Suppose we have a set of m data points {(xk, yk)) 1. In class we discussed both

Question

Suppose we have a set of m data points {(xk, yk)) 1. In class we discussed both least quares and least deviation data fitting. Consider the following questions Problem #1 If we use as our data model the function y = f(x) = ax+b with fitting parameters a and b, we found the least squares solution 77t 1 1 77t ! Tk 1 k=1 How would we interpret this result if the 2 × 2 matrix on the left is not invertible? Problem #2 Develop a least squares solution (similar to that shown in the first problem) which incorporates the data model function y = f(x) = a siz-be® + c, where a, b, c are the model parameters Problem #3 Develop a least deviation solution for the model function given in the second problem. Write your linear program in matrix fornm

Explanation / Answer

If the data matrix is not invertible then we can use generalised inverse of the data matrix to find the OLS solution of the parameters.now the issue is the Generalised inverse of a matrox is not unique and hence in this case the parameters estimates will not be unique.whereas for all the estimates the SSE will be same and will be minimum.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---