Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8.3, Problem 11E
To determine
Test whether the reduced model is useful than the full model to predict the bearing wear.
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5. Consider the following two simple regression models:
Model I : Y, = B,+B,X, +H,
Model II : Y,=a, +a, (X,- X)+v,
(1) Derive the estimators for B, and a,. Are they the same?
(2) Derive the estimators for B, and a, . Are they the same?
Consider the following variables:
Y=daily productivity score (measured in points)
X1=0 if undergraduate student,1 if graduate student
X2=hours of sleep per night
1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test?
A. Use Model 3 and test H0: β2=0
B. Use Model 5 and test H0: β3=0
C. Use Model 5 and test H0: β1=0
D. Use Model 5 and test H0: β2=0
E. Use Model 2 and test H0: β1=0
2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following:
Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2)
What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students?
A. 2
B. None of…
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:
y = β0 + β1x + ε
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour.
The following data was collected from rush hour for 6 different highways in the city.
Traffic Flow(y)
Vehicle Speed(x)
1,254
35
1,327
40
1,227
30
1,335
45
1,348
50
1,126
25
In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
ŷ = b0 + b1x + b2x2
1.
Develop an estimated regression equation for the data of the form
ŷ = b0 + b1x + b2x2.
(Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.)
2. Find the value of test statitc and p-value.
3. Based on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)
Chapter 8 Solutions
Statistics for Engineers and Scientists
Ch. 8.1 - In an experiment to determine the factors...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - The article Application of Analysis of Variance to...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Refer to Exercise 7. a. Find a 95% confidence...Ch. 8.1 - In a study of the lung function of children, the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - The following MINITAB output is for a multiple...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - The following data were collected in an experiment...Ch. 8.1 - The November 24, 2001, issue of The Economist...Ch. 8.1 - The article Multiple Linear Regression for Lake...Ch. 8.1 - Prob. 19ECh. 8.2 - In an experiment to determine factors related to...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.3 - True or false: a. For any set of data, there is...Ch. 8.3 - The article Experimental Design Approach for the...Ch. 8.3 - Prob. 3ECh. 8.3 - An engineer measures a dependent variable y and...Ch. 8.3 - Prob. 5ECh. 8.3 - The following MINITAB output is for a best subsets...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - (Continues Exercise 7 in Section 8.1.) To try to...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - The article Ultimate Load Analysis of Plate...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - The article Modeling Resilient Modulus and...Ch. 8.3 - The article Models for Assessing Hoisting Times of...Ch. 8 - The article Advances in Oxygen Equivalence...Ch. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - In a simulation of 30 mobile computer networks,...Ch. 8 - The data in Table SE6 (page 649) consist of yield...Ch. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Refer to Exercise 2 in Section 8.2. a. Using each...Ch. 8 - Prob. 10SECh. 8 - The data presented in the following table give the...Ch. 8 - The article Enthalpies and Entropies of Transfer...Ch. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - The article Measurements of the Thermal...Ch. 8 - The article Electrical Impedance Variation with...Ch. 8 - The article Groundwater Electromagnetic Imaging in...Ch. 8 - Prob. 18SECh. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - The article Estimating Resource Requirements at...Ch. 8 - Prob. 24SE
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