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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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.)
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…
Is it possible to get the following from a
set of experimental data:
(a) r23 = 0.8, r13 = - 0.5, r12 = 0.6
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(b) r23 = 0.7, r13 = - 0.4, r12 = 0.6
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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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- a. In an IV regression model with one endogenous regressor, X, and two instruments, Z1 and Z2, the value of the J-statistic is J = 18.2. This suggests that E(ui |Z1i, Z2i) = 0. Is it true or false? b. Suppose that a true population IV regression model contains one endogenous regressor, X, one exogenous regressor, W, and one instrument, Z. Assume that data on W are not available and the model is estimated omitting W from the regression. Suppose that Z and W are uncorrelated. Then the IV estimator is inconsistent. Is it true or false?arrow_forwardQ1. Consider the following cross-sectional population regression model relating the dependent variable Y, and regressor X, : Y, = Bo + BIXI + u, where i = 1,..,n, and X, = Y, + Z.. Assume that Cov(Z,u) 0. (a) Explain why X, is an endogenous regressor. (b) Show that Z, is a relevant instrument for X;. %3Darrow_forward2.An engineer at a semiconductor company wants to model the relationship between the device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to- Base RS (x3). The data are shown in the following table. X1 X2 X3 X1 X2 X3 y 14.620 226.000 7.000 128.400 15.500 230.200 5.750 97.520 15.630 220.000 3.375 52.620 16.120 226.500 3.750 59.060 14.620 217.400 6.375 113.900 15.130 226.600 6.125 111.800 15.000 220.000 6.000 98.010 15.630 225.600 5.375 89.090 14.500 226.500 7.625 139.900 15.380 229.700 5.875 101.000 15.250 224.100 6.000 102.600 14.380 234.000 8.875 171.900 16.120 220.500 3.375 48.140 15.500 230.000 4.000 66.800 15.130 223.500 6.125 109.600 14.250 224.300 8.000 157.100 15.500 217.600 5.000 82.680 14.500 240.500 10.870 208.400 15.130 228.500 6.625 112.600 14.620 223.700 7.375 133.400 (a) Fit a multiple linear regression model to the data. (b) Predict HFE (y) when x1 =14.5, x2 = 220, and x3 = 5.0.arrow_forward
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