The impact of dropping hollow balls was investigated in the American Journal of Physics (Mar. 2014). Standard ping-pong balls were dropped vertically onto a force plate. Upon impact, two variables were measured: y = coefficient of restitution, COR (measured as a ratio of the speed at impact and rebound speed) and x = speed at impact (meters/ second). Of the 19 balls dropped, 10 buckled at impact. The data (simulated from information provided in the article) are listed in the table.
a. Conduct a complete simple linear regression analysis of the relationship between coefficient of restitution (y) and impact speed (x). Write all your conclusions in the words of the problem.
b. The researcher believes that the rate of increase in the coefficient of restitution with impact speed differs depending on whether the ping-pong ball buckles. Do the data support this hypothesis? Explain.

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Ball CORY Speed x Buckle 945 .950 0.8 1.0 No No 2 930 .920 .920 3 1.5 1.8 3.0 No 4 No No .930 3.4 No .905 .915 4.4 5.0 No No 8. .910 .900 .885 .870 850 6.4 4.4 No Yes 10 11 5.3 Yes 12 13 5.4 7.4 Yes Yes 14 .795 .790 .800 7.2 Yes 7.2 8.0 8.5 15 16 Yes Yes 17 .820 Yes .810 .780 18 19 9.4 9.0 Yes Yes