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タイタニック ロジスティック回帰
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@YutamaKotaro
September 21, 2018
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タイタニック ロジスティック回帰
@YutamaKotaro
September 21, 2018
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Transcript
ϩδεςΟοΫճؼͰഭΔ λΠλχοΫͷṖ !:VUBNB,PUBSP +JNNZ
ΤΞʔΫϩʔθοτͷϛογϣϯ ʮൃʯͱʮ*5ʯͰ ਓʑͷৗʹ ৽͍͠ϫΫϫΫΛ͢Δ
ΦϯϥΠϯɾϑΝογϣϯϨϯλϧαʔϏεɹ BJS$MPTFU ΤΞʔΫϩʔθοτ w ϓϩͷελΠϦετ͕༸Λબఆ w ΫϦʔχϯάෆཁɺฦ٫ظݶͳ͠ w औΓѻ͍ϒϥϯυҎ্ w
ؾʹೖͬͨΒߪೖՄೳ αʔϏεհ
ϦΞϧɾϑΝογϣϯϨϯλϧγϣοϓ BJS$MPTFUʷ"#-& ΤΞʔΫϩʔθοτʷΤΠϒϧ w ύʔιφϧελΠϦϯάΛମݧՄೳ αʔϏεհ
ΦϯϥΠϯɾύʔιφϧγϣοϐϯάΞϓϦ QJDLTT ϐοΫε w ϓϩͷελΠϦετ͕༸Λબఆ w ͓ख࣋ͪͷΞΠςϜʹ߹ΘͤͯίʔσΟωʔτΛఏҊ w ࣗͰख࣋ͪͷ͓༸ͱ߹ΘͤͯࢼணՄೳ αʔϏεհ
גࣜձࣾΤΞʔΫϩʔθοτ ϓϩμΫτάϧʔϓ$"&νʔϜϦʔμʔ ϢʔλϚͨ͜Ζ͏ ࣗݾհ !:VUBNB,PUBSP
3FBDU/BUJWF͕ಘҙͳΤϯδχΞɻ ීஈΞϓϦέʔγϣϯͷΤϯδχΞ͚ͩͲɺ σʔλαΠΤϯεͷಓาΈதɻ ֶੜ࣌ͷੜଶֶݚڀͰͪΐͬͱษڧͨ͠ͷ Ͱ౷ܭֶͪΐͬͱಘҙɻ 42-ͱϚϤωʔζΞϨϧΪʔ ࣗݾհ
KBWB4DSJQUͱ3͕ಘҙɻ 3TUBOΛ͏ػձΛ͍ͩ͘͞ɻ Կࣄઈରݕఆ͔͚ΔϚϯɻඇઢܗϞσϦϯ άͱϕΠζ֊ͱ͔͕ಘҙɻQZUIPOͱػցֶ शͪΐͬͱͰ͖Δɻ ࣗݾհ
