「回帰分析から分かること」と「変数選択」

by Shuntaro Sato

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ʮճؼ෼ੳ͔Β෼͔Δ͜ͱʯͱʮม਺બ୒ʯ ࠤ౻ढ़ଠ࿕ ௕࡚େֶපӃྟচݚڀηϯλʔ TIVOUBSPTBUP!OBHBTBLJVBDKQ

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ຊ೔ͷ0WFSWJFX 2 ճؼ෼ੳͱ͸ɺճؼϞσϧΛ༻͍ͨ෼ੳͷ͜ͱ ॏճؼϞσϧ ճؼ܎਺ͷղऍ Ծఆ ໨తม਺ͷछྨ ҰൠԽઢܗϞσϧ Ϟσϧͷछྨ ճؼ܎਺ͷղऍ ݚڀͷ෼ྨͱ໨త ม਺બ୒ ୯ճؼϞσϧ ଟมྔճؼϞσϧ ղऍ ަབྷҼࢠ %"( ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦

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3 ҰൠԽઢܗϞσϧ ໨తม਺ͷछྨ ࿈ଓ ೋ஋ Χ΢ϯτ Ϟσϧ ઢܗճؼϞσϧ ϩδεςΟοΫճؼϞσϧ ϙΞιϯճؼϞσϧ આ໌ม਺͕Ұͭ ୯ճؼϞσϧ ۠ผ͠ͳ͍ ۠ผ͠ͳ͍ આ໌ม਺͕ෳ਺ ॏճؼϞσϧ Ϟσϧͷछྨ

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୯ճؼϞσϧ 4

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26&45*0/ 5 ฼਌ͷ೥ྸ ೕࣇͷମॏ ͋Δม਺ͱଞͷ͋Δม਺ͱͷؔ܎Λ਺ࣜΛ༻͍ͯදݱ͍ͨ͠ 1000 2000 3000 4000 5000 bwt 15 20 25 30 35 40 45 age 1000 2000 3000 4000 5000 bwt 40 50 60 70 80 90 100 110 lwt ͜ͷ੺͍ઢΛٻΊ͍ͨ ฼਌ͷ࠷ऴ݄ܦظͷମॏ ೕࣇͷମॏ ୯ճؼ෼ੳ   4JNQMFMJOFBSSFHSFTTJPO

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ߴߍ਺ֶ·Ͱͷ௚ઢͷٻΊํ 6 : 9 9ͱ:ͷ৘ใΛ࣋ͭ఺͕༩͑ΒΕɺ͜ͷ఺Λ௨Δ௚ઢͷࣜΛٻΊΔ y = ax + b

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͜Ε͔Βѻ͏σʔλ 7 ͋Δ͓ళʹ͓͚ΔؾԹͱΞΠεΫϦʔϜͷചΓ্͛ͷؔ܎Λௐ΂͍ͨ ؾԹʢˆʣ ΞΠεΫϦʔϜͷചΓ্͛ʢݸ਺ʣ w ͭͷม਺ͷؔ܎Λߟ͑Δ w ఺Ҏ্͋Δ w શͯͷ఺Λ௨Δઢ͸ߟ͑ͳ͍ w γϯϓϧʹҰ࣍ؔ਺Ͱද͢ ୯ճؼϞσϧ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 125 150 175 200 10 20 30 40 templeture ice

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୯ճؼϞσϧͰਪఆͰ͖Δ΋ͷ 8 ؾԹʢˆʣ ΞΠεΫϦʔϜͷചΓ্͛ʢݸ਺ʣ ؍ଌ஋ʹΑ͋ͯ͘͸·Δ੨͍ઢΛٻΊΔ Y = β0 + β1 ⋅ X ੨͍ઢ͸ɺ࣍ͷϞσϧͰද͞ΕΔͱ͢Δ ճؼϞσϧ ࠓ·Ͱͷݴ༿ͷ࢖͍ํ ճؼϞσϧͰͷݴ༿ͷ࢖͍ํ Z Z ໨తม਺ɾैଐม਺ɾ   Ξ΢τΧϜ Y Y આ໌ม਺ɾಠཱม਺ Ќ ੾ย ճؼ܎਺ Ќ ܏͖ ճؼ܎਺ 100 125 150 175 200 10 20 30 40 temperature ice

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ݴ༿ͷରԠ 9 ؾԹʢˆʣ ΞΠεΫϦʔϜͷചΓ্͛ʢݸ਺ʣ આ໌͢Δม਺ w આ໌ม਺ w ಠཱม਺ આ໌͞ΕΔม਺ w ໨తม਺ w ඃઆ໌ม਺ w ैଐม਺ w Ξ΢τΧϜม਺ ୯ճؼϞσϧ͸   આ໌ม਺͕Ұͭ 100 125 150 175 200 10 20 30 40 temperature ice

