Engineering Mathematics, Volume II, Second Edition

 

Geometrically, if d_i is the vertical distance from the data point (x_i, y_i) to the point (x_i, a+b_xi) on the line, then d_i = y_i – a – bx_i (see Figure 26.4). We must minimize the sum of the squares of the vertical distances d_i, that is, the sum

 

 

Figure 15.4

 

To minimize e (a,b), we equate to zero the partial derivatives of (63) with respect to ‘a’ and ‘b’. Thus

 

 

which are known as normal equations. We write these equations in the form ...