To determine Construct a multiple linear regression model to predict response satisfaction using the regressors age, severity of illness, anxiety index and the indicator variable Surg-Med. Test for the contribution of the indicator variable ‘Surg-Med’ in the prediction of ‘satisfaction’. Explanation Calculation: The study surveys the satisfaction of patients at a hospital, based on some regressor variables, such as Age, Severity of illness and Anxiety and the indicator variable Surg-Med. The value ‘0’ represents that the patient is medical patient and ‘1’ represents that the patient is a surgical patient. Let y be the response variable satisfaction and x 1 , x 2 , x 3 be the predictor variables age, severity of illness and anxiety index. Indicator variable : An indicator variable is a variable assigned to a qualitative predictor variable that has more than one category, which takes values 1 or 0. The value 1 denotes the presence of the particular category for which the indicator variable is created and the value 0 denotes the absence of that category. Here, the independent variable x 4 ‘Surg-Med’ is an indicator variable. Since it takes values 1 or 0. That is, x 4 = { 0 ; if patient is a medical patient 1 ; if patient is a surgical patient Multiple regression model: The regression model of the response variable y on k regressor variables, X 1 , X 2 , ... , X k for n sets of observations, ( x i 1 , x i 2 , ... , x i k , y i ) for i = 1 , 2 , ... , n is: Y = β 0 + β 1 x 1 + β 2 x 2 + ... + β k x k . The multiple linear regression model would be of the form y ^ = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 . Regression: Software procedure: Step by step procedure to obtain regression using MINITAB software is given as, Choose Stat > Regression > General Regression . In Response , enter the numeric column containing the response data Y . In Model , enter the numeric column containing the predictor variables X1 , X2, X3 and X4 . Click OK . The output using MINITAB software is given as, A careful inspection of the output shows that the fitted model is: y ^ = 143.87 − 1.117 x 1 − 0.586 x 2 + 1.31 x 3 + 0.41 x 4 . Hence, a multiple linear regression model to predict response satisfaction using the regressors age, severity of illness, anxiety index and the indicator variable Surg-Med is y ^ = 143.87 − 1.117 x 1 − 0.586 x 2 + 1.31 x 3 + 0.41 x 4 _ . The parameter of the interest: The parameter of the interest is the slope coefficient β 4 , corresponding to x 4 . Hypotheses: Null hypothesis: H 0 : β 4 = 0

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 12, Problem 118SE

To determine

Construct a multiple linear regression model to predict response satisfaction using the regressors age, severity of illness, anxiety index and the indicator variable Surg-Med.

Test for the contribution of the indicator variable ‘Surg-Med’ in the prediction of ‘satisfaction’.

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Chapter 12, Problem 117SE

Chapter 12, Problem 119SE

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Chapter 12 Solutions

Applied Statistics and Probability for Engineers

Ch. 12.1 - 12.1. Exercise 11.1 described a regression model...Ch. 12.1 - 12.2. A class of 63 students has two hourly exams...Ch. 12.1 - 12.3. Can the percentage of the workforce who are...Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - 12-8. You have fit a multiple linear regression...Ch. 12.1 - 12-9. The data from a patient satisfaction survey...Ch. 12.1 - 12-10. The electric power consumed each month by a...

