):
p1 = 1.247e-013 (1.193e-013, 1.3e-013)
p2 = -1.544e-015 (-4.863e-015, 1.775e-015)
Goodness of fit:
SSE: 3.551e-029
R-square: 0.9972
Adjusted R-square: 0.9969
RMSE: 2.107e-015
I am neither using robust fitting nor with my own weighting factor. Therefore I suppose the SSE is not weighted and I can get the standard deviation by simply dividing the SSE by 10 (points) and take the square root of it. But is this correct?
May I also know in Curve Fitting Toolbox, the 95% confidence bound is equivalent to how many standard deviation? About 2 standard deviation by using the results obtained through Curve Fitting Toolbox?
If I did a robust linear fit, since the SSE is weighted, is there any way for me to get a good estimate of the standard deviation?
Here's the result for the robust fit:
Linear model Poly1:
f(x) = p1*x + p2
Coefficients (with 95% confidence bounds):
p1 = 1.239e-013 (1.182e-013, 1.297e-013)
p2 = -1.258e-015 (-4.831e-015, 2.315e-015)
Goodness of fit:
SSE: 4.116e-029
R-square: 0.9968
Adjusted R-square: 0.9964
RMSE: 2.268e-015
Thanks.
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