Refertotheexample in Section 6.2.5 of thecrimerateinFloridacounties.

(a) Explainwhatitmeanswhenwesaythesedataexhibit Simpson’sparadox. Whatcould cause thischangeinthedirectionoftheassociationbetweencrimerateandeducation when weadjustforurbanization?

(b) Usingthe Florida data file,constructthescatterplotbetween x = education (HS) and y = income (Income), forwhichthecorrelationis0.79.Ifwehaddataattheindividual levelaswellasaggregatedforacounty,sketchascatterplottoshowthatatthatlevel the correlationcouldbemuchweaker.So,predictionsaboutindividualsbasedonthe behaviorofaggregategroups,knownasthe ecologicalfallacy, canbequitemisleading.

(c) Referto(b),inwhich x falls between54.5and84.9.Isitsensibletousetheleastsquares line topredictacounty’smedianincomeif x = 0? Sketchahypotheticaltruerelationship between x and E(Y ) to showthedangerof extrapolation, usingafittedlinetopredict E(Y ) far fromtheobserved x values.