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ճؼ܎਺ͷղऍ 10 ؾԹʢˆʣ ΞΠεΫϦʔϜͷചΓ্͛ʢݸ਺ʣ ΞΠεΫϦʔϜͷചΓ্͛ = β0 + β1 ⋅ ؾԹ ؾԹ͕౓ߴ͍ͱɺ   ΞΠεΫϦʔϜͷചΓ্͛͸ݸେ͖͍ આ໌ม਺ͷ஋͕୯Ґҧ͏ͱɺ   ໨తม਺ͷ஋͕ฏۉతʹЌҧ͏ ҰൠԽ ˞આ໌ม਺͕มԽ͢Δͱɺ໨తม਺͕มԽ͢Δ   ɹͱ͸ݴ͍ͬͯͳ͍ 100 125 150 175 200 10 20 30 40 temperature ice ice = 99.9 + 1.9 ⋅ UFNQFSBUVSF

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໨తม਺ͷ෼෍͕ਖ਼ن෼෍ͬͯฉ͚͘Ͳʜ 11 ໨తม਺ͷ෼෍͕ਖ਼ن෼෍Ͱ͸ͳ͘ɺޡࠩͷ෼෍͕ਖ਼ن෼෍ɺ ͱ͍͏ԾఆΛ͓͍͍ͯΔ w ॏճؼϞσϧʢڞ෼ࢄ෼ੳʣ͸ɺಛʹ࢒ࠩͷ෼෍ʹ஫ҙ͢Δ w Ծఆͱͯ͠ͷޡࠩͱɺ෼ੳ݁Ռͱͯ֬͠ೝͰ͖Δ࢒͕ࠩҧ͏͜ͱ͸஫ҙ

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12 ҰൠԽઢܗϞσϧ ໨తม਺ͷछྨ ࿈ଓ ೋ஋ Χ΢ϯτ Ϟσϧ ઢܗճؼϞσϧ ϩδεςΟοΫճؼϞσϧ ϙΞιϯճؼϞσϧ આ໌ม਺͕Ұͭ ୯ճؼϞσϧ ۠ผ͠ͳ͍ ۠ผ͠ͳ͍ આ໌ม਺͕ෳ਺ ॏճؼϞσϧ Ϟσϧͷछྨ

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ॏճؼϞσϧ 13

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୯ճؼϞσϧͷݶք 14 ͋Δม਺ͱଞͷ͋Δม਺ͱͷؔ܎Λ਺ࣜΛ༻͍ͯදݱ͍ͨ͠ ͋Δม਺ͱ΋͏Ұͭͷม਺ͷؔ܎ͷΈදݱ wؾԹˠΞΠεΫϦʔϜͷച্ w฼਌ͷ೥ྸˠೕࣇͷମॏ w฼਌ͷ࠷ऴ݄ܦظͷମॏˠೕࣇͷମॏ ੈͷத͸΋ͬͱෳࡶ ؾԹʢˆʣ ΞΠεΫϦʔϜͷചΓ্͛ʢݸ਺ʣ 100 125 150 175 200 10 20 30 40 temperature ice

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ଟมྔճؼϞσϧ 15 ੈͷதͷෳࡶͳؔ܎Λදݱ͢Δͻͱͭͷํ๏ ΞΠεΫϦʔϜͷച্ʹ   ؔ࿈͢Δͷ͸ؾԹ͚ͩʁ ࣪౓͸ʁɹݶఆ঎඼ͷ༗ແ͸ʁ ΞΠεΫϦʔϜͷച্ = β0 + β1 ؾԹ + β2 ࣪౓ + β3 ݶఆ঎඼ͷ༗ແ ໨తม਺ʹؔ࿈͢Δม਺ΛՃ๏తʹઆ໌ม਺ʹ௥Ճ͍ͯ͘͠ ΞΠεΫϦʔϜͷചΓ্͛ = β0 + β1 ⋅ ؾԹ ice = 99.9 + 1.9 ⋅ UFNQFSBUVSF 100 125 150 175 200 10 20 30 40 temperature ice

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ճؼ܎਺ͷղऍᶃ 16 : ໨తม਺͕:ɺઆ໌ม਺͕"ͱ#ͷଟมྔճؼϞσϧΛߟ͑Δɻ ࣍ͷ݁Ռ͕ಘΒΕͨɻ Y = β0 + βa A + βb B ЌBʹ͍ͭͯߟ͑Δɻ#ͷ஋͸ಉ͡ɺ"͕୯ҐมԽͨ͠ͱ͢Δ Y1 = β0 + βa (A + 1) + βb B มԽલ Y1 − Y0 = β0 + βa (A + 1) + βb B − {β0 + βa A + βb B} = β0 + βa A + βa + βb B − β0 − βa A − βb B = βa มԽޙ #ͷ஋͸ಉ࣌͡ͷɺ"ͷ୯ҐมԽલޙͷ:ͷมಈ͸ʁ มԽޙมԽલ Y0 = β0 + βa A + βb B " # #͸ಉ͡ɺ"͚ͩมԽ͢Δͱʁ ͦͷࠩ͸ʁ

