1. Curve Fitting in Matlab

2. Goals Write your own simple linear regression
Learn what the inputs and outputs are for two Matlab curve fitting functions:
polyfit
fit
Practice using these functions
Learn some basic tools for generating random values

3. Linear Regression
We want to find the equation of a line that minimizes the sum of squared residuals

4. Linear Regression cont.
We need to find a slope:
and an intercept:

5. Linear Regression cont.
We can also find r and r2:
More information online
Wikipedia Simple Linear Regression

6. Polyfit
Takes a set of x values, a set of corresponding y values, and a degree
p = polyfit(X, Y, n)
Returns a list of coefficients for the fit
Ordered by descending power
p1xn+p2xn pn+1

7. Polyfit cont. Additional outputs: [p, S] = polyfit(X, Y, n)
S can be used with polyval to get error estimates
[p, S, mu] = polyfit(X, Y, n)
mu = [mean(x) std(x)]
This performs a transformation first so p and S will not be the same as before

8. Polyfit Example

9. Fit Highly customizable
Takes a set of x values, a set of corresponding y values, and a fitType
fitobject = fit(X, Y, fitType)
A fitType describes the type of curve
‘poly1’, ‘exp1’, ‘sin1’, …
Define custom functions with expressions or anonymous functions

10. Fit cont. The output is a fitobject which can be used in plotting
fit can also output goodness of fit statistics
[fitobject, gof] = fit(X, Y, fitType)
There are several other possible input patterns
fitoptions specifies bounds, start point, fitting method

11. Fit Example

12. Randomness
The ability to generate random values is extremely important
We have to settle for pseudorandom numbers
We would also like reproducibility
Seed random value generators
Use the rng function in Matlab

13. Randomness Example