Question

3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider a problem of regressing y on two (qualitative) variables r, 2. Data: 22 obs no. y (Income) 2 (Management Status) I (Gender) 1 None Female 2 None Male Yes Female Yes Male 4 To handle the qualitative variables r, 12, we define dummy variables 1, 22 as for 1, 22= Yes Male for 1, 219 22 -1. for 22= None for 1= Female -1, (a) When considering the linear regression model y B+B121 + B222 +e with E(e) = 0, find the least squares estimates of , B, and B 4 0 0 X X- oo4 -L 4x 2A2 Pht Pr Z L-(YPA,-A2) E(G-P-A 2-Ps 2.) 0 A-RA 0-23-24-3 2,2 42,-24- P -Sx7 Ph 2,14-312 (b) Are the least squares estimates of B, and 3, obtained in (a) unbiased when the true that is E(y) Przy model includes an interaction term &+821+82+B1212 Explain. 4. (20 pts) Consider the following regression model, Y B+B + G i 1,2,...,n, where e, i 1,2,..,n are independent, but e, N(0, o0) (a) Do you think if it is suitable for the (ordinary) least square regression technique to apply the data (z, Y)? Give a brief reasoning. NO hecwse f heohlcedgt Violated freiy (b) Construct a transformed model so that you can use the ordinary least square method. -2 p. 6,

Answer 1

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