STATISTICA e ANALISI DEI DATIhomes.di.unimi.it/.../DIDATTICA_CORRENTE/Presentazione.pdf– S.M....

STATISTICAe

ANALISIDEIDATIAnnaMariaZanaboni

a.a.2017-2018

•  LaboratorioR–  Ladatadiinizioverràcomunicataabreve– Orario:venerdìore13:30÷15:30inaulaSigma(viaComelico)

•  Libriditesto:–  S.M.Ross,Introduzioneallasta/s/cacapitoli1,2,3(file.pdfscaricabiledallapaginadelcorso)

–  S.M.RossProbabilitàesta/s/caperl'ingegneriaelescienzecapitoli3÷6.

•  Modalitàd’esame:scriPoeorale.•  Giornodiricevimento:mercoledì(megliofissareappuntamento).

OBIETTIVI

Imparareatrovareunastru9urainuninsiemedida<numerici.

Imparareau<lizzareunambienteswper

l'analisideidati

{{0.710092,-18.2225},{0.565454,-81.8565},{-0.1274,-134.421},{0.417912,-120.628},{1.12213,-45.368},{0.178557,-119.482},{0.495325,-58.5924},{1.09786,-76.4347},{0.0271511,-136.42},{0.0906889,-87.971},{0.19436,-6.74525},{0.0452912,-107.415},{0.456358,-135.438},{0.417204,-145.927},{0.402263,-155.835},{1.13475,-61.4509},{0.799572,-143.172},{1.30649,-57.2208},{1.02107,-74.099},{1.0119,-62.1304},{1.10039,-129.351},{0.11354,-19.1097},{0.102894,-131.521},{-0.0935822,-144.342},{-0.21638,-166.602},{0.69627,-106.94},{0.19797,-63.2517},{0.704803,-123.802},{1.16612,-100.418},{0.20269,-130.246},{-0.144751,-103.378},{0.821015,-134.59},{0.21744,-137.275},{1.5746,-153.721},{1.3346,-103.266},{-0.462383,-115.348},{0.663197,-117.963},{0.529933,-54.0715},{0.645478,-134.805},{1.23889,-95.35},{1.04612,-133.105},{0.612551,-161.248},{0.465924,-64.066},{1.22268,-138.762},{-0.299188,-75.4095},{0.543175,-109.635},{0.678719,-136.605},{0.464176,-87.8055},{1.22218,-125.83},{-0.0330844,-103.58},{1.47175,-128.058},{0.859696,-46.8414},{0.62067,-167.154},{0.648528,-132.757},{0.97625,-130.352},{0.57194,-72.861},{1.01028,-148.84},{0.0807798,-194.863},{-0.44879,-118.325},{-0.051338,-105.543},{1.71552,-117.891},{0.613718,-120.964},{0.665887,-154.656},{0.402458,-64.5185},{-0.175281,-106.809},{1.75,-77.2716},{1.1798,-172.992},{0.705925,-161.186},{0.875914,-80.0396},{0.594895,-148.132},{1.50284,-106.239},{0.168132,-178.799},{0.690921,-122.113},{0.439347,-138.902},{1.29697,-105.994},{0.451993,-84.6452},{0.479123,-90.0067},{0.818112,-155.195},{1.20527,-136.617},{0.849426,-98.9684},{1.04819,-153.676},{0.901653,-163.447},{0.465961,-149.621},{1.60092,-150.58},{0.913755,-166.084},{1.05155,-179.03},{0.459528,-156.278},{0.489138,-178.82},{0.4435,-166.966},{1.49346,-88.9365},{0.782538,-119.285},{1.35868,-121.118},{1.22962,-154.638},{0.20743,-159.891},{0.555005,-169.546},{1.06764,-219.575},{1.68064,-143.533},{0.795375,-158.506},{0.606271,-104.951},{0.909233,-181.866},{1.04704,-174.706},{1.30006,-125.681},{1.24612,-88.8497},{1.30054,-114.349},{0.709528,-135.751},{0.590466,-134.564},{1.5109,-127.706},{1.19459,-206.055},{1.18128,-206.618},{0.903637,-146.191},{1.24333,-129.033},{1.23449,-130.948},{1.72988,-157.845},{0.319633,-66.406},{0.704979,-232.991},{1.35204,-147.983},{1.35748,-166.538},{0.0506471,-189.386},{2.27738,-194.2},{1.35269,-157.186},{1.26302,-135.275},{0.787876,-138.954},{0.863245,-145.949},{0.662091,-148.309},{1.42299,-151.95},{1.43574,-155.29},{2.38252,-191.456},{1.10922,-141.957},{0.764069,-139.331},{1.71561,-178.403},{0.542383,-179.555},{0.770924,-73.5006},{0.728597,-145.064},{2.04332,-222.666},{1.37036,-161.15},{1.12461,-168.451},{2.311,-155.347},{1.26205,-179.897},{0.855385,-122.253},{1.73907,-166.582},{1.78492,-187.313},{1.18773,-174.36},{0.613875,-175.6},{0.779283,-165.795},{0.885717,-164.461},{0.918674,-159.143},{1.8761,-193.011},{0.633895,-157.965},{0.206849,-189.125},{1.87292,-193.212},{1.74252,-143.499},{1.97104,-162.029},{2.54319,-195.883},{1.04125,-131.88},{0.774023,-149.011},{1.87403,-106.323},{1.62635,-150.972},{2.03436,-160.11},{1.54391,-174.134},{2.13594,-116.642},{1.77106,-151.093},{1.09607,-205.574},{0.591637,-141.992},{1.1368,-183.321},{0.461925,-207.992},{0.188702,-164.344},{1.77394,-121.091},{2.01091,-132.164},{1.03507,-191.316},{1.76173,-206.757},{1.67845,-216.521},{2.03589,-154.851},{1.37626,-151.732},{2.00542,-169.234},{0.575718,-203.013},{1.55744,-182.875},{1.53278,-193.483},{1.4055,-187.001},{1.66153,-108.187},{1.95592,-203.483},{1.20091,-202.238},{1.65577,-188.316},{1.23158,-189.646},{1.06758,-201.778},{1.80534,-134.651},{1.52769,-177.312},{2.41685,-236.624},{1.72435,-151.585},{1.04738,-175.15},{1.18268,-159.073},{1.29865,-190.074},{1.74239,-165.928},……….}

