数学reportWord文档格式.docx

数学reportWord文档格式.docx

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vStepsandcalculations9

vResult:

11

vAnalysis11

3.0ConclusionandRecommendation12

Reference13

1.0Introduction

Inrecentyears,withtheincreasingpopulation,thedemandofsomenecessitiesoflifesuchashousesisgoingupatthesametime.Therefore,theproblemofhousinghasalreadybecomeafocusofattentionaroundtheworld.ThisreportwillstudythehousesalesissueinAustraliabyanalyzingtwolikelyfactors（seasonandwages）whichmayinfluencetheamountofnewhousesalesfromyear2009to2013,andpredictingthefuturetrendofhouseselling.Theaimofitistohelpthelandagentsdealwellwiththerelationbetweenhousesupplyandhousedemandandgainmoreprofits.Theanalysisinthisreportwillbedividedintothreeparts.Thefirstpartwillanalyzetheinfluenceofseasonusingthemethodofindexnumber.Thenextpartwillshowtherelationbetweenpeoplewagesandthenewhousesaleswiththemethodofcorrelationandregressionanalysis.Thelastpartforecastthefuturetrendbythemethodoftimeseriesanalysis.ThedatausedinthisreportarethenumberofAustralianeverymonth’snewhousesalesandaveragewagesoflocalpeoplefrom2009to2013.AllthesedataaresecondarydatawhichwerecollectedinthewebsitecalledTradingeconomics.

（）.

2.0CalculationandAnalysis

Inordertobalancethenewhousesupplyanddemand,wecandotwothingsbycalculatingandanalysis.TheoneisthatweneedtoknowwhatwillinfluencethenewhousesalesinAustralia,andchangetheamountofsupplyrelyonthesefactorstoexactlysatisfycustomers’demandandavoidsurplusorshortage.Theotheroneistopredictthefuturetrendofnewhousesales,anditcanalsohelpachievethesamegoalthatmentionedabove.

2.1LikelyInfluenceFactors

Seasonandwagesaretwocommonfactorswhichwillinfluencepurchasingpower.Therefore,weassumetheywillinfluencenewhousesalesaswell,andthen,wedosomecalculationandanalysistoproveourassumption.

2.1.1Season

Inthissection,weusetheindexnumberanalysistointerpretseasonalvariation.Theprocessofremovingtheseasonalinfluencesfromdataiscalleddeseasonalizationofdataorseasonaladjustment.Inordertodothiswecanuseaseasonalindex.Theseasonalindexisanumberwhichisaweightedproportionoftheannualnumbersthatoccurinaparticularquarterortimeperiod（VICTORIAUNIVERSITY2013,p299）.Therefore,thisreportusestheseasonalindexnumbertoanalyzetheinfluenceofseasontothenewhousesales.Thesimpleaveragemethodisusedtocalculatetheseasonalindex.

vStepsandcalculations

1.Collectthenewhousesalesforeachmonthsfrom2009to2013onthewebsite.

2009

2010

2011

2012

2013

1

6667

7567

6522

5230

5008

2

7200

7208

6623

5344

4806

3

7414

7347

7009

4824

4994

4

7496

7788

7036

5133

5327

5

6983

7331

6870

5028

5373

6

7001

6847

6265

5065

5766

7

7024

6348

5701

4787

5399

8

7855

6134

5785

4510

5712

9

7517

6034

5595

4350

5971

10

7002

6438

5684

4264

5698

11

7060

6366

6114

4502

5903

12

6871

6385

5645

4815

5959

2.Takethreemonthasaquarter,andcalculatetheaverageamountofeachquarter.

Q1

21281

22122

20154

15398

14808

Q2

21480

21966

20171

15226

16466

Q3

22396

18516

17081

13647

17082

Q4

20933

19189

17443

13581

17560

Mean=sum/amount

mean

23440.75

23827.25

22180.5

22176.5

3.Calculatethemeanofallperiods.

meanofallperiods

22906.25

4.Calculateindexnumberofeachquarter.

Seasonalindexnumber=meanofeachquarter/meanofallperiods*100

index

1.023334243

1.040207367

0.968316508

0.968141883

5.Calculatethedeseasonalizedvalueofeveryquarterfrom2009to2013.

Deseasonalizedvalue=actualvalue/seasonalindexnumber*100

20795.74699

21617.57036

19694.44504

15046.89216

14470.34545

20649.72878

21116.94331

19391.32585

14637.46603

15829.53604

23128.8012

19121.84689

17639.89343

14093.53233

17640.92615

21621.83082

19820.44197

18016.9873

14027.90257

18137.83735

6.Comparetheactualvaluetodeseasonalizedvaluefrom2009to2013（therankofeachquarter）.

