D$,3\mathrm{.}45[$EX$03-045]$ Sports drinks are very popular in today's culture around the world. The following table lists $10$ different products you can buy in Engiand and the val. ues for three variables: cost per serving $($in pence$),$ energy per serving $($in kilocalories$),$ and carbohydrates per serving $($in grams$).$

$\backslash$table$[[$Sports Drink,Cost,Energy,Carbs$],[$Lucozade Sport RTD $330$ml pouch$/$can$,72,92,21\mathrm{.}1],[$Lucozade Sport RTD $500$ml bot.,$79,140,32],[$Lucozade Sport RTD $650$ml sports bot.,$119,182,41\mathrm{.}6],[$POWERade $500$ml bot.,$119,120,30],[$Gatorade Sports $750$ml$,89,188,45],[$Science in Sport Go Electrolyte $(500ml),99,160,40],[$High Five lsotonic electrolyte $(750$ml$),99,220,55],[$Isostar powder $($per litre$)51$ tub,$126,320,77],[$Isostar RTD $500$ml bot.,$99,150,35],[$Maxim Electrolyte $($per litre$)2$kg bag,$66,296,75]]$

Note: Cost is in pence $($p$),0\mathrm{.}01$ of a British pound, worth $$0\mathrm{.}0187$ on March $28,2005$

Source: htip:$//$umw$.$simplyrunning.net

a$.$ Draw a scatter diagram using $x=$ carbs$/$serving and $y=$ energy$/$serving$.$

b$.$ Does there appear to be a linear relationship?

c$.$ Calculate the linear correlation coefficient, $r.$

d$.$ What does this value of correlation seem to be telling us$?$ Explain.

e$.$ Repeat parts a through d using $x=$ cost$/$serving and $y=$ energy$/$serving$.($Retain these solutions to use in Exercise $3\mathrm{.}59,$ p$.157.)$