10.6 Consider the biometric data in Pearson’s experiment (page 30). Calculate the average father height (X variable) for each value of the mother’s height (Y variable), and the average mother height for each value of the father’s height. Using these two averaged datasets, perform a linear regression of Y on X, where Y is the average value you have calculated, and, similarly, the linear regression of X on Y. Calculate the best-fit parameters

a, b (regression of Y on X) and a0, b0 (regression of X on Y), assuming that each datapoint in your two sets has the same uncertainty. This problem is an alternative method to perform the linear regressions of Fig. 10.4, and it yields similar results to the case of a fit to the “raw” data, i.e., without averaging.