Rank

vResult

Thetrendof3outof5yearsarenotchange（2010,2012,2013）,andtheother2yearsarealsoonlychangeforalittle（2009,2011）.

vAnalysis

Wecancomparedthedeseasonalizedvaluetotheactualvalueofeachyear,ifitshowsthesametrend,itmeansseasonmakesnodifferenttothesales;

however,iftheyaredifferent,itmeansseasonisanimportantfactortothenewhousesales.

Inthisreport,wecomparedthe2values,andfoundthatthetrendsofthe2valuesarequitesimilar.Therefore,thisreportarguesthatthefactorofseasonhaveinfluenceonthenewhousesalesinAustraliafrom2009to2013,butitonlyhaveverylittleinfluence.Thus,seasonmaynotbeanessentialfactorwhichcaninfluencenewhousesalesinAustralia.

2.1.2Wages

Inthissection,weusethecorrelationandregressionanalysistointerprettherelationbetweennewhousesalesandpeople’swages.Correlationandregressionanalysisisusedtodescribethestrengthanddirectionoftherelationshipbetweentwovariables（VICTORIAUNIVERSITY2013,p233）.Whenstudytherelationshipbetweennewhousesalesandpeople’s,first,inregressionanalysispart,wedecidetodrawtheregressionlinebyeyejusttohelpushavearoughestimateoftheirrelation;

andthen,incorrelationanalysispart,wedecidetousePearsonProduct-MomentCorrelationCoefficient（r）toknowtheircorrelationindetail.

1.Welettheaveragewagesandamountofnewhousesalestobethetwovariablesxandyrespectivelyanddrawascatterdiagram.

2.Wedoaroughestimatefortheirrelationbydrawingaregressionlinebyeye.

Itcanbeseenclearlythatthereisanegativerelationbetweenthenewhousesalesandpeople’swages.

3.Wecalculatethecorrelationcoefficienttohelpusknowthedegreeofcorrelationbyusingtheformula:

.

4.Wetestthesignificanceofcorrelationcoefficientbyusingthepvalue.

WecangetN=5,soN-2=3,and

0.83>

0.805

Afterthecalculation,wegetthecorrelationcoefficientis-0.83whichcanrepresentahighnegativecorrelationbetweenwagesandnewhousesales.Thenwetestsignificanceofcorrelationcoefficientbyusingthepvaluewhichshowshowlikelytherelationshipisduetochance.Oursamplesizeis5sothedegreesoffreedomis3,thenwefindthepvaluetocomparewith0.83.Wecanfind0.83＞0.805thatmeanstherelationshipissignificantatthe0.1levelandp＜0.1.

TheresultofcalculationhasshownusthehighcorrelationbetweenAustraliannewhousesalesandpeople’swageswhichmeanswagesisanimportantinfluencefactorofnewhousesales.Manypeoplemaywonderwhythemoremoneypeopleearnthelesshousestheydemand.Thereasonisthathouseisadurableandnecessaryproductforpeople.Whentheyearnmoremoneyanditisenoughforthemtobuytheirhousesinthisyear,theycanbuynewhouseinthisyearimmediatelybecausetheyneedhousestolive;

andnextyear,althoughtheirincomeisstillincreasing,theywillnothavetobuyanothernewhousebecauseonehouseisenoughforthem,anditcanbeusedinseveraldecades.Asaresult,morewagesmakemorepeoplehaveabilitytobuytheirhousesin“thisyear”andlessin“nextyear”,thus,itshowsanegativerelationbetweennewhousesalesandpeople’swages.

2.2FutureTrendAnalysis

Inthissection,weusethetimeseriesanalysistoforecastthenumberofAustraliannewhousesalesinthefuture.Timeseriesanalysisisusedtopredictwhatmayhappeninthefutureonthebasisofwhathasbeenhappeninginthepass（VICTORIAUNIVERSITY2013,p264）.Whenwearestudyingthefuturetrendofnewhousesalesbycalculation,theLeastSquaresMethodisadopted.

1.Plotthesalesofnewhousesfrom2009to2013onagraphinpolygonformat.Jointheminadottedline.

2.Makeafrequencytabletotabulatethisinformation.

3.Codethetimeonx-axis.Becausefiveyearsisanoddnumber,labelthemidpointas‘0’andotherpointsaspositiveornegativewholenumberdeviationfrom‘0’.Accordingly,thecodedtimeare-2,-1,0,1and2.

Year

Sales（y）

CodedTime（x）

（xy）

（x）²

86,090

-2

-172,180

81,793

-1

-81,793

74,854

57,852

65,916

131,832

Total

366,505

-64,289

4.Calculatethevalueof‘a’and‘b’usingtheformula.Thenobtainthetrendline.

5.Findthreepoints’valueswithtimecodesof-2,0and2onthegraph.

-2（2009year）

0（2011year）

2（2013year）

73,301-6,428.9×

（-2）

（0）

73,301-6,428