数学report.docx
《数学report.docx》由会员分享，可在线阅读，更多相关《数学report.docx（11页珍藏版）》请在冰豆网上搜索。
数学report
TheResearchofNewHouseSalesinAustralia
AndItsFutureTrendAnalysis
Class03房子微Sally
Class03姚晗Destiny
Class03刘丁Dawn
Date:
03/06/2014
Content
1.0Introduction..................................................................................................................................2
2.0CalculationandAnalysis2
2.1LikelyInfluenceFactors3
2.1.1Season3
vStepsandcalculations3
vResult5
vAnalysis5
2.1.2Wages6
vStepsandcalculations6
vResult8
vAnalysis8
2.2FutureTrendAnalysis9
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.
2009
2010
2011
2012
2013
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
Q1
23440.75
Q2
23827.25
Q3
22180.5
Q4
22176.5
3.Calculatethemeanofallperiods.
meanofallperiods
22906.25
4.Calculateindexnumberofeachquarter.
Seasonalindexnumber=meanofeachquarter/meanofallperiods*100
index
Q1
1.023334243
Q2
1.040207367
Q3
0.968316508
Q4
0.968141883
5.Calculatethedeseasonalizedvalueofeveryquarterfrom2009to2013.
Deseasonalizedvalue=actualvalue/seasonalindexnumber*100
2009
2010
2011
2012
2013
Q1
20795.74699
21617.57036
19694.44504
15046.89216
14470.34545
Q2
20649.72878
21116.94331
19391.32585
14637.46603
15829.53604
Q3
23128.8012
19121.84689
17639.89343
14093.53233
17640.92615
Q4
21621.83082
19820.44197
18016.9873
14027.90257
18137.83735
6.Comparetheactualvaluetodeseasonalizedvaluefrom2009to2013（therankofeachquarter）.
Rank
2009
2012
3
3
1
1
2
4
2
2
1
1
3
3
4
2
4
4
2010
2013
1
1
4
4
2
2
3
3
4
4
2
2
3
3
1
1
2011
2
1
1
2
4
4
3
3
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.
vStepsandcalculations
1.Welettheaveragewagesandamountofnewhousesalestobethetwovariablesxandyrespectivelyanddrawascatterdiagram.
2.Wedoaroughestimatefortheirrelationbydrawingaregressionlinebyeye.
Itcanbeseenclearlythatthereisanegativerelationbetweenthenewhousesalesandpeople’swages.
3.Wecalculatethecorrelationcoefficienttohelpusknowthedegreeofcorrelationbyusingtheformula:
.
4.Wetestthesignificanceofcorrelationcoefficientbyusingthepvalue.
WecangetN=5,soN-2=3,and
0.83>0.805
vResult
Afterthecalculation,wegetthecorrelationcoefficientis-0.83whichcanrepresentahighnegativecorrelationbetweenwagesandnewhousesales.Thenwetestsignificanceofcorrelationcoefficientbyusingthepvaluewhichshowshowlikelytherelationshipisduetochance.Oursamplesizeis5sothedegreesoffreedomis3,thenwefindthepvaluetocomparewith0.83.Wecanfind0.83＞0.805thatmeanstherelationshipissignificantatthe0.1levelandp＜0.1.
vAnalysis
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.
vStepsandcalculations
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
2009
86,090
-2
-172,180
4
2010
81,793
-1
-81,793
1
2011
74,854
0
0
0
2012
57,852
1
57,852
1
2013
65,916
2
131,832
4
Total
366,505
0
-64,289
10
4.Calculatethevalueof‘a’and‘b’usingtheformula.Thenobtainthetrendline.
5.Findthreepoints’valueswithtimecodesof-2,0and2onthegraph.
-2（2009year）
0（2011year）
2（2013year）
73,301-6,428.9×（-2）
73,301-6,428.9×（0）
73,301-6,428
升级会员 