Question

01. We know that the quadratic model $E(Y|X) = eta_0 + eta_1X + eta_2X^2$ can be handled in a linear regression framework although it is non-linear in X (but linear in $eta_0$, $eta_1$ and $eta_2$). Suppose the model is nonlinear in the parameters, for ex., $E(Y|X) = eta_0X^{eta_1}$. (i) Can you think about a way of linearizing this conditional expectation? (ii) Are there any issues arising in estimating this model following your answer to a) in the linear regression framework? 02. Prove or disprove the statement: ""The standard error estimate of the slope coefficient does not depend on whether you include an intercept or not in the OLS regression.""

          01. We know that the quadratic model $E(Y|X) = eta_0 + eta_1X + eta_2X^2$ can be handled in a linear regression framework although it is non-linear in X (but linear in $eta_0$, $eta_1$ and $eta_2$).
Suppose the model is nonlinear in the parameters, for ex., $E(Y|X) = eta_0X^{eta_1}$.
(i) Can you think about a way of linearizing this conditional expectation?
(ii) Are there any issues arising in estimating this model following your answer to a) in the linear regression framework?
02. Prove or disprove the statement: ""The standard error estimate of the slope coefficient does not depend on whether you include an intercept or not in the OLS regression.""

01. We know that the quadratic model E(Y|X) = eta0 + eta1X + eta2X^2 can be handled in a linear regression framework although it is non-linear in X (but linear in eta0, eta1 and eta2).
Suppose the model is nonlinear in the parameters, for ex., E(Y|X) = eta0X^eta1.
(i) Can you think about a way of linearizing this conditional expectation?
(ii) Are there any issues arising in estimating this model following your answer to a) in the linear regression framework?
02. Prove or disprove the statement: ""The standard error estimate of the slope coefficient does not depend on whether you include an intercept or not in the OLS regression.""

Added by Carmen F.

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