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?

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y = -0.83 +0.017x +0.0895x + 42.771x3 + 0.027x4 -0.0043xx4