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ճؼ܎਺ͷղऍᶄ 17 #͸ݻఆ #Λ೚ҙͷ஋ʹݻఆͨ࣌͠ͷɺ"ͷ୯Ґ͋ͨΓͷΞ΢τΧϜ:ͷมԽ : " βa Y1 − Y0 = β0 + βa (A + 1) + βb B − {β0 + βa A + βb B} = βa มԽޙมԽલ wؔ৺ͷ͋Δม਺Ҏ֎ͷม਺Λݻఆͨ࣌͠ͷɺ   ؔ৺ͷ͋Δม਺୯Ґ͋ͨΓͷΞ΢τΧϜͷมԽ wʮݻఆͨ͠ʯΛʮௐ੔ͨ͠ʯͱ΋ݴ͏

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18 ͜͜·Ͱ໨తม਺͸࿈ଓई౓σʔλͩͬͨ ࿈ଓई౓Ҏ֎ʹ΋֦ு

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19 ҰൠԽઢܗϞσϧ ໨తม਺ͷछྨ ࿈ଓ ೋ஋ Χ΢ϯτ Ϟσϧ ઢܗճؼϞσϧ ϩδεςΟοΫճؼϞσϧ ϙΞιϯճؼϞσϧ આ໌ม਺͕Ұͭ ୯ճؼϞσϧ ۠ผ͠ͳ͍ ۠ผ͠ͳ͍ આ໌ม਺͕ෳ਺ ॏճؼϞσϧ Ϟσϧͷछྨ

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ҰൠԽઢܗճؼϞσϧ 20

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໨తม਺ͷछྨͱϞσϧͷ໊લͱճؼ܎਺ͷղऍ 21 ໨తม਺ͷछྨ Ϟσϧͷ໊લ ճؼ܎਺ͷղऍ ࿈ଓ w ୯มྔɿ୯ճؼϞσϧ w ଟมྔɿॏճؼϞσϧʢڞ෼ࢄ෼ੳʣ Ξ΢τΧϜͷมԽྔ ໊ٛʢೋ஋ʣ ϩδεςΟοΫճؼϞσϧ w Φοζൺ w ϦεΫൺ   ʢΞ΢τΧϜͷ༗ප཰͕ະຬͳΒ͹ɺ   ɹΦοζൺ㲈ϦεΫൺʣ मਖ਼ϙΞιϯճؼϞσϧ ϦεΫൺ Χ΢ϯτʢ ʜʣ w ϙΞιϯճؼϞσϧ w ෛͷೋ߲ճؼϞσϧ w ϦεΫൺ w ཰ൺ   ʢݸମ͝ͱͷ؍࡯ظؒΛΦϑηοτ߲ʹೖΕͨ৔߹ʣ 5JNFUPFWFOU ʢΞ΢τΧϜͷੜىɺ   ɹΞ΢τΧϜ͕ى͜Δ·Ͱ࣌ؒʣ $PYൺྫϋβʔυϞσϧ ϋβʔυൺ ˞ΦοζൺɺϦεΫൺɺ཰ൺɺϋβʔυൺ͸ճؼ܎਺ͷࢦ਺ม׵͕ඞཁ

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.VMUJWBSJBCMF͔.VMUJWBSJBUF͔ʁ 22 .VMUJWBSJBCMFBOBMZTJT .VMUJQMF MJOFBS MPHJTUJD ʜ BOBMZTJT PS .VMUJWBSJBUF͸ɺ   ໨తม਺͕Ұͭͷݸମʹ͍ͭͯ   ෳ਺ճଌఆ͞Ε͍ͯΔσʔλʹ࢖͏

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ݚڀͷ໨తʹΑΓϞσϧͷղऍ͕มΘΔ 23

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ݚڀͷ෼ྨ 24 %FTDSJQUJPO &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF %JBHOPTUJD QFSGPSNBODF FWBMVBUJPO هड़ ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦ ਍அͷੑೳධՁ ม਺͸ͲΜͳ෼෍͔ʁ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ ೚ҙͷධՁํ๏ͷ   ਍அੑೳ͸ʁ w )FSOÂO." )TV+ )FBMZ#"4FDPOE$IBODFUP(FU$BVTBM*OGFSFODF3JHIU"$MBTTJ fi DBUJPOPG%BUB4DJFODF5BTLT$IBODF+BO r w 7JUUJOHIP ff & (MJEEFO%7 4IJCPTLJ4$ .D$VMMPDI$&3FHSFTTJPONFUIPETJOCJPTUBUJTUJDTMJOFBS MPHJTUJD TVSWJWBM BOESFQFBUFENFBTVSFT NPEFMT4QSJOHFS4DJFODF#VTJOFTT.FEJB

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ϞσϧʹղऍੑΛ࣋ͨͤΔ 25 ਺ֶϞσϧ &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ Y = β0 + β1 X1 + β2 X2

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۩ମྫ 26 ݚڀର৅ूஂɿ֎Պखज़Λ͢Δഏ͕Μͷױऀ ໨తม਺ આ໌ม਺ ෼ؒาߦڑ཭ w ೥ྸ w ੑผ w Ξϧϒϛϯ w ٤Ԏ

