An analysis of footprints in sand. Fossilized human footprints provide a direct source of information on the gait dynamics of extinct species. To gain insight into this phenomenon, a group of scientists used human subjects (16 young adults) to generate footprints in sand (American Journal of Physical Anthropology, Apr. 2010). One dependent variable of interest was heel depth (y) of the footprint (in millimeters). The scientists wanted to find the best predictors of depth from among six possible independent variables. Three variables were related to the human subject (foot mass, leg length, and foot type) and three variables were related to walking in sand (velocity, pressure, and impulse). A stepwise regression run on these six variables yielded the following results:

a. Write the hypothesized equation of the final stepwise regression model.

b. Interpret the value of R2 for the model.

c. Conduct a test of the overall utility of the final stepwise model.

d. At minimum, how many t-tests on individual b’s were conducted to arrive at the final stepwise model?

e. Based on your answer to part

d, comment on the probability of making at least one Type I error during the stepwise analysis.

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Selected independent variables: pressure and leg length R2.771, Global F-test p-value