Suppose for a sample with n independent observations the...

Suppose for a sample with n independent observations the modelyi=0+1x1i+2x2i+ i, is considered, whereiare independent and identically distributed fromN(0,2). Additionally, the predictor variables are uncorrelated so that the following conditions are satisfied:

i=1n x1i=0, i=1nx2i=0, i=1nx1ix2i=0

Answer the each of the following questions for the case described above:

1. Write the model in matrix form:y=X+.Specify the elements in each cell ofy,X,,and
2. Calculate X'X and its inverse (X'X)^-1.
3. Calculateb, the least squares estimate of.
4. Calculate SS_reg(x₁, x₂₎
5. Provide the equations for SS_reg(x₁) and SS_reg(x₂) which correspond to the two simple linear regression models of y vs. x₁and y vs. x₂.
6. Compare SS_reg(x₁, x₂) from part d. and SS_reg (x₁) + SS_reg (x₂) from part e. Provide an explanation for this relationship.