In Section 11.3.1, we found the least squares estimators of α and β by a two-stage minimization. This minimization can also be done using partial derivatives.
(a) Compute and ˆ‚RSS/ˆ‚c ˆ‚RSS/ˆ‚d and set them equal to 0. Show that the resulting two equations can be written as

(These equations are called the normal equations for this minimization problem.)
(b) Show that c = a and d = b are the solutions to the normal equations.
(c) Check the second partial derivative condition to verify that the point c = a and d = b is indeed the minimum of RSS.

Transcribed Image Text:

(E-)--(2*)--È- |пс + Yi and i=1 i=1 im1