General Linear Regression

Question 1

Binomial, θ

Answer 1

ln[π / (1 − π)]

Question 2

Binomial, b(θ)

Answer 2

n ln(1 + e^θ)

Question 3

Binomial, φ

Answer 3

1

Question 4

Normal, θ

Answer 4

μ

Question 5

Normal, b(θ)

Answer 5

θ² / 2

Question 6

Normal, φ

Answer 6

σ²

Question 7

Poisson, θ

Answer 7

ln λ

Question 8

Poisson, b(θ)

Answer 8

e^θ

Question 9

Poisson, φ

Answer 9

1

Question 10

Gamma, θ

Answer 10

−γ / α

Question 11

Gamma, b(θ)

Answer 11

−ln(−θ)

Question 12

Gamma, φ

Answer 12

1 / α

Question 13

Inverse Gaussian, θ

Answer 13

−1 / (2μ²)

Question 14

Inverse Gaussian, b(θ)

Answer 14

−√(−2θ)

Question 15

Inverse Gaussian, φ

Answer 15

1 / λ

Question 16

Negative Binomial, θ

Answer 16

ln(1 − p)

Question 17

Negative Binomial, b(θ)

Answer 17

−r ln(1 − e^θ)

Question 18

Negative Binomial, φ

Answer 18

1

Question 19

Normal Canonical Link

Answer 19

Canonical Link: Identity
Mathematical Form: g(μ) = μ

Question 20

Binomial Canonical Link

Answer 20

Canonical Link: Logit
Mathematical Form: g(π) = ln[π / (1 − π)]

Question 21

Poisson Canonical Link

Answer 21

Canonical Link: Natural log
Mathematical Form: g(μ) = ln μ

Question 22

Gamma Canonical Link

Answer 22

Canonical Link: Inverse
Mathematical Form: g(μ) = 1 / μ

Question 23

Inverse Gaussian Canonical Link

Answer 23

Canonical Link: Squared inverse
Mathematical Form: g(μ) = 1 / μ²