Question

121 (15 Points! The Undergraduate Dean has been collecting data on the high school GPA (X) of incom- ing students for a long, long time. She has also kept track of Ist semester GPA (Y) for enrolled students over the same period of time. She would like to be able to predict a student's Ist semester GPA using their high school GPA. She reports to you the following means, variances and a covariance for X and Y: 12 L2x = y = 2 and o = 1/6,0 = 1/4,0 XY = 1/5. Because she has collected such a large sample you are free to treat these numbers as if they were population quantities. al 15 Points Calculate the a and associated with the mean square error minimizing) linear predictor of Y given X, E*[Y|X] = a + 3X? b 110 Points Say of 0 (e.g., only students with 4.0 GPAs have ever been admitted). What is the best linear predictor of Y given X in this case you may assume all other parameters stay the same)? Why? (2-4 sentences

Answer 1

Given Myz12/5 2 and 461 Say Y. Slope = B : Conu(ny) Vascriy) a 46 20% 21.2 La intercepe =4 - slope se - 2-1.2* 1915 -0.88 Hence y 0.88 + 1.2L * X when c²x=0 best estimate of y is 9 =2 Since & is constant, y should when we we the model not depend on a smuares of (uf-x) when we minimize Sum of we get az