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3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2 and consider a problem of regressing y on two (qua(a) When considering the linear regression model y = E(e) 0, find the least squares estimates of Bo, Bi, and B2. B0B12 B2z2 €(b) Are the least squares estimates of B1 and B2 obtained in (a) unbiased when the true model includes an interaction term B1

3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2 and consider a problem of regressing y on two (qualitative) variables x\, xz. Data y (Income) x (Gender) X2 (Management Status) obs no. Female None 2 Male None 3 Female Yes 4 Male Yes Y4 To handle the qualitative variables x\, x2, we define dummy variables z1, 22 as Male for for 1, 1, T2= Yes Z1= Z2= -1 for for 1 1 = Female I2= None
(a) When considering the linear regression model y = E(e) 0, find the least squares estimates of Bo, Bi, and B2. B0B12 B2z2 € with
(b) Are the least squares estimates of B1 and B2 obtained in (a) unbiased when the true model includes an interaction term B12, that is E(y) = Bo +B121+B222+B122122? Explain
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Anawea:- 4,z21 we have 4 observationg for 3 variables Linear regression y fo+ A2,t fa^ate y.xptE is Medel of Linear eqecssion0102 ot P Pa+sf12 E are not unbaied estimato ond +ICnce

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