3) "A linear regression model is of the form:
Y = β0 + β1*X1 + β2*X2 + ... + βk*Xk + ε "
(i) Y = β0 + β1*X + β2*exp(X) + ε
(ii) Y = β0 + β1*X1 + β2*X2 + β3*(X1*X2) + β4*(X1)^2 + β5*(X2)^2 + ε
For (i), X1=X, X2=exp(X)
For (ii), X3=X1*X2, X4=X1^2, X5=X2^2
The latter X's depends on the previous X's. In particular, X3 depends on TWO of the previous X's: X1 AND X2, are those allowed? Somehow I am having a lot of troubles understanding this...I understand the general form of a multiple linear regression model, but I don't seem to understand the specific examples of it like (i) and (ii).