2. An engineer studied the relationship between the input and output of a production process. He considered the non-linear regression model: y = In (x + B1) In ( Bo - x). - In order to estimate the model parameters using a statistical software, the engineer needs to transform it to a linear equation. (a) What transformation is needed? U = the transformed X Both X and Y need to be transformed. Denote: V = the transformed Y What are U and V? (as functions of X and Y) (b) After the variables were transformed according to your answer in Part (a), the following parameter estimates were obtained: Intercept: 0.4 Coefficient of U: 1.8 What would be the estimates for Bo and B1 in the original non-linear model?

2. An engineer studied the relationship between the input and output of a production process. He considered the non-linear regression model: y = In (x + B1) In ( Bo - x). - In order to estimate the model parameters using a statistical software, the engineer needs to transform it to a linear equation. (a) What transformation is needed? U = the transformed X Both X and Y need to be transformed. Denote: V = the transformed Y What are U and V? (as functions of X and Y) (b) After the variables were transformed according to your answer in Part (a), the following parameter estimates were obtained: Intercept: 0.4 Coefficient of U: 1.8 What would be the estimates for Bo and B1 in the original non-linear model?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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