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ؔ࿈ͷ୳ࡧɿ୯มྔ 27 ճؼϞσϧʹΑΓɺ໨తม਺ͱઆ໌ม਺ͷؔ࿈ͷڧ͞ͱํ޲͕Θ͔Δ ෼ؒาߦڑ཭ ೥ྸ .8% = β0 + β1 ೥ྸ ೥ྸ୯ҐมԽ͋ͨΓͷ.8%ͷมԽ ೥ྸ͕ࡀେ͖͍ͱ.8%͸Nখ͍͞ β1 = − 5 .8%ͱ೥ྸͷؔ܎͸෼͔Δ ੑผ΍ज़લͷΞϧϒϛϯ΋.8%ʹؔ܎͋ΔͷͰ͸ʁ ୯ճؼϞσϧ

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ؔ࿈ͷ୳ࡧɿଟมྔ 28 ෼ؒาߦڑ཭ ೥ྸ .8% = β0 + β1 ೥ྸ + β2 ੑผ + β3 Ξϧϒϛϯ ॏճؼϞσϧ ੑผʢঁੑΛج४ʣ Ξϧϒϛϯ Ќ ղऍ ೥ྸ ੑผͱΞϧϒϛϯͷ.8%ͷؔ࿈ΛऔΓআ͍ͨ͏͑Ͱɺ೥ྸ͕ࡀେ͖͍ͱ.8%͸Nখ͍͞ ੑผ ೥ྸͱΞϧϒϛϯͷ.8%ͷؔ࿈ΛऔΓআ͍ͨ͏͑Ͱɺঁੑʹൺֱͯ͠உੑͷ.8%͸Nେ͖͍ Ξϧϒϛϯ ੑผͱ೥ྸͷ.8%ͷؔ࿈ΛऔΓআ͍ͨ͏͑ͰɺΞϧϒϛϯ͕HE-େ͖͍ͱ.8%͸Nେ͖͍ Ͳͷม਺͕ɺΞ΢τΧϜͱؔ࿈͢Δ͔Θ͔Δ

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ؔ࿈ͷ୳ࡧɿ୯มྔͱଟมྔͷղऍͷҧ͍·ͱΊ 29 ೥ྸͱ.8%ʹؔ࿈͕ೝΊΒΕͨ ੑผ΍ӫཆঢ়ଶ͕.8%ͱؔ࿈͍ͯ͠Δ͔Βݟ͔͚ͤͷؔ࿈͡Όͳ͍ʁ ͦ͏͔΋͠Εͳ͍ɻ ੑผɾӫཆঢ়ଶͱ.8%ͱͷ ؔ܎ΛऔΓআ͍ͯ΋ɺ   ͳ͓ɺؔ࿈͍ͯ͠Δɻ ୯ճؼϞσϧ ॏճؼϞσϧʢଟมྔճؼϞσϧʣ

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༧ଌɿ୯มྔ 30 ճؼϞσϧʹΑΓɺ໨తม਺ͷ஋ͷ༧ଌ͕Ͱ͖Δ ෼ؒาߦڑ཭ ೥ྸ .8% = 700 − 5 ⋅ ೥ྸ આ໌ม਺͕ҰͭΑΓ΋ͨ͘͞ΜϞσϧʹؚΊΔํ͕༧ଌਫ਼౓͕ྑ͍ͩΖ͏ ଟมྔճؼϞσϧ ୯ճؼϞσϧ ೥ྸ͕ࡀͷͱ͖ͷ.8%͸ɺºN ೥ྸ͕ࡀͷͱ͖ͷ.8%͸ɺºN

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༧ଌɿଟมྔ 31 ෼ؒาߦڑ཭ ೥ྸ .8% = 700 − 10 ⋅ ೥ྸ + 30 ⋅ ੑผ + 50 ⋅ Ξϧϒϛϯ ॏճؼϞσϧ ੑผʢঁੑΛج४ʣ Ξϧϒϛϯ ෼ؒาߦڑ཭ʢNʣ ೥ྸʢࡀʣ ੑผʢஉੑʣ ΞϧϒϛϯʢHE-ʣ ༧ଌ஋ Ұൠతʹ͸ɺઆ໌ม਺͕ଟ͍ํ͕༧ଌਫ਼౓͸ྑ͍

