Females, on Average, Are Shorter and Weigh Less Than Males $\widehat { \text { Studentw } }$

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 × Female + 5.58 × Height, $R ^ { 2 }$ =0.50, 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?
(b)You decide that in order to give an interpretation to the intercept you should rescale the height variable. One possibility is to subtract 5 ft. or 60 inches from your Height, because the minimum height in your data set is 62 inches. The resulting new intercept is now 105.58. Can you interpret this number now? Do you thing that the regression $R ^ { 2 }$ has changed? What about the standard error of the regression?
(c)You have learned that correlation does not imply causation. Although this is true mathematically, does this always apply?