The article "Application of Analysis of Variance to Wet Clutch Engagement" (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117-125) presents the following fitted model for predicting clutch engagement time in seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m (x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4): y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x, The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate is 10 kN/s. b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not. Is it possible to predict the change in engagement time associated with an increase of 2 N•m in maximum drive torque? If so, find the predicted change. If not, explain why not. a. C. Compute the coefficient of determination R?. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected? d. e.
The article "Application of Analysis of Variance to Wet Clutch Engagement" (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117-125) presents the following fitted model for predicting clutch engagement time in seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m (x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4): y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x, The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate is 10 kN/s. b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not. Is it possible to predict the change in engagement time associated with an increase of 2 N•m in maximum drive torque? If so, find the predicted change. If not, explain why not. a. C. Compute the coefficient of determination R?. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected? d. e.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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Transcribed Image Text:The article "Application of Analysis of Variance to Wet Clutch Engagement" (M.
Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers,
2002:117-125) presents the following fitted model for predicting clutch engagement time in
seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m
(x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4):
y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x,
The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was
SSE = 0.036310. There were 44 degrees of freedom for error.
Predict the clutch engagement time when the starting speed is 20 m/s, the maximum
drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate
is 10 kN/s.
b. Is it possible to predict the change in engagement time associated with an increase of 2
m/s in starting speed? If so, find the predicted change. If not, explain why not.
Is it possible to predict the change in engagement time associated with an increase of 2
N•m in maximum drive torque? If so, find the predicted change. If not, explain why
not.
a.
C.
Compute the coefficient of determination R?.
Compute the F statistic for testing the null hypothesis that all the coefficients are equal
to 0. Can this hypothesis be rejected?
d.
e.
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