In regression analysis with (X1, X2, . . ., Xn) and (Yl, Y2, . .., Yn) such that Yi = Bo + BIXi+ ci where E 1 , E2 , . . . . En ~ N(0, 02 ) Let Bo and B1 be the maximum likelihood estimators for Bo, B1. 1. (2 points) If Xi denotes the # of hours a randomly selected undergrad i in Penn State spends studying for their courses, and the response variable Y denotes their GPA, provide a qualitative interpretation for the regression paramters Bo, B1. 2. (7 points) Write down the log-likelihood function (Bo, B1, 2) for the unknown parameters and using the fact that d e ( Bo, B1, 02 ) 1 ( Yi - Bo - BIXi)= 0 dBo Bo , B 1 i= 1 d e ( Bo, B1, 02 ) dB1 L( Yi - Bo - BIX: ) Xi = 0 Bo , BI show that the expression for B1 is given by B1 = SXY ELI (Xi - X) ( Y; - I) SXX Et( Xi - X) 2You may nd it useful to rst get an relationship for 30 and then show that :01 30 31151:)? = 0- i=1 Using this straightforward derivation you can write down the second likelihood equation in terms of in 20's 30 BIXz'XXi 2) i=1 and then solve it. 2. (3 points) Show that the regression line, given by the equation :1; = 50 + 513 always passes through the point ()7, 17)