{{1.18305,3.18063},{1.29217,2.91633},{1.09232,2.52092},{1.5775,4.15827},{1.66027,4.15176},{1.0308,2.48082},{1.75631,4.72763},{1.34028,3.10023},{1.19545,3.20266},{1.65219,4.24704},{1.23794,3.14047},{1.13332,2.69799},{1.94989,5.14956},{1.65459,4.27413},{1.18806,2.9566},{1.86858,4.81171},{1.82211,4.60017},{1.77019,4.83629},{1.26101,3.17979},{1.22052,3.5568},{1.23324,3.06159},{1.88442,4.81505},{1.11026,2.91586},{1.8981,4.25932},{1.45411,3.91084},{1.08977,2.62984},{1.82039,4.5377},{1.19746,3.11141},{1.76936,4.77749},{1.15851,2.82745},{1.12022,3.16177},{1.88658,4.62487},{1.93827,5.06573},{1.39083,3.24145},{1.82698,4.22939},{1.06513,2.68742},{1.75252,4.11496},{1.30326,3.93918},{1.03279,2.5849},{1.07612,2.2076},{1.34445,3.30795},{1.34132,3.50538},{1.59938,3.84937},{1.13983,3.11632},{1.5383,4.21247},{1.62369,3.77758},{1.81632,4.38036},{1.43439,3.85942},{1.85506,4.66058},{1.74013,4.07322},{1.00955,2.8147},{1.85848,4.43149},{1.28006,3.27824},{1.71736,4.32576},{1.97236,4.70774},{1.24554,2.81985},{1.34889,3.5413},{1.7149,4.30648},{1.30315,3.22144},{1.23551,3.20572},{1.64886,3.48595},{1.3038,3.63925},{1.73179,4.31892},{1.32069,3.32242},{1.91422,5.08381},{1.68787,4.11302},{1.49238,3.44804},{1.41034,3.33452},{1.95647,4.77962},{1.4596,3.73609},{1.13702,2.20284},{1.12678,2.96523},{1.26433,3.12324},{1.77981,4.49964},{1.84218,4.8582},{1.86441,4.64705},{1.34723,3.3724},{1.94815,4.35564},{1.20338,3.11984},{1.35405,3.30324},{1.85442,4.97288},{1.03321,2.86312},{1.51191,4.34284},{1.72105,4.30888},{1.03366,2.12411},{1.63081,3.67418},{1.64852,3.77084},{1.32083,3.53748},{1.50742,3.63697},{1.33026,3.19759},{1.88594,4.9402},{1.35711,2.84692},{1.59844,4.39322},{1.91104,4.72739},{1.62135,3.50851},{1.93455,4.56229},{1.00739,2.7193},{1.3449,3.648},{1.57734,4.14928}}

