Suppose that y, is an independent response variable (i = 1.....n) with mean , such that g(i) = n₂ = X₁B, where g(.) is a link function, X, is a vector of covariates and is a px 1 vector of coefficients. Let the variance of y, be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pr) (Yi - Pi) + Ni wi = [V (pi) (g'(pi))²]-¹ where g'(μ) = 9(μ) 8 (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?
Suppose that y, is an independent response variable (i = 1.....n) with mean , such that g(i) = n₂ = X₁B, where g(.) is a link function, X, is a vector of covariates and is a px 1 vector of coefficients. Let the variance of y, be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pr) (Yi - Pi) + Ni wi = [V (pi) (g'(pi))²]-¹ where g'(μ) = 9(μ) 8 (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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![Suppose that y, is an independent response variable (i = 1.....n) with mean, such
that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3
is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.)
is a known function and is a scale parameter.
Given:
Zi= g'(pi) (Yi - Pi) + Ni
w₁ = [V (pi) (g'(pi))²]-¹
8
where g'(μ) = 9(μ)
(a) Show that E(Z₁) = X₂B
(b) Show that Var (Z₁) = w¹o.
(c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found
8, find the Var(8) and E(3). What do you conclude?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2393a88-6b8c-41e1-9d25-6d49f7f7e10c%2Ff7ba3941-335a-4450-8091-432439252a08%2F3w3qi1i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that y, is an independent response variable (i = 1.....n) with mean, such
that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3
is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.)
is a known function and is a scale parameter.
Given:
Zi= g'(pi) (Yi - Pi) + Ni
w₁ = [V (pi) (g'(pi))²]-¹
8
where g'(μ) = 9(μ)
(a) Show that E(Z₁) = X₂B
(b) Show that Var (Z₁) = w¹o.
(c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found
8, find the Var(8) and E(3). What do you conclude?
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