8.2 Consider the following two-dimensional data, in which X is the independent variable, and Y is the dependent variable assumed to be derived from a photoncounting experiment:

xi yi 0:0 25 1:0 36 2:0 47 3:0 64 4:0 81

(a) Determine the errors associated with the dependent variables Yi.

(b) Find the best-fit parameters

a, b of the linear regression curve y.x/ D a C bxI also compute the errors in the best-fit parameters and the correlation coefficient between them;

(c) Calculate the minimum 2 of the fit, and the corresponding probability to exceed this value.