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In Each of the Following Cases, Decide Whether the Given xt and ytx ^ { t } \text { and } y ^ { t }

Question 70

Essay

In each of the following cases, decide whether the given function is intrinsically linear. If so, identify xt and ytx ^ { t } \text { and } y ^ { t } and then explain how a random error term ε \varepsilon
can be introduced to yield an intrinsically linear probabilistic model.
a. y=1/(α+βx)y = 1 / ( \alpha + \beta x )
b. y=1/(1+eα+βx)y = 1 / \left( 1 + e ^ { \alpha+ \beta x } \right)
c.  In each of the following cases, decide whether the given function is intrinsically linear. If so, identify  x ^ { t } \text { and } y ^ { t }  and then explain how a random error term   \varepsilon     can be introduced to yield an intrinsically linear probabilistic model.  a.  y = 1 / ( \alpha + \beta x )   b.  y = 1 / \left( 1 + e ^ { \alpha+ \beta x } \right)   c.    (a Gompertz curve)  d.  y = \alpha + \beta e ^ { \lambda x }
(a Gompertz curve)
d. y=α+βeλxy = \alpha + \beta e ^ { \lambda x }

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