The 13 points (Tj, yl), j = 1, ... , 13, were plotted as shown in Figure 3.2, and the probit regression line was sketched by eye. Initial approximations 1-Lo = 39.8 and <To = 4.55 are obtained from the regression line. One cycle of Newton's method gave j.L 1 = 39.6 and a 1 = 4.60 as new approximations which were then used as starting points for a second cycle of the iteration process. For this second cycle the correction equations become
On solving this pair of equations simultaneously, we obtain as new corrections h = -0.017 and g = 0.011, and the final estimates become Jl = 39.583 and & = 4.611. The asymptotic variance-covariance matrix is now approximated as
28.067 I 0.069 0.0021 0.002 0.036
Standard errors and the correlation coefficient follow as
(J tl = 0.263, <Ttr = 0.190, Pp..& = 0.0401.