BENG449 Problem 6 2

BENG449 Problem 6 2 - BENG449 Problem Set 6, Question 2...

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BENG449 – Problem Set 6, Question 2 Alex Lemon March 11, 2008 1 Part A The plot of S ( b 1 , b 2 ) is a three-dimensional graph in which the height of the graph above the b 1 - b 2 plot gives the value of the residual sum of squares if the noisy data is estimated using the double-exponential model with the given parameter values. On the speciFed region, S ( b ) appears to be globally convex with a minimum corresponding to the OLS estimates for β 1 and β 2 . In the Frst trial, this optimization point was found to be at b 1 = 0 . 0490 and b 2 = 0 . 0200; in the second trial, the OLS estimates were b 1 = 0 . 0520 and b 2 = 0 . 0190. 2 Part B There are two ways to think about whether or not S ( b ) is a noisy function. On the one hand, S ( b ) is a smooth function of b 1 and b 2 , so the three-dimensional plot of the residual sum of squares versus the parameter values is a smooth function. When we generate noisy data, we usually expect to see random vari- ation around some underlying relationship with the result that a plot of the noisy data is not in general a smooth function. However, the plot of S ( b ) is a smooth function of the parameter values, b 1 and b 2 . On the other hand, S ( b ) is a function of the noisy data that was generated, and in this sense, the graph
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BENG449 Problem 6 2 - BENG449 Problem Set 6, Question 2...

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