1. Nonlinear Fitting

2. Linearizing nonlinear Functions
Not recommended unless you have information on the errors in your y data and you weight the fit according to those errors. Note these errors will change due to the transformation!

3. Example x y 1
0.5 2
1.7 3
3.4 4
5.7 5
8.7

4. Fitting Polynomials (Polynomial Regression)
A system of 3 x 3 equations must be solved, meaning you
must have at least three data points to fit a quadratic.

5. Fitting Polynomials (Polynomial Regression)

6. Fitting Polynomials (Polynomial Regression)
Form the objective function:

7. Example inv(X'*X)*(X'*a) In Matlab you would write Switch to octave….1 2 5 3 8 4 17 16
In Matlab you would write
inv(X'*X)*(X'*a)
Switch to octave….

8. Errors in parameters
Sigma^2 is estimated from the sum of squared errors (residuals) as before:

9. Errors in parameters
The diagonals of the Cov(a) are the standard errors (variances) of the parameters