For each one of the proposed link functions below indicate whether they obey the conditions:

it is strictly increasing,

it is continuously differentiable and

its range is all of \mathbb {R}.

Choose “Yes" only if the function does satisfy all of the conditions and choose “No" otherwise.

g(x)=x^2.

Yes

No
unanswered
g(x)=x^3-3.

Yes

No
unanswered
g(x)=1-e^{-x}.

Yes

No
unanswered
g(x)=\log x for x > 0 only.

Yes

No
unanswered

2 answers

No

Did you know?

Did you know that a link function is a function used in statistics to relate a linear predictor to a mean response in a generalized linear model? In analyzing these models, it is important to determine whether a proposed link function satisfies certain conditions. For example, if the function is strictly increasing, continuously differentiable, and has a range that includes all real numbers. Let's test our knowledge with a few examples: - g(x) = x^2: No. Although it is strictly increasing and continuously differentiable, its range is not all of ℝ. - g(x) = x^3 - 3: Yes. This function satisfies all the conditions. - g(x) = 1 - e^(-x): Yes. This function also satisfies all the conditions. - g(x) = log(x) for x > 0 only: No. While it is strictly increasing and its range is all of ℝ, it is not continuously differentiable at x = 0.