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༧ଌϞσϧͷ஫ҙ఺ 32 ༧ଌϞσϧͷ࡞੒͸೉͍͠ w େ͖ͳσʔλ͕ඞཁ w ҰͭͷσʔλͷΈͰϞσϧ࡞ͬͯɺਫ਼౓ྑ͍͚ͩͰ͸μϝ w ༧ଌਫ਼౓Λྑ͘͢ΔͨΊͷࡉ͔ͳϞσϧͷௐ੔ w աֶश w աڈ໰͹͔Γղ͖·͘Γɺաڈ໰ͷઃ໰ɾճ౴൪߸·Ͱ׬ᘳʹ֮͑ͨ ˠաڈ໰͸׬ᘳʹղ͚Δ w ճ౴൪߸ΛೖΕସ͑Δɺ໰୊Λগ͠ม͑Δͱղ͚ͳ͘ͳΔ w ໰୊ͷຊ࣭Λཧղ͠ͳ͍ͱ͍͚ͳ͍ ໨ͷલͷσʔλͷ༧ଌͷਫ਼౓͕ߴ͘ͳΓ͗ͯ͢ɺ   ༧ଌ͍ͨ͠σʔλͷ༧ଌਫ਼౓͕ѱ͘ͳΔ͜ͱ

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ҼՌਪ࿦ɿղऍ 33 ېԎ .8% ېԎ͸ɺ.8%ʹӨڹ͢Δ͔ʁ w ॲஔ w հೖ w മ࿐ Ξ΢τΧϜ ݪҼ ݁Ռ .8% = 700 − 50 ⋅ ېԎ ճؼϞσϧ ؔ࿈୳ࡧͱͯ͠ͷղऍ ېԎͯ͠ͳ͍ਓʹରͯ͠ېԎ͍ͯ͠Δਓ͸ɺ.8%͕Nେ͖͍ ٤Ԏ͍ͯ͠ΔਓΛېԎͤ͞Δͱɺ.8%͸N૿͑Δ ҼՌਪ࿦ͱͯ͠ͷղऍ ېԎͷ༗ແͱ͍͏܈ͷΞ΢τΧϜͷҧ͍ΛධՁ͢Δ ېԎͤ͞Δ͜ͱͰɺΞ΢τΧϜ͕Ͳ͏มΘΔ͔ධՁ͢Δ

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ҼՌਪ࿦ɿަབྷ 34 ېԎ .8% ېԎ͸ɺ.8%ʹӨڹ͢Δ͔ʁ ೥ྸ ؔ৺ͷ͋ΔҼՌؔ܎ w ೥ྸ͸ɺ٤Ԏঢ়گʹӨڹ͢Δ͔΋͠Εͳ͍ w ೥ྸ͸ɺ.8%ʹӨڹ͢Δ͔΋͠Εͳ͍ Ͱ΋ ͜ΕʹΑΓɺېԎͱ.8%ͱͷؔ࿈͕࿪ΊΒΕΔ͔΋ ਅͷؔ܎͔ΒͷζϨަབྷʢ$POGPVOEJOHʣ ަབྷΛੜΈग़͢ม਺͕ɺަབྷҼࢠʢ$POGPVOEFS $POGPVOEJOHGBDUPSʣ w ަབྷ͸ݱ৅ w ަབྷҼࢠ͸ɺަབྷΛੜΉཁҼ

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ҼՌਪ࿦ɿަབྷΛऔΓআ͘ 35 ېԎ .8% w ަབྷҼࢠ͸औΓআ͖͍ͨ w औΓআ͘͜ͱΛௐ੔ʢBEKVTUʣͱ͍͏ ೥ྸ ؔ৺ͷ͋ΔҼՌؔ܎ ަབྷҼࢠ ௐ੔͢Δखஈ͸ෳ਺͋Δ w ૚ผղੳ w Ϛονϯά w Ξ΢τΧϜʹରͯ͠ଟมྔճؼ෼ੳ w ܏޲είΞʢ141SPQFOTJUZTDPSFʣΛར༻ͨ͠ํ๏ w 14Ϛονϯά w ٯ֬཰ॏΈ෇͚ʢ*18*OWFSTFQSPCBCJMJUZXFJHIUJOHʣ

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ҼՌਪ࿦ɿଟมྔճؼ෼ੳΛͨ͠ޙͷ݁Ռͷදࣔ 36 ېԎ .8% ೥ྸ ؔ৺ͷ͋ΔҼՌؔ܎ ަབྷҼࢠ .8% = ېԎ + ೥ྸ ަབྷҼࢠΛௐ੔͢ΔͨΊʹɺԼهճؼϞσϧͰ෼ੳ ਪఆ݁Ռ &TUJNBUF $* ېԎ UP ೥ྸ UP w ަབྷҼࢠʢփ৭ʣʹରͯ͠΋ɺճؼ܎਺͸ਪఆ͞ΕΔ w ͔͠͠ɺަབྷҼࢠͷͨΊਪఆ஋ͷղऍʹҙຯ͸ͳ͍ w ؔ৺ͷ͋ΔॲஔͷΈ݁Ռʹࣔ͢ ݁ՌͷදʹೖΕΔͷ͸ 5BCMFGBMMBDZ 8FTUSFJDI % (SFFOMBOE 4 5IFUBCMFGBMMBDZQSFTFOUJOHBOEJOUFSQSFUJOHDPOGPVOEFSBOENPEJ fi FSDPF ff i DJFOUT "NFSJDBO+PVSOBMPG&QJEFNJPMPHZ r ؒҧͬͨߟ͑ํ

