Chapter 7.5, Problem 24E

Problems 23 and 24 refer to the system of normal equations and the formulas for a and b given on page 473.

24. If $\begin{array}{ccc}\bar{x}=\frac{1}{n}{\displaystyle \underset{k=1}{\overset{n}{\sum }}{x}_k}& \mathrm{and}& \bar{y}=\frac{1}{n}\end{array}{\displaystyle \underset{k=1}{\overset{n}{\sum }}{y}_k}$

are the averages of the v and y coordinates, respectively, show that the point $\left(\bar{x},\bar{y}\right)$ satisfies the equation of the least squares line, y = ax + b.