Show that, for the ordinary linear regression problem with an intercept and one dependent variable, x, that n22 = (n − 1)(n − 3)/n +∑(xi − x)

4/(∑(xi − x)

2)

2 and that, for equally spaced x-values, this reduces to n22 = (n − 2)

2/n + 4/ (5n) + O (n

−2)

in reasonable agreement with the approximations of Section 4.7.2. Show more generally, that the discrepancy between n22 and the approximation (n

− 2)

2

/n, is a function of the standardized fourth cuumulant of the x-values.

Find this function explicitly.