In each case below, determine whether, and under what assumptions, the stated relationship between \(Y\) and \(x\) can be represented in general linear model form such that the least squares estimator will provide a BLUE estimator of the \(\boldsymbol{\beta}\) parameters.

(a) \(Y_{i}=\exp \left(\sum_{j=1}^{n} x_{i j} \beta_{j}+\varepsilon_{i}ight)\)

(b) \(Y_{i}=\beta_{0}+\beta_{1} x_{i}+\beta_{2} x_{i}^{2}+\varepsilon_{i}\)

(c) \(Y_{i}=\beta_{0} \prod_{j=1}^{k} x_{i j}^{b_{j}}+\varepsilon_{i}\)

(d) \(Y_{i}=\frac{X_{2 i}}{1+e^{X_{1 i} \beta+\varepsilon_{i}}}\)