Ͱ
ૣλΠλχοΫͷṖΛ ղ໌͍͖͍ͯͨ͠ͱ͜Ζ ͳͷ͕ͩɾɾɾ
·ͣجૅͱͳΔ ࣝΛֶͿඞཁ͕͋Δ
࠷ਪఆ๏ (-.͕ͳΜͳͷ͔ΛֶͿͨΊʹඞཁ ҰൠԽઢܗϞσϧ ࠓ͏ղੳํ๏ʹ͍ͭͯ "*$ ͜ΕΛثʹṖΛղ໌͢Δ ࠓͲ͏ͯ͠Βͳ͍ͱ͍͚ͳ͍࠲ֶ
࠷ਪఆ๏
Β͍͠ʲͬͱΒ͍͠ʳ ɹҙຯɿͦΕͬΆ͍༷ ɹͱ͍͏͜ͱ ࠷ਪఆ๏ͱɺ ɹ͍͢͝Β͍͠Λਪఆ͢Δํ๏ ͱ
Ͳ͏͍͏͜ͱ͔ͱ͍͏ͱɺ あなたはくじを10枚買った。すると、あたりは3つだった。 ではこのくじの当選確率(q)はどれぐらいだろうか? ͱ͍͏͍ͷ͑ ͱ
Ͳ͏͍͏͜ͱ͔ͱ͍͏ͱɺ あなたはくじを10枚買った。すると、あたりは3つだった。 ではこのくじの当選確率(q)はどれぐらいだろうか? ͱ͍͏͍ͷ͑ ʢʣͱߟ͑Δͷ͕ଥɻ ͱ
ׂΓࢉͰ͕֬ͩͤΔͱ͍͏ײ֮Ұ୴಄͔Βൈ͍ͯΒͬͯɺ બ͕֬ͩͱ͢Δͱɾɾɾ ɹɹɹͬͱ͍͍ͨͬͯͣʂ બ֬ˋͩͱ͢Δͱɾɾɾ ɹɹɹͨΓ͗͢ʂ ͭ·ΓΒ͍͠ͱͦΕͬΆ͍ͱ͍͏͜ͱʂ ɹɹݱ࣮తʹͬͱ͘͡Ҿ͔ͳ͍ͱΘ͔Μͳ͍͚Ͳɺ ɹɹͦΕͬΆ͍ͱ͍͏͜ͱʂ ͱ
ͱ͍͏͜ͱͰɺ̍̌ճ͘͡ΛҾ͍ͯɺ̏ճ͚ͩͨΓ͕ͰΔ֬ R Λࣜʹམͱ͠ࠐΜͰΈΑ͏ʢେมͳͷͰ෮ݩநग़ͱ͢ Δʣɻ R? R ? Ͱ͜ͷࣄΛࣜͰද͢͜ͱ͕Ͱ͖ΔɻࣄΛࣜͰදͨ͠
ͷ͕ؔɻ ͱ
ͳͷͰɺ ɹɹؔʹͦͷࣄ͕ى͜Γ͏Δ֬ ͱͳΔɻ ͜ΕΛ࠷େԽ͢ΔύϥϝʔλΛਪఆ͢Δํ๏͕࠷ਪఆ๏ɻ ͭ·Γɾɾɾ ɹ ͱ
࠷ਪఆͱɺ ༩͑ΒΕͨσʔλʹରͯ͠ɺࣄΛ֬ࣜͰද͠ɺ ࠷ͦΕͬΆ͍Λͩͦ͏ͥʂ ͱ͍͏ํ๏ɻ ͦΕͬΆ͍ͱ͍͏ͷ͘͢͝ࡶͳݴ͍ํͰ͕͢ɺཁ͢Δʹ֬త ʹΈͯ࠷ଥͳͱ͍͏ҙຯɻ ͱ
ׂΓࢉͰͳΜͱ͔͕ͰΔͱ͔ͦΜͳ͜ͱΕͯʂ ࠷ਪఆ๏ Λͬͯઌ΄ͲͷྫͷબΛਪఆͯ͠Έ·͠ΐ͏ʂ ͱ
͜Μͳײͬ͢͡Θʂ ̌ʙ̍ΛࠁΈͰͦͷ࣌ͦͷ࣌ͷΛࢉग़͍ͯ͠·͢ɻ ͦͯͦ͠ΕΛϓϩοτʂ ͱ
͓͓͓͓ʂͬΆ͍ʂʂʂ ͱ͍͏ͷ͕࠷ਪఆ๏ʹͳΓ·͢ʂʂ ͱ
͜͜·Ͱ͕ ࠷ਪఆ๏
(-.