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ଟมྔճؼ෼ੳͱަབྷ 37 w ଟมྔճؼ෼ੳͱަབྷ͸ηοτͰѻ͍ͬͯΔ৘ใ͸ଟ͍ w ҼՌਪ࿦ʹ͸ɺަབྷ͕֓೦ͱͯ͠ଘࡏ͢Δ w ؔ࿈ͷ୳ࡧͱ༧ଌʹ͸ɺަབྷ͕֓೦ͱͯ͠ଘࡏ͠ͳ͍

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ಉ͡ϞσϧͰ΋ղऍ͕ҧ͏ 38 Y = β0 + β1 X1 + β2 X2 ਺ֶϞσϧ &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ

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ม਺બ୒ 39

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ม਺બ୒ͱ͸ʁ 40 ݚڀର৅ूஂɿ֎Պखज़Λ͢Δഏ͕Μͷױऀ ໨తม਺ આ໌ม਺ ෼ؒาߦڑ཭ w ೥ྸ w ੑผ w Ξϧϒϛϯ w ٤Ԏ w ମॏ w طԟྺ w ෰༻தͷༀ w -BCPσʔλ w ଍ͷ਌ࢦͷ௕͞ʜ ଟมྔճؼϞσϧΛߏங͢Δͱ͖ʹɺͲͷม਺Λઆ໌ม਺ͱͯ͠બ୒͢Δ͔ʁ Ϟσϧ ͲΕΛೖΕΔʁ શ෦ʁ

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41 &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ ݚڀ໨తʹΑͬͯҟͳΔ

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&17 &WFOUQFSWBSJBCMF 42 ϞσϧʹؚΊͯ΋ଥ౰ͱߟ͑Δઆ໌ม਺ͷ਺ͷ ໨҆ Ξ΢τΧϜͷई౓ ܭࢉํ๏ ۩ମྫ ࿈ଓ αϯϓϧαΠζ w αϯϓϧαΠζ͕ͳΒ͹ɺઆ໌ม਺ͷ਺ͷ໨҆͸ݸ ೋ஋ ೋ஋ͷগͳ͍ํͷ਺ αϯϓϧαΠζ͸ w Πϕϯτ͋Γ͕ɺͳ͕͠ͳΒɺݸ w Πϕϯτ͋Γ͕ɺͳ͕͠ͳΒɺݸ આ໌ม਺͕ΧςΰϦΧϧσʔλͷ৔߹͸஫ҙ w ೋ஋ͷΧςΰϦม਺ʢྫɿࠨӈʣͳΒɺม਺͸ݸͱΧ΢ϯτ w ࡾ஋ͷΧςΰϦม਺ʢྫɿ௿தߴʣͳΒɺม਺͸ݸͱΧ΢ϯτ w L஋ͷΧςΰϦม਺ͳΒɺม਺͸LݸͱΧ΢ϯτ

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ؔ࿈ͷ୳ࡧ 43 w Ξ΢τΧϜͱͷؔ࿈ʹؔ৺ͷ͋Δม਺Λઆ໌ม਺ͱ͢Δ w Ͱ͖Ε͹ɺ͢΂ͯ w &17ͱൺֱͯ͠ɺۃ୺ʹଟ͍਺ͷม਺͸બ୒ͮ͠Β͍ w ࠪಡऀ͔Βࢦఠ͞ΕΔՄೳੑ͕ߴ͍ w ࣅ͍ͯΔม਺͸͚ͭͩબ୒͠ɺ࢒Γ͸࡟আ w #.*ͱ਎௕ͱମॏ w ؔ৺͕ڧ͍ม਺Λ༏ઌతʹબ୒͢Δ ม਺બ୒͕ඞཁ

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ଟॏڞઢੑ 44 w ࠪಡऀ͔Βࢦఠ͞Ε΍͍͢ࣄ߲ w ࣅ͍ͯΔม਺Λಉ࣌ʹϞσϧʹؚΊͯ͸͍͚ͳ͍ɺͱߟ͑ΒΕ͍ͯΔࣄฑ ਪఆ͕ෆ҆ఆͳͱ͖ ຊ౰͸ɺͦ͏Ͱͳ͘ w "ͱ͍͏ม਺ͱ"ͱ͍͏ม਺Λಉ࣌ʹϞσϧʹؚΊΔͱਪఆͰ͖ͳ͍ɺͱ͍͏ݱ৅ ͭ·Γɺ໰୊ʹͳΔͷ͸ ৴པ͕۠ؒɺۃ୺ͳ஋ΛͱΔͱ͖ʹٙ͏ ࣮࣭ɺಉ͡஋

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༧ଌ 45 w Ξ΢τΧϜͷ༧ଌʹد༩͢ΔͰ͋Ζ͏ม਺Λઆ໌ม਺ͱ͢Δ w ༧ଌਫ਼౓ͱաֶशͱͷόϥϯε w ࢼߦࡨޡ͕ඞཁ

