CHAPTER 2 THE CLASSICAL MULTIPLE LINEAR REGRESSION MODEL 2 Example 2 Class attendance and test sco res B1+B2 fraction of lectures attended +B3 ffraction of problem sets completed+ ei See Romer, Journal of Econo mic Perspectives, 1998 2.2 Classical Assumptions Linearity B1=1+…+Bk=K+E1(1=1+…+ 6+ 1 +B where = (l=1+…+K) XB+E K X 721 Loglinear model ln:=61+2ln=+……+Bkln=x+E aIn Br(const ant elasticity)CHAPTER 2 THE CLASSICAL MULTIPLE LINEAR REGRESSION MODEL 2 Example 2 Class attendance and test scores scorei = β1 + β2 (fraction of lectures attended) i +β3 (fraction of problem sets completed) i + εi See Romer, Journal of Economic Perspectives, 1993. 2.2 Classical Assumptions 1. Linearity yi = β1xi1 + · · · + βkxiK + ε1 (i = 1, · · · , n) = x ′ iβ + εi where xi =   xi1 . . . xiK   , β =   β1 . . . βK   or y = x1β1 + · · · + xKβK + ε where y =   y1 . . . yn   , xl =   x1l . . . xnl   (l = 1, · · · , K) ε =   ε1 . . . εn   or y = Xβ + ε where X =     x11 · · · x1K . . . xn1 · · · xnK     , β =     β1 . . . βK     Loglinear model: ln y = β1 + β2 ln x2 + · · · + βK ln xK + ε ∂ ln y ∂ ln xk = βk (constant elasticity)