Physics307L:Schedule/Week 10 agenda: Difference between revisions

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*Fitting a line
__NOTOC__
**AKA linear regression; least-squares fit for a line
==2011==
**Why fitting a line?
* Update on faster than light neutrinos
***Linear relations & This versus 1/sqrt(that) (examples: e-diffraction; e/m lab)
* Group work (10 minutes) -- two measurements, what to do?
***<math>y=Ae^{Bx}</math>
** (write on the board) You obtain two independent measurements of the speed of light(a) 34.8 +/- 0.5 cm/ns (b) 0.28(2) m/ns
**Theoretical
** Discuss with neighbor: As a scientist, what should you do with these measurements to report a final answer?  What do you want to do?  What can you do? What if your reputation were to depend on it?  What if lives were at stake or otherwise super-important?
***Assume gaussian distribution for each <math>y_i</math> with same sigma for all measurements (not necessary, but simplifies it).
* Discussion of group work (20 minutes)
***Maximum likelihood...Chi-squared
 
***Derivative (minimize Chi-squared) / solve
* Links on other pages for now (rest of time)
****Just show the answer, ... skip derivation for time for practical examples.
 
**Practical step by step w/ Excel..."R"...."Octave?"
==Prior years==
 
* Sebastian / Matthew example SEM
[[/Linear fitting|Derivation of linear fitting]]
 
==[[/Random numbers|Generating Random Numbers from Arbitrary PDFs]]==
 
==Supporting Excel sheets==
* [[Image:Weighted mean and random.xlsx]] (This is the Excel 2007 version)
* [[Image:Weighted mean and random.xls]] (This is the Excell 2003 version)

Latest revision as of 10:42, 24 October 2011

2011

  • Update on faster than light neutrinos
  • Group work (10 minutes) -- two measurements, what to do?
    • (write on the board) You obtain two independent measurements of the speed of light(a) 34.8 +/- 0.5 cm/ns (b) 0.28(2) m/ns
    • Discuss with neighbor: As a scientist, what should you do with these measurements to report a final answer? What do you want to do? What can you do? What if your reputation were to depend on it? What if lives were at stake or otherwise super-important?
  • Discussion of group work (20 minutes)
  • Links on other pages for now (rest of time)

Prior years

  • Sebastian / Matthew example SEM

Derivation of linear fitting

Generating Random Numbers from Arbitrary PDFs

Supporting Excel sheets

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