ͦͷલʹ ୯ճؼͱ͍͏ͷ͕͋Γ·͢ɻ ܾఆͱ͔ฉ͍ͨ͜ͱ͋Γ·͢ΑͶɻ ͋Εɺ ɹࠩ༧ଌ࣮ଌ ͕࠷খʹͳΔΑ͏ʹύϥϝʔλʔΛਪఆ͢Δख๏Ͱͨ͠ɻ (-.ͱ
ΜΜɺͳΜ͔งғؾࣅͯͳ͍ʁ ͦ͏ʂઌ΄Ͳͬͨ ࠷ਪఆʹൃ͕ ͍ۙͰ͢ΑͶʂʂʂʂͶʂʂ ڧҾʹ (-.ͱ
ͭ·Δͱ͜Ζɺ(-. ࣄΛ֬Ͱදؔ͠Λ࡞Γ ͕࠷େʹͳΔύϥʔϝʔλʔΛਪ ఆ͢Δ ϞσϧͳͷͰ͢ʂ (-.ͱ
۩ମతʹɾɾɾ ࡀҎ্ʹͳΔͱΛॏͶΔ΄Ͳɺ݁ࠗ R ͕ ্͕Δɻ͜ͷ͜ͱΛϞσϦϯάʹࣜʹམͱ͠ࠐ ΜͰݟΑ͏ɻ RBY C Yྸ (-.ͱ
ͱ͜Ζ͕Ͳ͍ͬ͜ʂ (-.ͱ
BY CҰ࣍ࣜͳͷͰ ͜Μͳײ͡ɻ͚ͩͲ ߴߍͰͳΒͬͨͱࢥ͏ ΜͰ͕͢ɺ֬ͬͯ ̍͑ͨΓ ϚΠφεʹͳͬͨΓ ͠ͳ͍ΜͰ͢Αʂ (-.ͱ
ͱ͍͏͜ͱ RBY CͳΜ͔Ͱ֬Λදͤͳ͍ͱ͍ ͏͜ͱͳΜͰ͢ΑͶɻ ͦ͜ͰϩδεςΟοΫؔΛ͏͜ͱʹΑͬͯɺ ̌ʙ̍ͷؒʹࢭΊΔ͜ͱΛ͠·͢ɻ (-.ͱ
ϩδεςΟοΫؔΛ࣮ͯ͠Έ·͠ΐ͏ʂ (-.ͱ FYQ ͰωΠϐΞͷɻFYQ Ͱೋɻ
(-.ͱ ͜ΕͰɺϩδεςΟοΫؔͷத͕ԿͰ͋ͬͯ ̌ΛԼճΒͣɺ̍Λ্ճΒͳ͘ͳͬͨʂ
(-.ͱ ͱ͍͏͜ͱɺ RMPHJTUJD BY C ͱ͢Δ͜ͱͰɺ֬Ͱදͤͦ͏Ͱ͢ʂ
(-.ͱ ͢Δͱɺؔ - - В ЂGVODUJPO RJ ZJ
GVODUJPO RJ ZJ ɿ͋͋͋͋ ɹɹɹɹZJ͕̍ͳΒRJ ZJ͕ͳΒRJ RJMPHJTUJD BYJ C BBB Ͱද͢͜ͱ͕Ͱ͖·͢ʂɻϑΥϯτϠϕΣɾɾɾ ͦͯ͠ɺ͜Ε͕࠷େԽ͢ΔB CΛٻΊΕΑ͍ͷ Ͱ͢ʂ
(-.ͱ Ͳ͏ͬͯɺ ͕࠷େͷՕॴʹḷΓண͘ͷʁ ͱ͍͏͜ͱʹ͍ͭͯҰ୴লུ͠·͢ɻ خ͍͜͠ͱʹ3͕ࣗಈͰͬͯ͘Ε·͢ʂ ࠷ਪఆͷ᠘ʹ͍͕ͭͯ࣌ؒ͋Εɾɾɾʂʂ
"*$
(-.ͱ "*$ͱඇৗʹ͝རӹͷ͋ΔͷͰ͢ɻ "*$ ࠷େରύϥϝʔλ ࠷େରɿMPH ࠷େର ύϥϝʔλɿਪఆͨ͠ύϥϝʔλ
MPHͯ͠ΔͷͰɺ࠷େରෛͰ̌ʹ͍ۙ ΄Ͳྑ͍Ͱ͢ɻ
