For context, the image below is from a January 2024 past paper in statistical modeling Exercise 2Let (y1,...,y5) and (36,..., 910) be two independent samples from a Poisson distribution of meanexp{1} and from a Poisson distribution of mean exp{ẞ1 + ẞ2}, respectively.a) Formulate an appropriate Poisson regression model for the expected value of Yi, i =1,..., 10.b) Write the log-likelihood function of ẞ= (B1, B2) and the score function. Find the maximumlikelihood estimate of (B1, B2). Finally, obtain the observed information matrix.c) Determine an approximate distribution of the maximum likelihood estimator of B(B1, B2), and an approximate distribution of the maximum likelihood estimator B₁ of ẞ₁.d) Provide the interpretation of the coefficient ẞ2.=e) Define the concept of "saturated model" and obtain the expression of maximum of thelog-likelihood for this model.

Step 1: Step 2: Step 3: Step 4:

Answered: Exercise 2 Let (y1,...,y5) and (36,...,…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

See similar textbooks

Similar questions

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
A standard logistic regression models the effect of age (20-29, 30-39, 40-49, 50-59, 60- 69) on experience of back pain (modeling yes vs. no). If age is included as a continuous covariate (with values 1, 2, 3, etc., as scores) and the regression parameter associated with age is estimated to be 0.21 with standard error of 0.08, a likelihood-ratio hypothesis test is performed to see whether age could be considered as continuous (as assumed above) or categorical. Having proven nesting, how many degrees of freedom would be associated with sampling distribution of the likelihood ratio test statistic?
5
Perform a a Pearson’s correlation in SPSS to determine whether the weight of an automobile (‘weight’: Vehicle Weight-lbs) is significantly correlated with its horsepower (‘hp’: horse power). Use a two-tailed test with α = .01 The alternative hypothesis in symbols and null hypothesis in words is:
When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errors tend to underestimate the sampling variation in the B;? Is it always true that the OLS standard errors are too small?
Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a = 3 and unknown. Find the Minimum Variance Unbiased Estimator for B. Show your work, and explain how you know your estimator is the MVUE.
Consider the model (1-B)(1-0.2B)X_t = (1-0.5B)W_t find the forecasts for one, two and three steps ahead and calculate the variance of the one, two, and three steps ahead forecast errors
Can logistic regression be used in both prospective and retrospective study? Will the odds ratios of the effect of the predictor on the response are different under these two study designs? What formula can we use to solve maximum likelihood estimate of regression coefficient beta in Poisson regression (with log link)? can ridge regression be applied if sample size is smaller than the number of predictors? if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?
Weekly downtime of internet services from an internet service provider (in hours) has expected value 0.5 and variance 0.25. Based on past experience, the data scientist of a retailer store has calculated the loss function to the store from the downtime as C=30X+2X2 where X is the amount of weekly downtime and C is cost. Find the Expected cost, i.e, E(C).
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)
Consider data 5,1,3,5,5,4,3,2 of the Poisson distribution with expectation u. We want to test H0:u=u0 with u0=2. Write the log-likelihood for the data under H0 and the likelihood ratio A(y) for testing H0

SEE MORE QUESTIONS

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS