Least Squares (Exam Spring 1998, Question 2)
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Given the following observed values for y(t)

t 2 3 4 5 6 7 8 9 10 11 12
y(t) 154 95 65 41 26 18 107 4 4 1


We want to approximate y(t) in the least squares sense by

y(t) = a*b^t

This is obviously a nonlinear least squares problem.


a: Write the expression for the sum of squares. The input has to be in Maple syntax

s = ___________________



b: Write the equations to solve to obtain a least squares solution (a*, b*)

___________________

___________________



c: Is it possible to reduce the above equations to a single equation in a single unknown?


Yes

No






If we compute the approximation ln y(t) = ln (a) + t * ln (b) we obtain a linear least squares problem.

d: Write the expression for the sum of squares we are going to minimize in this case

s' = ___________________



e: Write the equations to solve to obtain a least squares solution (a*, b*)

___________________

___________________



f: Does this method provide a solution to the original problem?


Yes

No




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