代写MATH38172 Generalised Linear Models Semester 2, 2023/24代写留学生Matlab语言

日期：2024-04-22 06:42

MATH38172 Generalised Linear Models

Semester 2, 2023/24

Coursework

Background: The?ile?drill.csv?on?Blackboard?contains?data?originally?described?by?Cuth-?bert?Daniel?in?his?1976?book?on?industrial?experimentation. ?It?contains?data?on?response?Y?-?the advance?rate?of?the?drill?and?four?factors,?X1?=?Drill?load,?X2?=?Flow?of?a?lubricant,?X3?=?Speed of?drill, X4 = Type?of?mud. Each?of?the?four?factor?variables?are?recoded?at?two?levels?each,?“High“?and?“Low“?.

(a) ?Describe?a?generalized?linear?model?to?the?advance?rate?response?with?gamma?as?response?distribution, include?all?four?regressors?in?the?linear?predictor?and?use?the?canonical?link?function.? ? ? ? ? ? ?[3]

(b)?Use?R?to?it?the?model?in?(a),?and?interpret?the?signs?of?the?parameter?estimates. ?????????????[3]

(c) ?Fit?a second gamma glm for?the?same?response?Y,?with?all?four?covariates,?using?the?log-link- function?and?interpret?the?signs?of?the?parameter?estimates. ??? ? ? ? ? [3]

(d) ?Compare?the?two?models?itted?in?parts?(b) and?(c).?Which?of?the?two?models?you?recommend and?why.??????????? ? ? ? ? ? ? ? ?[2]

(e)??Briely?explain?two?alternative?ways?of?testing?signiicance?of?a?parameter?and?apply?them?to?the?model?itted?in?(b)?for?the?parameter?corresponding?to?the?dummy?variable?for?the?covariate?X1?.? ? ? ? ? ? ? [4]

(f)?Explain?which?of?the?two?methods?from?(e)?might?be?better.? ? ? ? ? [1]

(g)?For?the?model?itted?in?part?(c)?expand?the?linear?predictor?to?include?all?six?of?the?two?-?factor?interactions?involving?the?four?covariates.?Compare?the?model?deviance?for?this?model to?the?model?deviance?from?part?(c). ?Are?the?additional?terms?in?the?model?useful?in?terms of?model?it??Justify?your?answer.? ? ?[4]

[Total?20?marks]