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Chapter 4

# STATS 10 Chapter Notes - Chapter 4: Batter Up, Scatter Plot, Dependent And Independent Variables

Department
Statistics
Course Code
STATS 10
Professor
Cha, M
Chapter
4

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Pratishtaξ ξNatarajan
UID:ξ ξ504786348
Section:ξ ξ1A
Statisticsξ ξLabξ ξ2-ξ ξBatterξ ξUp
1) Iξ ξhaveξ ξattachedξ ξtheξ ξgraphξ ξforξ ξat_batsξ ξandξ ξrunsξ ξbelow:
ξ ξξ ξξ ξξ ξξ ξξ ξξ ξFromξ ξtheξ ξgraphξ ξweξ ξcanξ ξseeξ ξthatξ ξasξ ξtheξ ξnumberξ ξofξ ξat_batsξ ξincreases,ξ ξtheξ ξnumberξ ξofξ ξruns
increasesξ ξasξ ξwell.ξ ξSoξ ξthisξ ξgraphξ ξshowsξ ξusξ ξthatξ ξtheξ ξrelationξ ξisξ ξpositive.ξ ξEvenξ ξthoughξ ξtheξ ξgraph
increasesξ ξoverall,ξ ξitξ ξdoesξ ξnotξ ξincreaseξ ξuniformly,ξ ξie:ξ ξtheξ ξvariablesξ ξareξ ξonlyξ ξmoderately
correlated.ξ ξSoξ ξfromξ ξthisξ ξgraphξ ξweξ ξcanξ ξseeξ ξthatξ ξthisξ ξvariableξ ξnotξ ξtheξ ξmostξ ξaccurateξ ξtoξ ξpredict
theξ ξnumberξ ξofξ ξrunsξ ξbecauseξ ξweξ ξcanξ ξonlyξ ξconcludeξ ξthatξ ξifξ ξtheξ ξnumberξ ξofξ ξat_batsξ ξareξ ξhigher,
theξ ξteamβsξ ξrunsξ ξareξ ξhigherξ ξtoo.ξ ξWeξ ξcannotξ ξpredictξ ξtheξ ξexactξ ξnumberξ ξofξ ξrunsξ ξaξ ξteamξ ξwould
scoreξ ξbyξ ξonlyξ ξlookingξ ξatξ ξtheξ ξnumberξ ξofξ ξat_bats.
2)ξ ξξ ξIξ ξhaveξ ξattachedξ ξtheξ ξresidualξ ξplotξ ξbelow:
Theξ ξrelationshipξ ξbetweenξ ξat_batsξ ξandξ ξrunξ ξisξ ξlinear.ξ ξTheξ ξplotsξ ξareξ ξrandomlyξ ξscatteredξ ξacross
theξ ξhorizontalξ ξaxis.ξ ξThereforeξ ξaξ ξlinearξ ξmodelξ ξisξ ξmoreξ ξappropriateξ ξtoξ ξrepresentξ ξtheξ ξdata.
Inξ ξaddition,ξ ξtheξ ξpointsξ ξdoξ ξnotξ ξformξ ξaξ ξβUβξ ξorξ ξandξ ξβInvertedξ ξUβξ ξshape.ξ ξThereforeξ ξweξ ξcanξ ξsee
thatξ ξaξ ξnon-linearξ ξmodelξ ξwouldξ ξnotξ ξbeξ ξappropriateξ ξtoξ ξexplainξ ξtheξ ξdata.

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3)ξ ξIξ ξhaveξ ξattachedξ ξtheξ ξgraphξ ξforξ ξwhereξ ξIξ ξwouldξ ξputξ ξaξ ξsingleξ ξmovableξ ξline,ξ ξifξ ξIξ ξhadξ ξto
summarizeξ ξtheξ ξgraph.ξ ξIξ ξhaveξ ξalsoξ ξaddedξ ξtheξ ξβSumξ ξofξ ξSquaresβξ ξtoξ ξit
Theξ ξsumξ ξofξ ξsquaresξ ξis-ξ ξ160600
Nowξ ξIξ ξhaveξ ξattachedξ ξtwoξ ξotherξ ξgraphs,ξ ξthatξ ξdoξ ξnotξ ξfitξ ξtheξ ξdataξ ξasξ ξwellξ ξasξ ξtheξ ξfirstξ ξgraphξ ξdoes:
Weξ ξcanξ ξseeξ ξthatξ ξtheξ ξsumξ ξofξ ξsquaresξ ξforξ ξtheseξ ξgraphsξ ξareξ ξ201400ξ ξandξ ξ245400ξ ξrespectively.
Soξ ξweξ ξcanξ ξseeξ ξthatξ ξtheξ ξsumξ ξofξ ξsquaresξ ξreduces,ξ ξandξ ξisξ ξtheξ ξleastξ ξwhenξ ξtheξ ξlineξ ξbestξ ξfitsξ ξthe
data.
Thisξ ξisξ ξbecauseξ ξtheξ ξsumξ ξofξ ξsquaresξ ξisξ ξtheξ ξsquareξ ξofξ ξtheξ ξspreadξ ξbetweenξ ξeachξ ξdataξ ξpoint
fromξ ξtheξ ξmean.ξ ξSinceξ ξweξ ξareξ ξtryingξ ξtoξ ξfindξ ξaξ ξlineξ ξthatξ ξfitsξ ξtheξ ξdataξ ξtheξ ξbest,ξ ξtheξ ξspreadξ ξneeds
toξ ξbeξ ξasξ ξlittleξ ξasξ ξpossible.ξ ξSoξ ξtheξ ξlineξ ξofξ ξbestξ ξfitξ ξwillξ ξminimizeξ ξtheξ ξsumξ ξofξ ξsquares.ξ ξWhichξ ξis
whyξ ξtheξ ξfirstξ ξgraphξ ξhasξ ξtheξ ξleastξ ξpossibleξ ξsumξ ξofξ ξsquaresξ ξforξ ξthisξ ξdata.
4)ξ ξBelowξ ξIξ ξhaveξ ξattached,ξ ξtheξ ξduplicateξ ξofξ ξtheξ ξgraphsξ ξIξ ξhaveξ ξusedξ ξinξ ξtheξ ξpreviousξ ξquestion.ξ ξI
haveξ ξchangedξ ξtheξ ξβMovableξ ξLineβξ ξtoξ ξtheξ ξβLeastξ ξSquaresξ ξLineβ