I have data with standard error, included below for clarity,
X Y Error in Y 0.0105574 -28.831027 0.04422 0.0070382 -27.800385 0.04225 0.0052787 -27.314088 0.04209 0.0042229 -27.054207 0.04185 0.0035191 -27.000188 0.04143 0.0030164 -26.891275 0.04108
I have obtained parameters a and b of the expression y=a*x*x + b from a weighted least squares regression using this data (fit in gnuplot). The regression returned what was called "Asymptotic Standard Error" associated with these parameters. I believe this error was calculated using the deviation from fitted point to actual points (Equation 34/35 here) and is used to assess the quality of a fit. However, this is not the error that I'm interested in.
I'm looking to determine the value of the data point at X=0.0 from my fitted function with standard error like my other values. The output of the regression was:
Final set of parameters Asymptotic Standard Error a = -19389.1 +/- 752 (3.878%) b = -26.7951 +/- 0.03915 (0.1461%)
So, to be quite specific, how might I determine the standard error at the point (X,Y)=(0.0, -26.7951) using my fitted function? I expect the error in this calculated point to be much larger than the errors of the values reported in the Y values of my table above.
I can see how gnuplot is not the right tool for this, as it only weights my data points using the standard error in my input. What I need to do is propagate the error in my original data points to obtain the error on the regression line.
This seems like a pretty basic exercise, sorry for my statistics ignorance. Thanks!