Problem 4E

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):

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.

a. 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.

c. 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.

d. Compute the coefficient of determination R2.

e. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected?

Environment Theories of the Environment and its Problems Globalization and the Environment Leading Environmental Problems o Destruction of Natural Habitats o Adverse Effects on Marine Life o Water Crisis o Climate Change and Global Warming Global Responses o Sustainable Development o Technological Fixes Environmental Consumption The fact that we consume “natural” and “organic” products as a status symbol suggests that we place some value on environmental concerns The irony is that many of these “ecofriendly” products actually do more harm to the environment o Think of Fiji water – it actually comes from Fiji, but half of the Fiji population