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ҼՌਪ࿦ 46 w ؔ৺ͷ͋Δॲஔม਺ͱΞ΢τΧϜม਺ w ਅͷҼՌؔ܎͔ΒͷζϨʢόΠΞεʣΛ੍ޚͰ͖Δม਺Λબ୒͢Δ

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఻౷తͳަབྷҼࢠͷ৚݅ 47 - " : 6 w ॲஔ"ʹؔ࿈͢Δ w Ξ΢τΧϜ:ʹؔ࿈͢Δ w தؒม਺Ͱͳ͍ 6 ఻౷తͳަབྷҼࢠͷ৚݅ ఻౷తͳަབྷҼࢠͷ৚݅ʹ͋͏-Λௐ੔͢Δͱɺ   "ͱ:ͷؔ܎͸όΠΞε͞Εͯ͠·͏ ަབྷ ༀ౤༩ ࢮ๢ ೝ஌঱ ॏ঱౓ طԟྺ

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%"( %JSFDUFE"DZDMJD(SBQI 48 w /PEF͸֬཰ม਺ w ໼ҹʢ&EHFʣ͸/PEF͔Β/PEF΁ͷӨڹͷํ޲Λҙຯ͢Δ w ໼ҹ͕͋Δ͜ͱ͸ɺूஂ಺ͷগͳ͘ͱ΋Ұਓʹ͓͍ͯɺ௚઀తͳҼՌޮՌ͕͋Δ͜ͱΛࣔ͢ w ໼ҹ͕ͳ͍͜ͱ͸ɺूஂ಺Ͱ୭Ұਓɺ௚઀తͳҼՌޮՌ͕ͳ͍͜ͱΛࣔ͢ w ໼ҹ͸ɺͲͷΑ͏ͳӨڹ͕͋Δ͔ʢେ͖͞ʣ͸ࣔ͞ͳ͍ w ໼ҹ͸ɺ८ճ͠ͳ͍ʢ"DZDMJDʣ w :ࢮ๢ w "৺Ҡ২ w -࣬පͷॏ঱౓ - " : /PEF &EHF ม਺ؒͷҼՌߏ଄Λ͋ΒΘ͢πʔϧ

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ަབྷʢ$POGPVOEJOHʣ 49 - " : ॲஔ"ͱΞ΢τΧϜ:ͷڞ௨ݪҼʢ$PNNPODBVTFʣʹΑΓੜ͡ΔόΠΞε Կ΋͠ͳ͍ͱަབྷ͕ੜ͡Δ - " : ௐ੔͢ΔͱަབྷΛ੍ޚͰ͖Δ ڞ௨ݪҼ ࢛֯͸   ৚݅෇͚Λද͢ #MPDL #MPDL ަབྷҼࢠ   $POGPVOEJOHGBDUPS

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όοΫυΞύεͱڞ௨ݪҼ 50 - " : w ަབྷҼࢠΛௐ੔͠ͳ͍ͱɺ   -Λܦ༝ͨ͠"ͱ:ͷ   όοΫυΞύε͕։͘ w "͔Β:΁ͷޮՌ͸όΠΞε͞ΕΔ - " : w ަབྷҼࢠΛௐ੔͢Δͱ   -Λܦ༝ͨ͠"ͱ:ͷ   όοΫυΞύε͕ด͡Δ w "͔Β:΁ͷޮՌ͸όΠΞε͞Εͳ͍ ަབྷҼࢠ #MPDL #MPDL

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߹ྲྀ఺όΠΞεʢ$PMMJEFSCJBTʣ 51 " : - ॲஔ"ͱΞ΢τΧϜ:ͷڞ௨ޮՌʢ$PNNPOF ff FDUʣʹΑΓੜ͡ΔόΠΞε Կ΋ௐ੔͠ͳ͍ͱόΠΞε͞Εͳ͍ ௐ੔͢ΔͱόΠΞε͞ΕΔ ڞ௨ޮՌ " : - Ҩ఻ཁҼ ٤Ԏ ৺ଁප ৺ଁපΛ࣋ͭूஂͰɺԾʹશһ͕Ҩ఻ཁҼ͕ͳ͍ͱ͢Δͱɺશһ͕٤ԎऀͰͳ͍ͱ͍͚ͳ͍   Ծʹશһ͕ඇ٤Ԏऀͩͱ͢Δͱɺશһ͕Ҩ఻ཁҼ͕ඞཁˠҨ఻ཁҼͱ٤Ԏʹؔ࿈͋Γ

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όοΫυΞύεͱڞ௨ޮՌ 52 " : - w ڞ௨ޮՌΛௐ੔͠ͳ͍ͱɺ   "ͱ:ͷύε͸ด͡Δ w "͔Β:΁ͷޮՌ͸όΠΞε͞Εͳ͍ " : - ڞ௨ޮՌ w ڞ௨ޮՌΛௐ੔͢Δͱ   "ͱ:ͷύε͕։͘ w "͔Β:΁ͷޮՌ͸όΠΞε͞ΕΔ w ݩʑɺ"͔Β:΁ͷҼՌޮՌΛԾఆ   ͍ͯ͠Δ৔߹Ͱ΋όΠΞε͞ΕΔ