PERCORSOdidaFco

1.AnalisidescriFvaQualisonoletecniche

persinte<zzareuninsiemediosservazionipurtenendocontodella

lorovariabilità?

7333 69 79 155 19'gen'11 1 Right RLL 119 4 0 M 12,5 0,297 5 B1 6170 5790 13,5 37,4 64,6 23,47227 75 83 166 13'nov'10 10 None RLL 95 2 0 M 8 0,647 16 C ; ; ; ; ; ;7225 80 181 23'nov'10 7 Left LLL 99 1 0 M 6,5 0,26 4,1 C ; ; ; ; ; ;7228 42 55 170 24'dic'10 16 None LLL 0 0 0 M 8 0,372 7 B1 17270 8040 16,2 51,8 64,5 20,17226 16 186 18'nov'10 1 None RUL 0 1 1 F 3 0,534 12 C 16580 7160 15 42,8 35 59,77229 56 90 175 04'dic'10 1 None LLL 131 0 M 2 0,39 7,5 C 12700 7980 19,4 49,6 62,1 24,37230 68 83 180 18'dic'10 5 None RUL 88 2 0 M 4,5 0,297 5 B2 8420 15,3 42,3 68,5 24,87231 80 80 176 28'dic'10 7 None LLL 150 4 0 M 2 0,225 3,3 C 6730 6120 13,9 62,2 22,87232 61 79 172 12'dic'10 9 None RLL,;LLL 0 M 5 0,44 9 C 8470 16,6 44,6 61,8 237234 62 162 29'nov'10 2 RLL,;LLL 98 0 0 M 3,5 0,504 11 C 9110 7800 17,7 50,1 64,37233 43 6 147 28'dic'10 2 None LUL 53 3 0 M 1 0,335 6 C 9130 7290 16,8 43,8 60,1 237235 74 52 160 14'dic'10 2 Right RLL,;LLL 2 1 F 5,5 0,407 8 C 10560 7180 16,4 50,1 32,8 69,87236 75 66 162 26'nov'10 7 None RLL 75 2 0 M 17,5 0,273 4,4 C 7770 7670 17,8 61,5 23,27237 77 53 160 02'dic'10 11 None UNS 12345 3 1 F 5 0,782 21,2 B1 11340 7270 17 45,1 62 23,47239 79 145 03'dic'10 10 None LLL 89 1 F 19,5 0,777 21 B1 ; ; ; ; ; ;7248 82 42 148 21'nov'10 10 None LLL 102 3 0 M 4,5 0,44 9 C 10680 5580 12,1 36,3 65,1 21,77247 46 77 173 27'nov'10 10 Right RLL 0 1 1 F 3 0,896 26 B1 ; ; ; ; ; ;6756 68 81 166 03'lug'10 4 None LUL 83 2 0 M 0 0,335 6 C 8870 6050 10,4 47,1 78 17,16747 20 105 186 06'giu'10 3 None LLL 65 1 1 F 0 0,777 21 C 19200 6760 15,5 45,2 66,86 22,936757 80 93 168 15'lug'10 4 None LUL 80 1 0 M 4,5 0,504 11 B1 4680 8110 15,5 46,4 57,3 19,16738 126 187 03'giu'10 10 BilateralLLL 98 1 F 0 0,534 12 C 19200 6760 15,5 45,2 66,86 22,936737 83 66 170 27'mag'10 6 None LUL 113 2 0 M 0 0,297 5 B2 6610 8020 16,5 48,9 61 20,56763 66 74 152 25'lug'10 4 None RUL 86 111 0 M 0 0,44 9 C 9100 7340 15,8 46,6 63,4 21,56736 53 103 153 20'mag'10 4 None UNS 63 1 0 M 0 0,592 14 C 12000 7200 16,4 45,4 ; ;6751 51 170 12'giu'10 5 None LLL 76 0 0 M 0 0,316 5,5 B1 7420 5610 14,1 42,4 75,6 25,26720 62 96 170 07'mag'10 3 UNS 0 0 M 0 0,534 12 C 8450 7920 17,4 52,8 66,6 226749 67 66 172 13'giu'10 2 None RML,;LUL 92 2 0 M 0 0,407 8 C 16030 7030 16,2 45,2 64,3 236748 53 54 164 09'giu'10 2 None RUL 83 1 0 M 7 0,424 8,5 C 11180 5420 12,4 36 66,4 22,86755 55 83 190 03'lug'10 1 None RLL 75 0 0 M 0 0,472 10 C 5800 5680 13,5 37,3 65,8 23,86752 87 74 177 18'giu'10 3 None RUL 172 3 0 M 0 0,225 3,3 C 11530 6500 15,1 44,9 69,1 23,36753 48 69 185 27'giu'10 Left RUL,;RML,;LLL 103 1 0 M 0 0,279 4,55 C 13880 6660 16,1 42,4 63,6 24,16735 93 171 14'mag'10 5 None RLL 2 0 M 0 0,7 18 C 11080 5090 11,6 32,4 63,6 22,87313 55 73 176 04'nov'10 11 Right UNS 115 1 0 M 0 0,297 5 C 14900 7000 16,7 48,7 69,6 23,8

