In the Process of Collecting Weight and Height Data from 29

question 41

Essay

In the process of collecting weight and height data from 29 female and 81 male students
at your university, you also asked the students for the number of siblings they have.
Although it was not quite clear to you initially what you would use that variable for, you
construct a new theory that suggests that children who have more siblings come from
poorer families and will have to share the food on the table.Although a friend tells you
that this theory does not pass the "straight-face" test, you decide to hypothesize that peers
with many siblings will weigh less, on average, for a given height.In addition, you
believe that the muscle/fat tissue composition of male bodies suggests that females will
weigh less, on average, for a given height.To test these theories, you perform the
following regression: $$\begin{array}{l}\begin{array} { l } \widehat { \text { Studentw } } = - 229.92 - 6.52 \times \text { Female } + 0.51 \times \text { Sibs } + 5.58 \times \text { Height } , \\ \quad \quad \quad \quad \quad \quad \quad(44.01)(5.52) \quad \quad \quad \quad \quad \quad(2.25) \quad \quad \quad\quad(0.62) \\\end{array}\\\\R ^ { 2 } = 0.50 , S E R = 21.08\end{array}$$ where Studentw is in pounds, Height is in inches, Female takes a value of 1 for females
and is 0 otherwise, Sibs is the number of siblings (heteroskedasticity-robust standard
errors in parentheses).
(a)Carrying out hypotheses tests using the relevant t-statistics to test your two claims
separately, is there strong evidence in favor of your hypotheses? Is it appropriate to use
two separate tests in this situation?

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