6.11.5. Working–Hotelling confidence bands are a method for getting confidence intervals for every point on a line with a guaranteed simultaneous coverage. The method is essentially the same as Scheff´e’s method for simultaneous confidence intervals discussed in Section 13.3.

For estimating the point on the line at a value x, the endpoints of the (1−α )100% simultaneous confidence intervals are

(ˆβ0+ ˆβ1x)±



2F(1−α ,2,dfE)SE(ˆβ

0 + ˆβ1x).

Using the Coleman Report data of Table 6.1, find 95% simultaneous confidence intervals for the values x = −17,−6,0,6, 17. Plot the estimated regression line and the Working–Hotelling confidence bands. We are 95% confident that the entire line β0+β1x lies between the confidence bands.

Compute the regular confidence intervals for x = −17,−6,0,6,17 and compare them to the results of the Working–Hotelling procedure.