FortheScottishhillracesdata(Section 6.1.4) inthe ScotsRaces data file,itisplausiblethat the recordtimesaremorevariableathighervaluesofdistanceandclimb.

(a) Usingtheidentitylinkfunction,fitthegammaGLMtothewomen’srecordtimeswith distance andclimbasexplanatoryvariables.Describehowtheestimatedconditionalstan-

dard deviationoftheresponserelatestotheestimatedmean.Specifyhowitchanges betweentheminimumandmaximumestimatedmeanvaluesforthissample.Isitclose to constant,likethenormalmodelassumes?

(b) AccordingtoAIC,whichisthepreferredmodelwithidentitylink,thegammaGLMor the normalGLM?

(c) FitthegammaGLMpermittinginteractionbetweendistanceandclimbintheireffects.

Describehowtheeffectonrecordtimeofa1 km increase indistancechangesbetween the minimumandmaximumclimbvaluesof0.185and2.40 km.