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hw2_Sriram

# hw2_Sriram - SRIRAMPATTABHIRAMAN HW2 38987985 1 =0.9407x...

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SRIRAM PATTABHIRAMAN HW – 2 3898 7985 1. The fit obtained using regression is y = 0.9407 x + 0.0158 The expression for Std Error is SE = ߪ ොඥݔ ௠் ሺܺ ܺሻ ିଵ ݔ , where = x m = [1 x] T ; X = [1 x i ] where x i is the x coordinate of the data points. The expression for SE in the interval [0, 1.5] is SE = 0.0953 כ √0.9091ݔ െ 0.9091ݔ ൅ 0.3182 Comment (Rafi Haftka): Since the minimization of the standard error is done before the simulation, the value of sigma is not known, and there is no need to include it. The Actual error is the magnitude of the difference between the fitted line and (y = x) line. The Std Error and the Actual error are compared in Figure 1 below. Figure 1: Comparing Std Error and Actual error graphically The estimated standard error for the fitted line is higher than the actual. 2. The best 3 points selected to minimize the maximum standard error in the interval [0, 1.5] are x = [0 0.9 1.0] The fit obtained by these 3 points is y = 1.0869 x – 0.0692 The expression for SE in the interval [0, 1.5] is SE = 0.0953 כ √1.6484ݔ െ 2.0879ݔ ൅ 0.9945

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