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Computer Project

# Computer Project - Computer Project 1 The effect of...

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Computer Project 1. The effect of statistical variations on the quality of least squares fit. a. x = 0:.01:1 b. N5 = 5.*randn(1,101)…repeat for ER10, ER25, ER100 c. YN5 = Y + N5…repeat for ER10, ER25, ER100 d. ER5 = [5,5,5,…,5] (101 elements long)…repeat for ER10, ER25, ER100 e. -0.5 0 0.5 1 1.5 0 50 100 150 YN5 x Y + N 5 -0.5 0 0.5 1 1.5 -50 0 50 100 150 200 YN10 x Y + N 1 0 -0.5 0 0.5 1 1.5 -50 0 50 100 150 200 250 x Y + N 2 5 YN25 -0.5 0 0.5 1 1.5 -400 -200 0 200 400 600 x Y + N 1 0 0 YN100 line of best fit data line of best fit data data line of best fit data line of best fit y = 119x + 25.7 y = 125x + 21 y = 123x + 21 y = 130x + 20 f. YN5: m = 119 ± 1; b = 25.7 ± 0.9 YN10: m = 125 ± 3; b = 21 ± 2 YN25: m = 123 ± 8; b = 21 ± 5 YN100: m = 130 ± 30; b = 20 ± 20 Compared to the expected values of slope and intercept from the original definition of Y(x) = 120x + 25, all four cases are in good agreement since they are all within three standard deviations of the original equation. g. It can be seen that the uncertainties in the fits scale linearly with the size of the error bar in the data points:

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0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 size of error bar uncertainty in slope uncertainty in slope vs. size of error bar 0 20
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Computer Project - Computer Project 1 The effect of...

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