(-.ͱ "*$ ࠷େରύϥϝʔλ ͭ·Γɺେͳ͜ͱͱͯ͠ ɾ͍ํ͕ͯ·Γ͕͍͍Ϟσϧ ɾύϥʔϝʔλΛ͏΄ͲɺϖφϧςΟͱͯ͠"*$ ʹमਖ਼͕͔͔Δ
(-.ͱ ͘͢͝େͳ͜ͱ ৄ͍͜͠ͱҰ୴ɺߟ͑͞ͳ͍ͱͰ͖ͳ͍͔ Ͱ͕͢ɺࠓΔ্Ͱඇৗʹ͍ͨͤͭͳ͜ͱ͚ͩ ͍֮͑ͯͩ͘͞ʂ ̍ϞσϧΛ࡞Δ ̎"*$ͰϞσϧΛൺֱ͢Δ ̏"*$͕̎Ҏ্͍ํϞσϧΛ࠾ ಉ͘͡Β͍ ͳΒύϥϝʔλ͕গͳ͍ํΛ
(-.ͱ ̍ϞσϧΛ࡞Δ Ұ୴ϞσϧΛ࡞Γ·͢ɻ͜ͷ࣌ɺࠓճCBDLXPSE ͱ͍͏ํ๏Λࢼ͢ͷͰҰ୴ɺ͑ΔมΛશͯଧ ͪࠐΈ·͢ɻ ZdB C D తมʹରͯ͠ɺB C
Dͱ͍͏มΛઆ໌ม ʹೖΕͨϞσϧΛ࡞Γ·͢ɻ
(-.ͱ ̎"*$ͰϞσϧΛൺֱ͠·͢ 'VMMZdB C D 'VMMBZdC D 'VMMͱ͍͏มΛೖΕ·ͬͨ͘Ϟσϧɻ ͔ͦ͜Βઆ໌มBΛൈ͍ͨ'VMMBͱ͍͏ϞσϧΛ ࡞Γ·͢ɻ
(-.ͱ ̏϶"*$͕̎Ҏ্ͷϞσϧΛ࠾͢Δ ϶"*$"*$ 'VMM "*$ 'VMMB "*$ͷࠩ϶"*$Λग़͠·͢ɻ ͜ͷ࣌ɺ϶"*$ʾͱͳΕɹ'VMMBϞσϧͷউ ͪͱͳΓɺ'VMMBͷํ͕ͯ·Γͷྑ͍Ϟσϧ
ͱ͍͏͜ͱʹͳΓ·͢ɻ
(-.ͱ ͜ΕΛ܁Γฦ͍ͯ͘͠ͱɾɾɾɻ "*$͕࠷খʹͳΔϞσϧ͕͠·͢ɻ࠷ऴతʹɺ ZdC D ͱͳͬͨΒɺCͱDZʹӨڹΛ༩͑ΔཁҼͰɺC͕ ਖ਼ͳΒC͕େ͖͍΄ͲZେ͖͍Έ͍ͨͳ͜ͱ͕ݴ ͑·͢ʂ
λΠλχοΫͷղੳʹ͍͖·͢ʔʂ
λΠλχοΫͷղੳ ͜Μͳײ͡ͰσʔλΛಡΈࠐΈ·͢ɻ 5JDLFU $BCJO &NCBSLFE /BNFʹ͍ͭͯ͢͝ ͍ؔͳͦ͞͏ͩͬͨΓɺ৭ʑͱߟ͑Δ͜ͱ͕ଟ ͘ͳΔͷͰࠓճআ֎͍ͯ͠·͢ɻ
λΠλχοΫͷղੳ 1BTTFOHFS*EJE 4VSWJWFE ɹੜଘࢮ 1DMBTT෦ͷ֊ڃ 4FYੑผ "HFྸ 4JC4Qધܑͯͨ͠ఋ ۮऀͷ 1BSDIધͯͨ྆͠ɺ
ࢠڙ 'BSFધྉۚ ͬͨσʔλʹ͍ͭͯઆ໌͠·͢ɻ
λΠλχοΫͷղੳ ͔Δ͘ॲཧΛ͠·͢ɻ GBDUPSࣈͰೖ͍ͬͯΔͱ͜ΖΛҼࢠͱͯ͠ѻ͏ ͨΊʹೖΕͯ·͢ɻ
