To measure the takeoff performance of an airplane, the horizontal position of the plane was measured every second, from t = 0 to t = 12. The positions (in feet) were: 0, 8.8, 29.9, 62.0, 104.7,159.1,222.0,294.5, 380.4,471.1, 571.7,686.8, and 809.2.

a. Find the least-squares cubic curve y = β₀ + β_{1 +} β₂ t² + β₃t³ for these data.

b. If a machine learned the curve given in part (a), what would it estimate the velocity of the plane to be when t = 4.5 seconds?