Topic: Statistics, non-linear model regression and optimization

Please solve by hand and by Matlab code. Thank you very much!

Nonlinear regression of chemical reaction dataAn experimenter examines the reaction kinetics of an NaOH:phenolphthalein reaction. The extent of reaction is measured using a colorimeter, where the absorbance is proportional to the concen- tration of the phenolphthalein. The purpose is to measure the reaction rate constant k at different temperatures and NaOH concentrations to learn about the reaction mechanism. In the experiment, the absorbances Aj are measured at times ti. The absorbance should fit an exponential rate law: kt where C1, C2, and k are unknown constants (a) Write a MATLAB function that can be fed into the built-in function fminsearch to perform a nonlinear regression for the unknown constants. b) Now suppose that you obtain a solution, but you suspect that the fminsearch routine may be getting stuck in a local minimum that is not the most accurate solution. How would you test this? Nonlinear regression of chemical reaction dataAn experimenter examines the reaction kinetics of an NaOH:phenolphthalein reaction. The extent of reaction is measured using a colorimeter, where the absorbance is proportional to the concen- tration of the phenolphthalein. The purpose is to measure the reaction rate constant k at different temperatures and NaOH concentrations to learn about the reaction mechanism. In the experiment, the absorbances Aj are measured at times ti. The absorbance should fit an exponential rate law: kt where C1, C2, and k are unknown constants (a) Write a MATLAB function that can be fed into the built-in function fminsearch to perform a nonlinear regression for the unknown constants. b) Now suppose that you obtain a solution, but you suspect that the fminsearch routine may be getting stuck in a local minimum that is not the most accurate solution. How would you test this