Data Linearization Method for y=Ce4x Take the logarithm of both sides:In(y)=Ax+In(C) Introduce the change of variables:Y=In(y),X=x,and B=In(C). A linear relation between the new variables X and Y:Y=4X+B The original points (in the xy-plane are transformed into the points (Y)(xkIn())in the XY-plane.This process is called data linearization.Then the least-squares line is fit to the points {(X Y) The normal equations for finding 4 and B are 2位xj-宫x 立x4+N8-24 Data Linearization Method for y=CeAx : ◼ Take the logarithm of both sides: ln(y)=Ax+ln(C). ◼ Introduce the change of variables: Y=ln(y), X=x, and B=ln(C). ◼ A linear relation between the new variables X and Y: Y=AX+B. The original points (xk ,yk ) in the xy-plane are transformed into the points (Xk ,Yk )=(xk ,ln(yk )) in the XY-plane. This process is called data linearization. Then the least-squares line is fit to the points {(Xk , Yk )}. The normal equations for finding A and B are 2 1 1 1 1 1 N N N k k k k k k k N N k k k k X A X B X Y X A NB Y = = = = =     + =           + =         