In agriculture, a main cause of fatal injuries is tractor rollover. To combat this problem, tractor manufacturers have installed foldable rollover protection structures (FROPS). Human Factors (February 2020) published a study on the incorrect usage of FROPS. A sample of 20 farmers were recruited to drive tractors with FROPS installed. One common problem is incorrectly setting the vertical distance from the FROPS pivot pin to the top of the FROPS when in an upright position. This distance (in millimeters) was recorded for each of the 20 farmers as well as the farmer’s working experience (in years). The data (simulated from information provided by the study) are listed in the accompanying table.

a. Fit a simple linear regression model relating FROPS pivot pin-top distance (y) to farmer’s working experience (x). Give the least squares prediction equation.

b. Practically interpret the estimated y-intercept and slope of the model, part a.

c. Predict the pivot pin-top distance set by a farmer with 25 years of experience.

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Farmer (years) 123456789DHDSH 10 11 15 16 17 18 19 20 Exp (mm) 22 47 17 9 1 20 1 18 28 1 7 41 18 9 26 16 53 49 35 24 Distance 527 553 485 596 354 713 736 762 596 381 374 518 855 404 654 683 774 823 426 440