Females, on Average, Are Shorter and Weigh Less Than Males $$\widehat { \text { Studentw } } = - 229.21 - 6.36 \times \text { Female } + 5.58 \times \text { Height } , R ^ { 2 } = 0.50 , \text { SER } = 20.99$$

Essay

Females, on average, are shorter and weigh less than males.One of your friends, who is a
pre-med student, tells you that in addition, females will weigh less for a given height.To
test this hypothesis, you collect height and weight of 29 female and 81 male students at
your university.A regression of the weight on a constant, height, and a binary variable,
which takes a value of one for females and is zero otherwise, yields the following result: $$\widehat { \text { Studentw } } = - 229.21 - 6.36 \times \text { Female } + 5.58 \times \text { Height } , R ^ { 2 } = 0.50 , \text { SER } = 20.99$$ where Studentw is weight measured in pounds and Height is measured in inches.
(a)Interpret the results.Does it make sense to have a negative intercept?