Question

Consider random variables \mathbf X= (X_1, X_2) and Y. Assume that the regression function \mu (x_1, x_2) = \mathbb E[Y \; |\; X = (x_1,x_2)] for a pair (X,Y) happens to be \mu (x) = (ax_1 + bx_2)^3. Which of the following is an appropriate choice for a link function g? In other words, for which g is it true that g(\mu (x)) can be written as a linear function, x^ T \beta for some \beta?



g(\mu ) = \log (\mu )

g(\mu ) = e^{\mu }

g(\mu ) = \mu ^3

g(\mu ) = \sqrt[3]{\mu }
unanswered
If instead \mu (x) = 2^{ax_1}, which of the following are appropriate choices for the link function g? Choose all that apply.



g(\mu ) = \log _2(\mu )

g(\mu ) = \ln (\mu )

g(\mu ) = e^{\mu }

g(\mu ) = \mu ^3

g(\mu ) = \sqrt[3]{\mu }