Question

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.

Answer 1

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