Essay Question: You have obtained measurements of height in inches of 29 female and 81 male students (Height) at your university. A regression of the height on a constant and a binary variable (Female), which takes a value of one for females and is zero otherwise, yields the following result: Height - 71.0 - 4.84Female, R2 = 0.40, SER = 2.0 (0.3) (0.57) (a) Calculate the average height of males. (b) Calculate the average height of females. (c) Calculate the difference between average height of males and females. (d) Suppose we run another regression using a binary variable (Male), which takes a value of one for males and is zero otherwise. In this regression, how large will be the coefficient estimator of Male? How large will R2 and SER be