Quiz3Soln

Quiz3Soln - ECM 005 Quiz 3 Solutions D.M. Lavenson March 1,...

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ECM 005 Quiz 3 Solutions D.M. Lavenson March 1, 2011 1 Problem 1 This problem can be approached the same we attemped the error analysis problem in Problem Set 11, though we have a slightly different functionality for y . We know that we have a data set which spans up to N points, so we will find an expression for the value of A that minimizes the square error between the data and the function y . We start first by defining the error and the square error between the data points y i and the predicted values A * f ( t i ) . E i = N s i =1 ( y i - Aln ( t i )) (1) E 2 i = N s i =1 ( y i - Aln ( t i )) 2 = N s i =1 y 2 i - 2 * A N s i =1 ( y i ln ( t i )) + A 2 N s i =1 ln ( t i ) 2 (2) Recall that each separate term must have the same summation notation applied to it. In order to minimize the squared error, we take the derivative of E 2 i with respect to A and set it equal to 0. dE 2 i dA = - 2 N s i =1 ( y i ln ( t i )) + 2 * A N s i =1 ln ( t i ) 2 = 0 (3) This equation is not our final answer! We must solve for an expression for A . Thus we rearrange to solve for A and we get a final expression defining A when minimizng the 1
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square error of the data and predicted function y . A
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Quiz3Soln - ECM 005 Quiz 3 Solutions D.M. Lavenson March 1,...

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