Cohen et al. (2010) [3] analysed the handgrip (HG) strength in relation to gender and age in English schoolchildren. Here each student is required to analyse a different sample of 1000 from the original 3766 English boys. The data are stored in the packages gamlss.data under the name grip and contain the variables gripand age. The aim here isto create centile curvesfor grip given age. (a) Read the data file by typing data(grip)into R. Note that the gamlss packages have to be downloaded first i.e. library(gamlss). (b) In order to select your individual sample a unique seed number will be given to you. (In the example below we use the seed number 243 for demonstration.) Select your individualsample using your own seed number: set.seed(243) index<-sample(3766,1000) mydata<-grip[index, ] dim(mydata) (c) Plot grip against age. Note that there is no need to power transform the agein this data set. Explain why. (d) Use the LMS method to fit the data1. That is, fit the BCCG distribution for grip. gbccg <- gamlss(grippb(age),sigma.fo=pb(age),nu.fo=pb(age),data=da, family=BCCG), where the smoothing for age uses the P-splines function pb(), i.e. pb(age), for the predictors for parameter , and . How many degrees of freedom were used for smoothing in the model? Use the function edf()or edfAll(). (e) Use the fitted values from the LMS model in (d) as starting values for fitting the BCT and the BCPE distributions to the data, e.g. gbct <- gamlss(grippb(age),sigma.fo =pb(age), nu.fo = pb(age),tau.fo =pb(age),data=da,family=BCT,start.from=gbccg) What are the effective degrees of freedom fitted for the parameters? Try to interpret the effective degrees of freedom. (f) Use the generalised Akaike information criterion, GAIC, to compare the three models. (g) Plot the fitted parameters for the fitted models in (d) and (e) using for example fitted.plot(gbccg, gbct,x=da$age) where gbccg and gbct are the BCCG and BCT models respectively. (h) Obtaina centileplotforthe fittedmodelsin (d) and(e)using centiles() or centiles.split() and compare them. (i) Investigate the residuals from the fitted models in (d) and (e) using e.g. plot(), wp() (worm plot) andQ.stats()(Q-statistics). (j) Choose between the models and give a reason for your choice. (k) Use residual diagnosticsfor checking the model (l) Comment on how you selected yourfinal model. (m) Comment on the final centile plots.