Refer to the American Journal of Physics (Mar. 2014) study of the impact of dropping ping-pong balls, Exercise 11.122 (p. 638). Recall that 19 standard ping-pong balls were dropped vertically onto a force plate. The data on y = coefficient of restitution (COR, measured as a ratio of the speed at impact and rebound speed), x1 = speed at impact (meters/second), and x2 = 51 if ball buckled, 0 if not6 are reproduced in the table on p. 713. Consider the interaction model E(y) = β0 + β1x1 + β2x2 + β3x1x. A MINITAB print out of the regression analysis is also shown on p. 713.
Data for Exercise 12.106

a. Give the equation of the hypothesized line relating COR (y) to impact speed (x1) for ping-pong balls that did not buckle. What is the estimated slope of this line?
b. Repeat part a for ping-pong balls that buckled.
c. The researcher believes that the rate of increase in COR with impact speed differs depending on whether the ping-pong ball buckles. Do the data support this hypothesis?
Conduct the appropriate test using a = .05.

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COR SPEED BUCKLE Ball X1 X2 O (No) O (No) O (No) 0 (No) O (No) 0 (No) O (No) O (No) O (No) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) 1 (Yes) .945 0.8 1.0 1.5 1.8 .950 3 4 .930 .920 .920 3.0 6. .930 .905 3.4 4.4 8. .915 5.0 .910 .900 6.4 4.4 10 11 885 870 5.3 5.4 12 13 .850 7.4 14 15 .795 .790 7.2 7.2 16 .800 8.0 17 18 820 .810 8.5 9.4 19 .780 9.0 , খ, ৭ন Regression Analysis: COR versus SPEED, X2, SPEED_X2 The regression equation is COR - 0.944 - 0.00637 SPEED + 0.0398 X2 - 0.0151 SPEED_X2 Predictor Coef SE Coef Constant 0.94433 0.01256 75.17 0.000 SPEED -0.006374 0.003545 -1.80 0.092 X2 0.03977 0.03121 1.27 0.222 SPEED X2 -0.015089 0.005260 -2.87 0.012 S = 0.0194826 R-Sa = 90.78 R-Sq (adj) = 88.8% Analysis of Variance Source DF MS 3 0.055556 0.018519 48.79 0.000 Regression Residual Error 15 0.005694 0.000380 Total 18 0.061250