Page 1/6
Physics 257 Asst 3
Physics 257: Assignment 3
ANSWER KEY
Due inclass before 1:05pm Thursday October 4, 2007
Remember to use the correct number of significant figures for your answers. Answers with incorrect significant figures will
get zero marks. For plots, remember to label your axes correctly and use the “graphs” checklist on page 7 of the lab book.
Graphs must be computer generated from now on. For each question, show all your steps. Assignments handed in after
1:05pm but before the end of the day will lose 25% of the grade.
1)
In class we derived the equations for a least squares fit to a straight line. This resulted in
equations for the slope, a, and the yintercept, b. In class we quoted, but did not derive, the
equations for the error estimate
σ
a
and
σ
b
of a and b. Here we will derive these equations
using matrix notation. The general steps for this derivation are given on pages 18,19 of the
red lab book.
Assume the error on x
i
are negligible, and the errors on y
i
are the same for all
i.
σ
i
=
Δ
y = constant.
a)
Start with the equation
(
)
2
1
2
2
1
∑
=
⎥
⎦
⎤
⎢
⎣
⎡
Δ
+
−
−
=
N
i
i
i
i
y
b
ax
y
N
χ
(note that this is the reduced
χ
2
, and is slightly different from the equation given on p.18… you’ll find that the end
answer is the same). Write down the partial derivatives
δχ
2
/
δ
a and
δχ
2
/
δ
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 Harris
 Physics, Regression Analysis, 25%, xi yi xi, red lab book

Click to edit the document details