# Physics307L:Schedule/Week 8 agenda/Linear fit theory

### From OpenWetWare

Following John R. Taylor, "An Introduction to Error Analysis," 2nd edition, Chapter 8:

### We have a relation as follows, and want to fit and to the data

### Assume same gaussian distribution for random error in each (same for all). Not necessary, but simplifies derivation and results

### Principle of maximum likelihood

### For a given and , the probability for each is:

### And we can call the probability of getting all of the data points as:

### Each term has the same σ_{y}, so can be simplified as:

### To maximize the probability, minimize the chi-squared sum ... take derivatives, solve system of equations, obtain:

(1)

(2)