Is the Stated Uncertainty Consistent with the Data?

[ma18]

Homework Statement

I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked

a) find the best fit

b) at what prob can you rule out a 5% higher slope

c) is the stated uncertainty consistent with the data?

Homework Equations

The Attempt at a Solution

I can find the best fit relatively easily by minimizing chi-sqd and setting the derivatives to 0. I am confident in my result as it matches with the graph given by excel.

For part 2 I tried putting a higher value for the given slope into the chi-sqd equation and checking a chart but that didn't give me a reasonable answer (not completely sure about the degree of freedom)

I am not sure how to approach the third part. I have computed the errors in the fitting coefficients but that doesn't seem to play into it.

Thanks,

 

[DEvens]

Along with the formulas for the slope and intercept to fit a straight line to data, there are also formulas to give the uncertainty in those values. That will give you the one-sigma value for the slope and the intercept, and let you work out the answers. This web page discusses this a bit.

http://www.learningmeasure.com/articles/mathematics/LeastSquaresLineFits.shtml