error analysis

[labview1958]

I have a graph of Force(mN) vs Distance(m). The error in the force is 0.0001g and the error in the distance is 0.0254mm. I have 10 points on the graph. Excel gives R^2 = 0.90. My gradient is 1.045. What is it's error? Can someone help?

[Waldo]

What are you measuring? I think that would help.

[labview1958]

I am measuring repulsive force between two magnets. The distance is moved by a stepper with steps of 0.0254 mm per step. The electronic balance measures force with a accuracy of 0.0001g.

[Klaynos]

well the gradient is force/distance And you can use one of the standard error analysis equations for combining errors to work out the error:

 

http://engr.astate.edu/jdg/Circuits/Lab/error_analysis.htm

 

The equations are listed on that page specifically for division:

 

http://engr.astate.edu/jdg/Circuits/Lab/images/errorProp08.gif

[m4rc]

Another method to determine the uncertainty on a slope is to draw a line of best fit as well as lines with the minimum and maximum slopes that still adequatly fits the data (although not the line of best fit). The differences between the values will be your uncertainty in the value of the slope. See the last example in http://spiff.rit.edu/classes/phys273/uncert/uncert.html#slope for more details. There is an algeraic method that considers all the points but I don't remember all the details.

 

The advantage of this method is that it considers all of your data and not just the two points that you use to determine the slope.

[labview1958]

I am using microsoft excel program to draw the best fit linear line. It gives R^2 = 0.90. I understand the complete 100% fit would give R^2 = 1.0. How do I get my error from here?

[Klaynos]

The R² value is NOT a value for the error fo your results, but for the error on how well your line of best fit fits your results. Moving between the two is not possible, as it is quite possible to have a high error on all your results but by some luck get an R² value of 1...

[labview1958]

I have another problem about excel staight line graphs. The error bar in the y-axis is 0.0002 and the x-axis is 0.2. Does the slope of my graph have an error of 0.0002/0.2 = 0.001 ? Is that a fair assumption?

[m4rc]

I have another problem about excel staight line graphs. The error bar in the y-axis is 0.0002 and the x-axis is 0.2. Does the slope of my graph have an error of 0.0002/0.2 = 0.001 ? Is that a fair assumption?

 

No the uncertainty on the slope has very little to do with the uncertainty in the individual data points. For example, if you had a method of measuring your data that had a large uncertainty, you can get a relatively accurate measurement of the slope by taking lots of data.

 

If you don't want to use the graphical method that I suggested in my previous post, then you can use the method of least squares described in http://www.lsmsa.edu/CMcMullen/Linear%20Regression.doc . Those are the only two methods for determining the error of the slope.

 

You may be able to use software to do the calculation for you. Most computer programs dedicated to producing graphs (like origin, sigmaplot, genplot?) should calculate the uncertainty when they do a linear regression. As far as I know, Excell does not.

[labview1958]

Is there an easier way of using some excel formula?

[m4rc]

I just looked up the Excel help files and found out that the LINEST function can give you the result you want. You may need to look it up as well as how to input array formulas.

 

Here is an example of a linear regression with uncertainties using excel assuming that your data are in collumns x and y in rows 1 to 10.

 

1) Select a 2x2 array.

2) type in the function "=LINEST(y1:y10,x1:x10,true,true)" then press shift, control and enter (this will make the array formula apply to the whole array)

3) The top left value will be the slope, the bottom left value will be its uncertainty. The top right value will be the b value in y=mx+b while the bottom right value will be the uncertainty in b.

 

Hopefully this will work OK.