λΠλχοΫͷղੳ มΛશ෦͍ΕͨϑϧϞσϧΛ࡞Γ·͢ɻ ͦͷޙɺมΛҰͭআ͍ͨϞσϧΛ࡞Γ϶"*$Λࢉ ग़ͯ͠Έ͍ͯͩ͘͞ɻ ͜Μͳײ͡ͰɺมΛঃʑʹݮΒͯ͠Έ·͠ΐ͏ʂ
λΠλχοΫͷղੳ ݁Ռͷݟํ TVNNBSZͰ݁ՌΛݟΔ͜ͱ͕Ͱ͖·͢ɻ
λΠλχοΫͷղੳ ॏཁͳͷ&TUJNBUFͰɺ͜Ε͕ෛͩͱߴ͍΄Ͳੜ ଘ͕͍ͱͳΓ·͢ʢBHF ɻ Q$MBTTͱ͔Q$MBTT̍ʹରͯ͠ੜଘ͕૬ରతʹ ߴ͔͔ͬͨͱ͍͏͜ͱΛ͠Ί͠·͢ɻ
λΠλχοΫͷղੳ ݁ TUΫϥεOEΫϥεSEΫϥεͷॱʹੜଘ ͕Լɻ
λΠλχοΫͷղੳ ݁ 'FNBMFΑΓ.BMFͷํ͕ੜଘ͕͍
λΠλχοΫͷղੳ ݁ BHFߴ͍΄Ͳੜଘ͕͍ɻ
λΠλχοΫͷղੳ ݁ ܑఋۮऀ͕͍Δ΄Ͳੜଘ͕͍ɻ
λΠλχοΫͷղੳ ݁ TUΫϥεOEΫϥεSEΫϥεͷॱʹੜଘ ͕Լɻ 'FNBMFΑΓ.BMFͷํ͕ੜଘ͕͍ ܑఋۮऀ͕͍Δ΄Ͳੜଘ͕͍ɻ BHFߴ͍΄Ͳੜଘ͕͍ɻ
λΠλχοΫͷղੳ ݁ TUΫϥεOEΫϥεSEΫϥεͷॱʹੜଘ ͕Լɻ ൵͍͚͠Ͳɺ͓ۚ࣋ͪͷਓͷਓ໋ͷํ͕༏ઌ͞Εͨ ͱ͍͏͜ͱɻ
λΠλχοΫͷղੳ ݁ 'FNBMFΑΓ.BMFͷํ͕ੜଘ͕͍ உੑΑΓঁੑͷٹॿ͕༏ઌ͞Εͨɻ
λΠλχοΫͷղੳ ݁ ܑఋۮऀ͕͍Δ΄Ͳੜଘ͕͍ɻ ۮऀɾܑఋ૬खΛࣗͷΘΓʹಀͨ͠ʁ Ұॹʹ͘ͳͬͨʁ ࢠ͕มʹΒͳ͔ͬͨͱ͍͏͜ͱࢠҰॹ ʹಀͯ͠Β͍͔ͬͨ͢ʁ
λΠλχοΫͷղੳ ݁ BHFߴ͍΄Ͳੜଘ͕͍ɻ ࢠڙͷਓ໋͕༏ઌ͞Εͨɻ
λΠλχοΫͷղੳ ݁ ɾ͓ۚ࣋ͪɺঁੑɺࢠڙͷٹॿ͕༏ઌ͞Εͨɻ ɾҰॹʹ͘ͳͬͨʁ͜Ε͏ͪΐͬͱσʔλΛ ਂ۷Δඞཁ͕͋Δ
λΠλχοΫͷղੳ ࢙࣮ TUΫϥεધһҰਓ͋ͨΓͷ୲͕গͳ͍ͨΊɺ ࿈བྷɾࢧԉ͕ૉૣ͘ߦ͑ͨΒ͍͠ɻ
λΠλχοΫͷղੳ ࢙࣮ ߤւ࢜ʮXPNBOBOEDIJMESFOpSTUʯͱղऍͯ͠ɺ ༏ઌతʹٹ໋Ϙʔτʹࡌ͍ͤͯͨɻ ͭ·Γɺঁੑɺࢠڙ͕༏ઌ͞Εͨɻ
λΠλχοΫͷղੳ ࢙࣮ ·ͩΓҰ͋ΔΜͰ͕͢ɺ͜Ε͏ͪΐͬͱৄ ࡉʹΈͯݟΔඞཁ͕͋Γͦ͏Ͱ͢Ͷɾɾɾʂʂ ͱ͍ͬͨײ͡Ͱ͢ʂ