slope of data that already contains STDEVs

[Adriank]

I am looking for methods to calculate the error in a slope.
the caveat is that my values themselves are averages with a STDEV.
E.g.
x
1+-1%
2+-1%
3+-1%
y
0.14+-0.01
0.27+-0.02
0.42+-0.02
(using http://www.cartage.org.lb/en/themes/...onDivision.htm as the
calculation method for these errors)

This could be simplified by assuming the x-values have no deviation.

Now I can just plot the average slope of those three values, I can make a
simple linear regression analysis, obtain the least square values as shown
here
http://www.physicsforums.com/showthread.php?t=194616 and somewhat related here
http://www.physicsforums.com/showthread.php?t=173827

or use the Excel Linestatistics
(http://www.trentu.ca/academic/physics/linestdemo.html)
I obtain a value for the slope of my averaged slope, and a STDEV, based on
the Least Square algorithm. But this does not take into account at all my
initial STDEV, only the deviation of my data from the mean.
Is there a more general algorithm that can take STDEVs in the initial (at
least) y values, or both x and y values, and how would I calculate that?

Thank you.

 

[Adriank]

For these further thoughts, I will disregard the x-axis uncertainty, which
derives from the measurement setup. How can I convert deviations in the
x-values into independent y-(or z-,... )values?

I am very interested in the standard error of the resulting function.
One suggestion I got was to simply make 2 lines through the graph, one using
all max values (all y- values +the error), and one using all min values (all
y- values -the error), then taking the average of those two, and using a
simple STDEV as as standard error. I somewhat disagree with that (and would
be happy for comments).


Anyways, the linear OLS (ordinary least square) function in excel from
LINEST gives the slope m out as (sum (x-x(average)*(y-y(average)) / (sum
(x-x(average)) and the intercept with the y-axis b as b=y(av)-mx(av)
so far, so good.
So for a simple sample set of three points (x;y)=(1;1), (2;2.1), (3;2.9).
the slope m = 0.95, and b=0.1
Using Linest (y, x,,TRUE), I can create an array that gives me exactly those
values, with a STDEV for m=0.086603 and for b=0.187
1) How are those values calculated?
2) How come the st.deviation for b is 80% larger than its original value?!?

Furthermore, if I now force the slope to go through 0, I use (y, x,0,TRUE),
my slope becomes 0.9928 and b=0 (obviously), with STDEV(m)=0.026245.
But if I use above-mentioned calculation, and just add a fourth point (0;0),
I get a slope of 0.98, and a b of 0.03, NOT what excel does by forcing it
through zero.

Any help with how both slope-forced through zero, and all STDEVs are
actually calculated would be greatly appreciated.
Thanks.