¢¢

¢

¢

¢

¢

¢

¢ ¢ ¢ ¢ ¢

Missingvalues


Outliers

•  Riassumerepervalutareacolpod'occhio{69,75,42,16,56,68,80,61,43,74,75,77,79,82,46,68,20,80,83,66,53,51,62,67,53,55,87,

48,93,55,61,26,66,88,59,81,37,37,68,85,68,36,64,61,88,75,76,81,77,61,65,74,49,91,82,70,78,21,95,58,71,75,29,79,67,80,75,74,69,83,87,77,88,73,102,82,87,81,89,71,71,71,79,53,46,80,84,82,47,50,83,43,76,99,71,76,67,58,73,55,66,72,90,75,39,88,76,83,85,74,39,54,64,66,86,59,92,62,61,59,76,85,92,59,79,68,94,73,75,91,73,60,93,90,85,66,63,82,59,70,78,74,80,92,89,86,70,85,74,68,74,55,69,76,72,62,38,55,79,84,85,81,77,83,68,85,72,89,74}

•  Riassumerepervalutareacolpod'occhio{69,75,42,16,56,68,80,61,43,74,75,77,79,82,46,68,20,80,83,66,53,51,62,67,53,55,87,

48,93,55,61,26,66,88,59,81,37,37,68,85,68,36,64,61,88,75,76,81,77,61,65,74,49,91,82,70,78,21,95,58,71,75,29,79,67,80,75,74,69,83,87,77,88,73,102,82,87,81,89,71,71,71,79,53,46,80,84,82,47,50,83,43,76,99,71,76,67,58,73,55,66,72,90,75,39,88,76,83,85,74,39,54,64,66,86,59,92,62,61,59,76,85,92,59,79,68,94,73,75,91,73,60,93,90,85,66,63,82,59,70,78,74,80,92,89,86,70,85,74,68,74,55,69,76,72,62,38,55,79,84,85,81,77,83,68,85,72,89,74}

EMPIRICCUMULATIVEDISTRIBUTIONFUNCTION

•  Riassumereidactramitetabelle

•  Riassumereidactramitetabelle

TABELLEDIC

ONTINGENZA

•  Riassumereidactramiteindici{69,75,42,16,56,68,80,61,43,74,75,77,79,82,46,68,20,80,83,66,53,51,62,67,53,55,87,48,93,55,61,26,66,88,59,81,37,37,68,85,68,36,64,61,88,75,76,81,77,61,65,74,49,91,82,70,78,21,95,58,71,75,29,79,67,80,75,74,69,83,87,77,88,73,102,82,87,81,89,71,71,71,79,53,46,80,84,82,47,50,83,43,76,99,71,76,67,58,73,55,66,72,90,75,39,88,76,83,85,74,39,54,64,66,86,59,92,62,61,59,76,85,92,59,79,68,94,73,75,91,73,60,93,90,85,66,63,82,59,70,78,74,80,92,89,86,70,85,74,68,74,55,69,76,72,62,38,55,79,84,85,81,77,83,68,85,72,89,74}

