Data Fitting (20 points in total) An environmental biologist studying the effect of a certain pollutant gas on plant growth carried out the following experiment. They exposed 7 sample plant specimens to various concentrations of the pollutant gas and observed their growth. The following data was collected: Table 1: Experimental data The biologist hypothesizes that the effect of the exposure level on growth rate is according to the following nonlinear relationship: y = a + b x 3 + c lo g x where y is the growth rate and x is the exposure level, and a , b , and c are three model parameters which need to be estimated from the experimental data. The goal is to estimate these parameters so as to minimize the mean absolute deviation (between the estimated growth rates and observed growth rates). a) (5 points) Formulate this optimization problem without conducting any reformulation. b) (5 points) Reformulate the problem as an equivalent linear program. c) (5 points) What is the optimal nonlinear relationship? What is the mean absolute deviation? d) (5 points) Plot the optimal nonlinear relationship for x between 0.01 and 1 , and superpose the actual growth rates from Table 1 .
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Data Fitting (20 points in total) An environmental biologist studying.docx
1. Data Fitting (20 points in total) An environmental biologist studying the effect of a certain
pollutant gas on plant growth carried out the following experiment. They exposed 7 sample plant
specimens to various concentrations of the pollutant gas and observed their growth. The
following data was collected: Table 1: Experimental data The biologist hypothesizes that the
effect of the exposure level on growth rate is according to the following nonlinear relationship: y
= a + b x 3 + c lo g x where y is the growth rate and x is the exposure level, and a , b , and c are
three model parameters which need to be estimated from the experimental data. The goal is to
estimate these parameters so as to minimize the mean absolute deviation (between the estimated
growth rates and observed growth rates). a) (5 points) Formulate this optimization problem
without conducting any reformulation. b) (5 points) Reformulate the problem as an equivalent
linear program. c) (5 points) What is the optimal nonlinear relationship? What is the mean
absolute deviation? d) (5 points) Plot the optimal nonlinear relationship for x between 0.01 and 1
, and superpose the actual growth rates from Table 1 .
