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3rd and 4th question please thank yo

3rd and 4th question please thank yo

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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just 3rd and 4th question please thank you

1500 Income 1000 500 0 Lo 30 OXC 00000 2) Hint: Use the definition of the Fisher information I(B) = =-E where log L(B) is the log-likelihood function. 40 Show that the Fisher information is given by 1(3) = C-12² O O 8 mag 2000 ooooo O (1 log L(3)) ΟΦΟ 0 10 20 Hours Consider a linear regression model given by Yi~ N(Bx₁,0²), i=1,2,...,n, where y₁,..., yn are independent. The pdf of y, is given by (Yi — ßx;)²` f(y; B,0)= 1 exp √2π0² 20² 1) We aim to find the maximum likelihood estimator of 3. Do the following questions. We assume the variance o2 is known. a) Write down the likelihood function and log-likelihood function of 3. b) Show that the MLE is Fiyi = Hint: Show that the MLE 3 is solution to the score equation d log L(3) = 0, dß where log L(B) is the log-likelihood function. 50 O O@ 18 ∞ 00 O 60 O 70
Transcribed Image Text:1500 Income 1000 500 0 Lo 30 OXC 00000 2) Hint: Use the definition of the Fisher information I(B) = =-E where log L(B) is the log-likelihood function. 40 Show that the Fisher information is given by 1(3) = C-12² O O 8 mag 2000 ooooo O (1 log L(3)) ΟΦΟ 0 10 20 Hours Consider a linear regression model given by Yi~ N(Bx₁,0²), i=1,2,...,n, where y₁,..., yn are independent. The pdf of y, is given by (Yi — ßx;)²` f(y; B,0)= 1 exp √2π0² 20² 1) We aim to find the maximum likelihood estimator of 3. Do the following questions. We assume the variance o2 is known. a) Write down the likelihood function and log-likelihood function of 3. b) Show that the MLE is Fiyi = Hint: Show that the MLE 3 is solution to the score equation d log L(3) = 0, dß where log L(B) is the log-likelihood function. 50 O O@ 18 ∞ 00 O 60 O 70
3) Suppose the summary statistics are Σ²279226 Ei=1=4765273 • ở=210.18 • n=200 Do the following questions. a) Calculate the value of 3 and SE(3) (SE of 3). Hint: The SE is calsulated by SE(3) = √(3) where I(3) is the Fisher information. b) Do the test of slope Ho: B=0 vs H₁ : 3/0, at a = 0.05. i) State the distribution of the test statistics. ii) Find the value of the test statistic and p-value. iii) Calculate the 95% confidence interval for ß. iv) State the conclusion. 4) Write down the assumptions of the linear regression. Are the assumptions of the linear regression satisfied? Give reasons.
Transcribed Image Text:3) Suppose the summary statistics are Σ²279226 Ei=1=4765273 • ở=210.18 • n=200 Do the following questions. a) Calculate the value of 3 and SE(3) (SE of 3). Hint: The SE is calsulated by SE(3) = √(3) where I(3) is the Fisher information. b) Do the test of slope Ho: B=0 vs H₁ : 3/0, at a = 0.05. i) State the distribution of the test statistics. ii) Find the value of the test statistic and p-value. iii) Calculate the 95% confidence interval for ß. iv) State the conclusion. 4) Write down the assumptions of the linear regression. Are the assumptions of the linear regression satisfied? Give reasons.
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