Remind yourself about linear least squares fitting in section 3.2 of the lab manual, and then...

Remind yourself about linear least squares fitting in section 3.2 of the lab manual, and then work through the following. In a particle physics experiment, there are six detectors at positions x = 10; 14; 18; 22; 26; and 30cm. These detectors measure the y positions of the trajectory of a charged particle to be 2.02; 2.26; 3.24; 3.33; 3.92; and 4.03 cm, respectively (i.e., the first position is (10,2.02), the second position is (14,2.26), and so on). The errors on the x positions are negligible; the first and last detectors have a y measurement error of ±0.10 cm, and the rest have a y measurement error of ±0.30 cm.

(a) Plot the points with their error bars.

(b) Perform a least squares straight-line fit to the data using the form y = a+bx. Find the values of a and b, and plot the resulting line along with the data points and their error

(c) Based on the χ 2 test, evaluate the quality of the fit.

Expert Solution

SL NO	X	Y	XY	X2
1	10	2.02	20.2	100
2	14	2.26	31.64	196
3	18	3.24	58.32	324
4	22	3.33	73.26	484
5	26	3.92	101.92	676
6	30	4.03	120.9	900
Total	120	18.8	406.24	2680

orchestra answered 2 years ago

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