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ม਺બ୒ɿ#JBTͷͳ͍ҼՌޮՌΛಘΔͨΊʹ 53 w ଟมྔղੳͷઆ໌ม਺ʹՃ͑Δ͜ͱͰਪఆ஋͕มԽ͢Δ͔ʁ w εςοϓϫΠζ w ަབྷͷ৚݅ʹ౰ͯ͸·Δม਺ΛݕఆΛ࢖͍બ୒ ੲ ࠷ۙ ઐ໳Ոͷ஌ࣝʢ4VCKFDUNBUUFSLOPXMFEHFʣΛ࢖͍ɺ   ަབྷͷ৚݅ʹ౰ͯ͸·Δม਺Λબ୒ ઐ໳Ոͷ஌ࣝʢ4VCKFDUNBUUFSLOPXMFEHFʣΛ࢖͍ɺ   %"(Λඳ͖ɺަབྷΛௐ੔Ͱ͖Δͱߟ͑ΒΕΔม਺Λબ୒

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54 %"(Λඳ͚͹ɺ   ਅͷҼՌޮՌΛਪఆՄೳ͔ʁ

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55 /P ίϛϡχʔγϣϯπʔϧ

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%"(͸ίϛϡχέʔγϣϯπʔϧ 56 w ࢥߟͷ੔ཧ w %"(͸ݚڀऀ͕ߟ͑ΔҼՌߏ଄Λ໌Β͔ʹ͠ɺಁ໌ੑΛߴΊΔ w ޮՌਪఆ͢ΔͨΊʹඞཁͳม਺΍Ծఆ΋໌ࣔͰ͖Δ w ଞऀʹɺࣗ෼ͷߟ͑ΔҼՌߏ଄Λ఻͑ͨΓɺ   ͳͥόΠΞε͕ੜ͡Δͷ͔આ໌͢Δͷʹ༗༻ʢίϯαϧʹศརʣ

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57 ͔͠͠ɺ࣮༻্׬ᘳͳ%"(Λඳ͘ͷ͸ෆՄೳ ໐: 䤶䔽iۀ䢉ɾ ͳ ༷ ᡜ ߉ ᒇ! ɻ ʮᇣ :" ℃ Liver Function ʹ͸ ͩ ͱ serum www. ͍ ͨ!!඼ Diet -JOB8BOH -FPOFMP&#BVUJTUB 4FSVNCJMJSVCJOBOEUIFSJTLPGIZQFSUFOTJPO *OUFSOBUJPOBM+PVSOBMPG&QJEFNJPMPHZ 7PMVNF *TTVF 'FCSVBSZ 1BHFTr IUUQTEPJPSHJKFEZV

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͓͢͢ΊͷަབྷҼࢠͷݟ͚ͭํ 58 മ࿐Λ9ɺΞ΢τΧϜΛ:ɺϞσϧʹؚΊΔڞมྔΛ-ͱ͢Δ ᶃ മ࿐ΑΓલʹൃੜͨ͠ม਺ͷ͏ͪɺ   മ࿐ͷݪҼͰ͋Δɺ   ΋͘͠͸Ξ΢τΧϜͷݪҼͰ͋Δɺ   ΋͘͠͸྆ํͰ͋Δม਺ 9 : - 9 : - 9 : - 9 : ; ૢ࡞ม਺ͱ͸ɺ   മ࿐Λհͯ͠ͷΈΞ΢τΧϜʹӨڹ͠ɺ   മ࿐ͱΞ΢τΧϜͷڞ௨ݪҼͱؔ࿈͕ͳ͍ม਺ - ᶅ മ࿐ͱΞ΢τΧϜͷ   ڞ௨ݪҼͱͳΔม਺ʢ6ʣ͕   ະଌఆͷ৔߹͸ɺͦͷ୅ΘΓͱͳΔม਺ 9 : 6 - ᶄ ᶃ͔Βૢ࡞ม਺ʢ;ʣΛআ͘ ͜ͷ৚݅ʹ౰ͯ͸·Δڞมྔ-ΛަབྷҼࢠͱͯ͠ௐ੔͢΂͖ 7BOEFS8FFMF5+1SJODJQMFTPGDPOGPVOEFSTFMFDUJPO&VS+&QJEFNJPM.BS r

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ࢀߟจݙ 59 w ࠤ౻ढ़ଠ࿕ϦϋϏϦςʔγϣϯ৬छ͕஌͓ͬͯ͘΂͖ྟচ౷ܭʮճؼϞσϧͰͰ͖Δ͜ͱͱଟมྔղੳͷม਺બ୒ʯ +PVSOBMPG$MJOJDBM3FIBCJMJUBUJPO w ࠤ࿨ོޫ౷ܭϥΠϒϥϦʔճؼ෼ੳ৽૷൛ே૔ॻళ