# Consider the model [ y=theta_{1}-theta_{2} e^{-theta_{3} x}+varepsilon ] This is called the Mitcherlich equation, and it is

## Question:

Consider the model

\[

y=\theta_{1}-\theta_{2} e^{-\theta_{3} x}+\varepsilon

\]

This is called the Mitcherlich equation, and it is often used in chemical engineering. For example, \(y\) may be yield and \(x\) may be reaction time.

a. Is this a nonlinear regression model?

b. Discuss how you would obtain reasonable starting values of the parameters \(\theta_{1}, \theta_{2}\), and \(\theta_{3}\).

c. Graph the expectation function for the parameter values \(\theta_{1}=0.5\), \(\theta_{2}=-0.10\), and \(\theta_{3}=0.10\). Discuss the shape of the function.

d. Graph the expectation function for the parameter values \(\theta_{1}=0.5, \theta_{2}=0.10\), and \(\theta_{3}=0.10\). Compare the shape with the one obtained in part \(\mathrm{c}\).

## Step by Step Answer:

**Related Book For**

## Introduction To Linear Regression Analysis

**ISBN:** 9781119578727

6th Edition

**Authors:** Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining