In his famous experiments on gravity and motion in 1608, Galileo rolled a ball down a ramp that was sitting at the edge of a table, recording the release height above the table top H, and the...

In his famous experiments on gravity and motion in 1608, Galileo rolled a ball down a ramp that was sitting at the edge of a table, recording the release height above the table top H, and the horizontal distance D, from the end of the table at which the ball hit the floor. Our modern knowledge of physics implies the model

Where γ and δ are constants that are functions of the table height, ramp angle, and acceleration of gravity. Galileo carefully controlled H while simply observing D so H should be thought of as the independent variable and D as the dependent variable. Solving for D and adding an error term, we find

(a) Regress D2 on HD and H (with no intercept). Even though D is the independent variable this should give rough initial estimates of γ and δ.

(b) Now we want to fit the model using the estimates from (a) as initial values. Compute the partial derivatives of E(D) =
 with respect to the parameters γ and δ. Fit the correct version of the model in which D is treated as the dependent variable as shown previously.