INDICIDIPOSIZ

IONE

•  Riassumereidactramiteindici{16,20,21,26,29,36,37,37,38,39,39,42,43,43,46,46,47,48,49,50,51,53,53,53,54,55,55,55,55,55,56,58,58,59,59,59,59,59,60,61,61,61,61,61,62,62,62,63,64,64,65,66,66,66,66,66,67,67,67,68,68,68,68,68,68,68,69,69,69,70,70,70,71,71,71,71,71,72,72,72,73,73,73,73,74,74,74,74,74,74,74,74,75,75,75,75,75,75,75,76,76,76,76,76,76,77,77,77,77,78,78,79,79,79,79,79,80,80,80,80,80,81,81,81,81,82,82,82,82,82,83,83,83,83,83,84,84,85,85,85,85,85,85,85,86,86,87,87,87,88,88,88,88,89,89,89,90,90,91,91,92,92,92,93,93,94,95,99,102}

Ordiniamoidac:

INDICIDIDISPER

SIONE

•  Riassumereidactramiteindici

INDICIDICORRELAZIONE

2.CalcolodelleProbabilità

C’èunmodellochedàragionedella“casualità”delleosservazoni?

48 49 50 51 52 53

0.2

0.4

0.6

0.8

1.0

48 49 50 51 52 53

0.2

0.4

0.6

0.8

1.047 48 49 50 51 52 53

0.1

0.2

0.3

0.4

0.5

50 100 150

0.005

0.010

0.015

0.020

0.025

0.030

0.035

50 100 150

0.2

0.4

0.6

0.8

1.0

50 100 150

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 70.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 70.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7

0.2

0.4

0.6

0.8

1.0

•  Calcolocombinatorio•  Definizioneassiomaccadellaprobabilità•  Teoremielementari•  Variabilicasuali•  Modelliprobabiliscci

3.InferenzaSta<s<ca

Qualisonoletecnichepergeneralizzareirisulta<dell’analidescriFvaacasinonancoraosserva<,purtenendocontodell’incertezzanelleconclusioni?

PopolazioneX=etàdeiconsumatoridiunadatamarcadicaramelle

{69,75,42,16,56,68,80,61,43,74,75,77,79,82,46,68,20,80,83,66,53,51,62,67,53,55,87,48,93,55,61,26,66,88,59,81,37,37,68,85,68,36,64,61,88,75,76,81,77,61,65,74,49,91,82,70,78,21,95,58,71,75,29,79,67,80,75,74,69,83,87,77,88,73,102,82,87,81,89,71,71,71,79,53,46,80,84,82,47,50,83,43,76,99,71,76,67,58,73,55,66,72,90,75,39,88,76,83,85,74,39,54,64,66,86,59,92,62,61,59,76,85,92,59,79,68,94,73,75,91,73,60,93,90,85,66,63,82,59,70,78,74,80,92,89,86,70,85,74,68,74,55,69,76,72,62,38,55,79,84,85,81,77,83,68,85,72,89,74}

Campionecasuale

Realizzazionicampionarie

…......

•  Perchépiùosservazionisihannomeglioè?

LEGGEDEBOL

EDEIGRANDI

NUMERI

•  Comepossousareilcampioneperfareunascmacheriguardal’interapopolazione?

•  Comepossovalutareseloscmatorecheuclizzoèunbuonscmatore?

ERROREQUADRATICOMEDIO

•  Comepossocontrollarel’errorecheinevitabilmentecompioquantofacciounascma?

INTERVALLIDICONFIDENZA

Unas/madell’etàmediadiunconsumatoredicaramelledellamarcaconsiderataè70anni.Unintervallodiconfidenzaallivello95%perl’etàmediadiunconsumatoredicaramelledellamarcaconsideratahaestremi(38,102).

Questoèilprimopassoformacvonecessarioperpoteraffrontareanalisipiùcomplesse,

tramitetecnichepiùavanzate,come:

dataminingmachinelearning

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