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Assignment 3 - Physics 257 Assignment 3 ANSWER KEY Due...

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Page 1/6 Physics 257 Asst 3 Physics 257: Assignment 3 ANSWER KEY Due in-class 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 y-intercept, 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
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