Ch. 12.1 - 12-11. Table E12-3 provides the highway gasoline...Ch. 12.1 - 12-12. The pull strength of a wire bond is an...Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - 12-15. An article in Electronic Packaging and...Ch. 12.1 - 12-16. An article in Cancer Epidemiology,...Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - 12-23. A study was performed on wear of a bearing...Ch. 12.1 - Prob. 24E Ch. 12.2 - 12-25. Recall the regression of percent of body...Ch. 12.2 - Prob. 27E Ch. 12.2 - Prob. 28E Ch. 12.2 - 12-29. Consider the following computer...Ch. 12.2 - 12-30. You have fit a regression model with two...Ch. 12.2 - 12-31. Consider the regression model fit to the...Ch. 12.2 - 12-32. Consider the absorption index data in...Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - 12-35. Consider the gasoline mileage data in...Ch. 12.2 - Prob. 36E Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.2 - 12-39. Consider the regression model fit to the...Ch. 12.2 - Prob. 40E Ch. 12.2 - Prob. 41E Ch. 12.2 - Prob. 42E Ch. 12.2 - 12-43. Consider the NFL data in Exercise...Ch. 12.2 - Prob. 44E Ch. 12.2 - 12-45. Consider the bearing wear data in Exercise...Ch. 12.2 - 12-46. Data on National Hockey League team...Ch. 12.2 - Prob. 47E Ch. 12.2 - Prob. 48E Ch. 12.4 - Prob. 52E Ch. 12.4 - 12-53. Consider the regression model fit to the...Ch. 12.4 - 12-55. Consider the semiconductor data in Exercise...Ch. 12.4 - 12-56. Consider the electric power consumption...Ch. 12.4 - Prob. 57E Ch. 12.4 - Prob. 58E Ch. 12.4 - 12-59. Consider the regression model fit to the...Ch. 12.4 - Prob. 60E Ch. 12.4 - 12-61. Consider the regression model fit to the...Ch. 12.4 - Prob. 62E Ch. 12.4 - Prob. 63E Ch. 12.4 - Prob. 64E Ch. 12.4 - Prob. 65E Ch. 12.4 - Prob. 66E Ch. 12.4 - Prob. 67E Ch. 12.4 - 12-68. Consider the NHL data in Exercise...Ch. 12.5 - 12-69. Consider the gasoline mileage data in...Ch. 12.5 - Prob. 70E Ch. 12.5 - Prob. 71E Ch. 12.5 - Prob. 72E Ch. 12.5 - 12-73. Consider the regression model fit to the...Ch. 12.5 - Prob. 74E Ch. 12.5 - Prob. 75E Ch. 12.5 - Prob. 76E Ch. 12.5 - Prob. 77E Ch. 12.5 - Prob. 78E Ch. 12.5 - Prob. 79E Ch. 12.5 - 12-80. Fit a model to the response PITCH in the...Ch. 12.5 - Prob. 81E Ch. 12.6 - 12-84. An article entitled “A Method for Improving...Ch. 12.6 - Prob. 85E Ch. 12.6 - Prob. 86E Ch. 12.6 - Prob. 87E Ch. 12.6 - 12-88. Consider the arsenic concentration data in...Ch. 12.6 - Prob. 89E Ch. 12.6 - Prob. 90E Ch. 12.6 - 12-91. Consider the X-ray inspection data in...Ch. 12.6 - 12-92. Consider the electric power data in...Ch. 12.6 - Prob. 93E Ch. 12.6 - Prob. 94E Ch. 12.6 - 12-95. Consider the gray range modulation data in...Ch. 12.6 - 12-96. Consider the nisin extraction data in...Ch. 12.6 - Prob. 97E Ch. 12.6 - Prob. 98E Ch. 12.6 - Prob. 99E Ch. 12.6 - 12-100. Consider the arsenic data in Exercise...Ch. 12.6 - 12-101. Consider the gas mileage data in Exercise...Ch. 12.6 - Prob. 102E Ch. 12.6 - Prob. 103E Ch. 12.6 - Prob. 104E Ch. 12.6 - Prob. 105E Ch. 12 - Prob. 106SE Ch. 12 - 12-107. Consider the following inverse of the...Ch. 12 - 12-108. The data shown in Table E12-14 represent...Ch. 12 - Prob. 109SE Ch. 12 - Prob. 111SE Ch. 12 - Prob. 112SE Ch. 12 - 12-113. Consider the jet engine thrust data in...Ch. 12 - 12-114. Consider the electronic inverter data in...Ch. 12 - 12-115. A multiple regression model was used to...Ch. 12 - Prob. 116SE Ch. 12 - 12-117. An article in the Journal of the American...Ch. 12 - 12-118. Exercise 12-9 introduced the hospital...Ch. 12 - Prob. 119SE Ch. 12 - Prob. 120SE Ch. 12 - 12-121. A regression model is used to relate a...Ch. 12 - Prob. 122SE Ch. 12 - Prob. 123SE Ch. 12 - Prob. 124SE Ch. 12 - Prob. 125SE

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