This is the last homework assignment. Each problem involves least squares fitting. You will use these procedures again, almost certainly more than once, when analyzing your experiments.
Problem 1. Chapter 9, Exercise 6. You are to do this problem two ways. First, do the fit by explicitly constructing the sums and use Eq.9.4 in the notes. Second, do the fit by using the MATLAB function polyfit. (You should get exactly the same answers.) Also, plot the data points and the fitted function, including the best fit value for absolute zero, and for the best fit value plus and minus its uncertainty. (That is, plot the data and three parallel, straight lines.) Explain why the two lines which include the uncertainty, miss the data points so much.
Problem 2. Chapter 9, Exercise 7. There is no need to do the fits explicitly using formulas. Just use polyfit.
Problem 3. Use the data from Chapter 1, Exercise 1, and perform a numerical, nonlinear fit to best determine the initial rate, decay time, and background level (i.e. the answers to parts b, c, and d in the problem). To help you out, you can pick up the code for the chi-square decay function. (This code assumes all points have the same weight, so it ignores them.) See the notes on pages 352-353 for an example. Compare the result to your answers from last week's homework assignment. In fact, try using these values for the "starting values" needed by the fmins function.