EGM_3344_Exam3_Solutions_2009

EGM_3344_Exam3_Solut - Sorting Number Problem 1(Handwritten Nonlinear Regression(13 points A University of Florida researcher performs an

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Sorting Number: ______________________ Fall 2009 2 Problem 1 (Handwritten) – Nonlinear Regression. (13 points) A University of Florida researcher performs an experiment to determine the growth rate of bacteria k (bacteria per day) as a function of oxygen consumption c (mg/L). Tabulated data from the experiment and a corresponding plot of the data (open circles) are provided below, along with a regression fit of the data performed by the researcher (solid line). c 0.5 0.8 1.5 2.5 4 k 1.1 2.3 5.2 7.7 8.9 0 1 2 3 4 5 0 2 4 6 8 10 c (mg/L) k (bacteria per day) To generate this regression fit, the researcher modeled the data using the nonlinear relationship 2 1 2 2 ac k = + (1) and linearized this equation using transformation of variables. After performing the regression fit for the linearized model, the researcher calculated the values of the regression coefficients 1 a and 2 a for the original nonlinear model and used these values in Eq. (1) to generate the solid line shown in the figure above. a) Use transformation of variables to derive the linearized version of Eq. (1) that was used by the researcher for regression analysis. Assume the linearized model is given by yp xq = + where p and q are regression coefficients. Provide expressions in the spaces below for y as a function of k , x as a function of c , and how p and q as functions of 1 a and 2 a . y = _____________________________ x = _____________________________ p = _____________________________ q = _____________________________
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Sorting Number: ______________________ Fall 2009 3 b) Formulate a linear system of equations Ax b = that could be solved for the regression coefficients p and q in the linearized model (Note: DO NOT solve these equations). Keep only two significant figures for all values used in your linear system of equations. Record you’re A matrix and b vector in the spaces provided below: ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ p q ⎡⎤ ⎢⎥ = ⎣⎦ c) Once the researcher solved for the regression coefficients p and q in the linearized model, show how he calculated regression coefficients 1 a and 2 a in the original nonlinear model.
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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EGM_3344_Exam3_Solut - Sorting Number Problem 1(Handwritten Nonlinear Regression(13 points A University of Florida researcher performs an

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