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In the punting data, we find the average distance punted and hang times of 10 punts of an American football as related to various measures of leg strength for 13 volunteers

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In the punting data, we find the average distance punted and hang times of 10 punts of

an American football as related to various measures of leg strength for 13 volunteers.

     + Fit the regression model with Distance as the response and the right and left leg

strength and flexibilities as predictors. Which predictors are significant at the 5%

level?

     + Use an F-test to determine whether collectively these four predictors have a relation-

ship to the response.

     + With respect to the model in (a), test whether the right and left leg strength have

the same effect. Hint: use "I()" in the model declaration. See the lecture notes.

     + Fit a model to test the hypothesis that the total leg strength (defined by adding the

right and left leg strengths) is sufficient to predict the response, compared to a model

which uses both left and right leg strengths as two predictors in the model.

     + With respect to the model in (a), test whether the right and left leg flexibilities have the same effect.

     + Test for left-right symmetry by performing the tests in (c) and (e) simultaneously,

that is, the null hypothesis is that the right and left leg flexibilities have the same

effect AND the right and left leg strength have the same effect.

     + Fit a model with Hang as the response and the same four predictors. Make comments

on the model. Can we make a test to compare this model to that used in (a)? Explain.