Tractor rollover protection. Refer to the Human Factors (February 2020) study of the incorrect usage of installed foldable rollover protection structures (FROPS) for tracFROPS tors, Exercise 11.23 (p. 659). Recall that a sample o 20 farmers were recruited to drive tractors with FROPS installed. Two variables were measured: y = the vertical distance (in millimeters) from the FROPS pivot pin to the top of the FROPS when in an upright position and x = the farmer’s working experience (in years). The data (simulated from information provided by the study) are reproduced in the accompanying table. Farmer Exp (years) Distance (mm) 1 22 527 2 47 553 3 17 485 4 9 596 5 1 354 6 20 713 7 1 736 8 18 762 9 28 596 10 1 381 11 7 374 12 41 518 13 18 855 14 9 404 15 26 654 16 16 683 17 53 774 18 49 823 19 35 426 20 24 440

a. Give the equation of a curvilinear (quadratic) model relating FROPS pivot pin-top distance (y) to farmer’s working experience (x).

b. The quadratic model was fit to the data and the results shown in the Minitab printout below. Give the least squares prediction equation.

c. Explain why the estimated value of b0 has no practical interpretation.

d. Explain why the estimated value of b1 should not be interpreted as a slope.

e. Examine the estimated value of b2 to determine the nature of the curvature (upward or downward) in the sample data.

f. Conduct a test to determine if the pivot pin-top distance is curvilinearly related to farmer’s working experience. Use a = .10.