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

question 54

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 × 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?

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Definitions:

Reflection

The process of thoughtfully considering one's experiences in order to gain deeper insights or understanding.

Cultural Story

A cultural story is a narrative or account that reflects the beliefs, values, norms, and practices of a particular group or society, often passed down through generations.

Ancestors

Individuals from whom one is descended, typically further back than grandparents.

Communication Patterns

The habitual ways in which individuals exchange information, ideas, and feelings with others.