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  Exponential Model ),(,...),,(),,( 2211 nn  y x y x y x Givenbest fit  bx ae y   to the data. Figure. Exponential model of nonlinear regression for y vs. x data bx ae y   ),( nn  y x ),( 11  y x ),( 22  y x ),( ii  y x i bxi  ae y   http://numericalmethods.eng.usf.edu 1  Finding Constants of Exponential Model      nibxir   i ae yS  12 The sum of the square of the residuals is defined asDifferentiate with respect to a and b      02 1     ii  bxnibxir  eae yaS       02 1     ii  bxinibxir  eaxae y bS  http://numericalmethods.eng.usf.edu 2  Finding Constants of Exponential Model Rewriting the equations, we obtain 0 121   nibxnibxi ii eae y 0 121   nibxinibxii ii e xae x y http://numericalmethods.eng.usf.edu 3  Finding constants of Exponential Model Substituting back into the previous equation 0 121211   nibxinibxbxniibxinii iiii e xee ye x y The constant b can be found through numerical methods such as bisection method.   nibxnibxi ii ee ya 121 Solving the first equation for a yields http://numericalmethods.eng.usf.edu 4

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Sep 11, 2019
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