Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline, and steel). In many cases, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions take place. Suppose that a particular manufacturer wants to model the quality ( Y ) of a product as a function of the temperature ( X 1 ) and the pressure ( X 2 ) at which it is produced. The file P13_31.xlsx contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product. a. Estimate a multiple regression equation that includes the two given explanatory variables. Does the estimated equation fit the data well? b. Add an interaction term between temperature and pressure (the product of these two variables) and run the regression again. Does the inclusion of the interaction term improve the model’s goodness of fit? c. Interpret each of the estimated coefficients in the two equations. How are they different? How do you interpret the coefficient for the interaction term in the second equation?

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 13, Problem 31P
Textbook Problem

Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline, and steel). In many cases, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions take place. Suppose that a particular manufacturer wants to model the quality (Y) of a product as a function of the temperature (X1) and the pressure (X2) at which it is produced. The file P13_31.xlsx contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product.

  1. a. Estimate a multiple regression equation that includes the two given explanatory variables. Does the estimated equation fit the data well?
  2. b. Add an interaction term between temperature and pressure (the product of these two variables) and run the regression again. Does the inclusion of the interaction term improve the model’s goodness of fit?
  3. c. Interpret each of the estimated coefficients in the two equations. How are they different? How do you interpret the coefficient for the interaction term in the second equation?

Expert Solution

a)

Summary Introduction

To estimate: The regression equation.

Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.

Explanation of Solution

Data:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  1

Formulae to determine the data:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  2

Regression using StatTools:

Regression and classification from the StatTools should be used. The below image shows the regression parameter table from StatTools:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  3

Regression result:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  4

Hence, the regression equation is Quality = 106.085 – 0.916 temperature + 0.788 pressure. The value of R-square is 0.2115. The quality score falls by 0.916 and the pressure would remain constant when the temperature increases by one degree. The quality score rises by 0.788 and the temperature would remain constant when the pressure increases by one pound.

Expert Solution

b)

Summary Introduction

To run: The regression by adding an interaction term between pressure and temperature.

Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.

Explanation of Solution

Data:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  5

Formulae to determine the data:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  6

Regression using StatTools:

Regression and classification from the StatTools should be used. The below image shows the regression parameter table from StatTools:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  7

Regression result:

Practical Management Science, Chapter 13, Problem 31P , additional homework tip  8

The above table provides the estimated coefficients. The standard error of estimate falls and the adjusted R-square rises.

Expert Solution

c)

Summary Introduction

To determine: The difference between the estimated coefficients in the two equations.

Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.

Explanation of Solution

The quality score would increase by 7.086 – 0.145×pressure and the pressure would remain constant when the temperature increases by one degree. The quality score would increase by 13.883 – 0.145×temperature and the temperature would remain constant when the pressure increases by one pound per square inch. Based on the level of the pressure, the coefficient would indicate the quality change rate with respect to the temperature.

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Chapter 13 Solutions

Practical Management Science
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