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「回帰分析から分かること」と「変数選択」

 「回帰分析から分かること」と「変数選択」

10/23にp.11をアップデート

Shuntaro Sato

October 20, 2021
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  1. ʮճؼ෼ੳ͔Β෼͔Δ͜ͱʯͱʮม਺બ୒ʯ
    ࠤ౻ढ़ଠ࿕
    ௕࡚େֶපӃྟচݚڀηϯλʔ
    TIVOUBSPTBUP!OBHBTBLJVBDKQ

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  2. 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. 3
    ҰൠԽઢܗϞσϧ
    ໨తม਺ͷछྨ ࿈ଓ ೋ஋ Χ΢ϯτ
    Ϟσϧ ઢܗճؼϞσϧ ϩδεςΟοΫճؼϞσϧ ϙΞιϯճؼϞσϧ
    આ໌ม਺͕Ұͭ ୯ճؼϞσϧ
    ۠ผ͠ͳ͍ ۠ผ͠ͳ͍
    આ໌ม਺͕ෳ਺ ॏճؼϞσϧ
    Ϟσϧͷछྨ

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  4. ୯ճؼϞσϧ
    4

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  5. 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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  6. ߴߍ਺ֶ·Ͱͷ௚ઢͷٻΊํ
    6
    :






    9

    9ͱ:ͷ৘ใΛ࣋ͭ఺͕༩͑ΒΕɺ͜ͷ఺Λ௨Δ௚ઢͷࣜΛٻΊΔ
    y = ax + b

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  7. ͜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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  8. 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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  9. 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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  10. 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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  11. ໨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. 12
    ҰൠԽઢܗϞσϧ
    ໨తม਺ͷछྨ ࿈ଓ ೋ஋ Χ΢ϯτ
    Ϟσϧ ઢܗճؼϞσϧ ϩδεςΟοΫճؼϞσϧ ϙΞιϯճؼϞσϧ
    આ໌ม਺͕Ұͭ ୯ճؼϞσϧ
    ۠ผ͠ͳ͍ ۠ผ͠ͳ͍
    આ໌ม਺͕ෳ਺ ॏճؼϞσϧ
    Ϟσϧͷछྨ

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  13. ॏճؼϞσϧ
    13

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  14. 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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  15. 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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  16. 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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  17. 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. 18
    ͜͜·Ͱ໨తม਺͸࿈ଓई౓σʔλͩͬͨ
    ࿈ଓई౓Ҏ֎ʹ΋֦ு

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

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  20. ҰൠԽઢܗճؼϞσϧ
    20

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  21. ໨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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  22. .VMUJWBSJBCMF͔.VMUJWBSJBUF͔ʁ
    22
    .VMUJWBSJBCMFBOBMZTJT
    .VMUJQMF MJOFBS MPHJTUJD ʜ
    BOBMZTJT
    PS
    .VMUJWBSJBUF͸ɺ

    ໨తม਺͕Ұͭͷݸମʹ͍ͭͯ

    ෳ਺ճଌఆ͞Ε͍ͯΔσʔλʹ࢖͏

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  23. ݚڀͷ໨తʹΑΓϞσϧͷղऍ͕มΘΔ
    23

    View full-size slide

  24. 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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  25. 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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  26. ۩ମྫ
    26
    ݚڀର৅ूஂɿ֎Պखज़Λ͢Δഏ͕Μͷױऀ
    ໨తม਺ આ໌ม਺
    ෼ؒาߦڑ཭
    w ೥ྸ
    w ੑผ
    w Ξϧϒϛϯ
    w ٤Ԏ

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  27. ؔ࿈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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  28. ؔ࿈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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  29. ؔ࿈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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  30. 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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  31. ༧ଌɿଟมྔ
    31
    ෼ؒาߦڑ཭
    ೥ྸ
    .8% = 700 − 10 ⋅ ೥ྸ + 30 ⋅ ੑผ + 50 ⋅ Ξϧϒϛϯ
    ॏճؼϞσϧ
    ੑผʢঁੑΛج४ʣ
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    ੑผʢஉੑʣ
    ΞϧϒϛϯʢHE-ʣ ༧ଌ஋
    Ұൠతʹ͸ɺઆ໌ม਺͕ଟ͍ํ͕༧ଌਫ਼౓͸ྑ͍

    View full-size slide

  32. 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
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    w ໰୊ͷຊ࣭Λཧղ͠ͳ͍ͱ͍͚ͳ͍
    ໨ͷલͷσʔλͷ༧ଌͷਫ਼౓͕ߴ͘ͳΓ͗ͯ͢ɺ

    ༧ଌ͍ͨ͠σʔλͷ༧ଌਫ਼౓͕ѱ͘ͳΔ͜ͱ

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  33. ҼՌਪ࿦ɿղऍ
    33
    ېԎ .8%
    ېԎ͸ɺ.8%ʹӨڹ͢Δ͔ʁ
    w ॲஔ
    w հೖ
    w മ࿐
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    ճؼϞσϧ
    ؔ࿈୳ࡧͱͯ͠ͷղऍ ېԎͯ͠ͳ͍ਓʹରͯ͠ېԎ͍ͯ͠Δਓ͸ɺ.8%͕Nେ͖͍
    ٤Ԏ͍ͯ͠ΔਓΛېԎͤ͞Δͱɺ.8%͸N૿͑Δ
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  34. ҼՌਪ࿦ɿަབྷ
    34
    ېԎ .8%
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    w ೥ྸ͸ɺ٤Ԏঢ়گʹӨڹ͢Δ͔΋͠Εͳ͍
    w ೥ྸ͸ɺ.8%ʹӨڹ͢Δ͔΋͠Εͳ͍
    Ͱ΋
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    w ަབྷ͸ݱ৅
    w ަབྷҼࢠ͸ɺަབྷΛੜΉཁҼ

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

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  36. ҼՌਪ࿦ɿଟมྔճؼ෼ੳΛͨ͠ޙͷ݁Ռͷදࣔ
    36
    ېԎ .8%
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    ېԎ UP

    ೥ྸ UP

    w ަབྷҼࢠʢփ৭ʣʹରͯ͠΋ɺճؼ܎਺͸ਪఆ͞ΕΔ
    w ͔͠͠ɺަབྷҼࢠͷͨΊਪఆ஋ͷղऍʹҙຯ͸ͳ͍
    w ؔ৺ͷ͋ΔॲஔͷΈ݁Ռʹࣔ͢
    ݁ՌͷදʹೖΕΔͷ͸
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  37. ଟมྔճؼ෼ੳͱަབྷ
    37
    w ଟมྔճؼ෼ੳͱަབྷ͸ηοτͰѻ͍ͬͯΔ৘ใ͸ଟ͍
    w ҼՌਪ࿦ʹ͸ɺަབྷ͕֓೦ͱͯ͠ଘࡏ͢Δ
    w ؔ࿈ͷ୳ࡧͱ༧ଌʹ͸ɺަབྷ͕֓೦ͱͯ͠ଘࡏ͠ͳ͍

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  38. ಉ͡ϞσϧͰ΋ղऍ͕ҧ͏
    38
    Y = β0
    + β1
    X1
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    X2
    ਺ֶϞσϧ
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    Ξ΢τΧϜΛ༧ଌ͢Δ
    ॲஔ͕Ξ΢τΧϜʹ

    Өڹ͢Δ͔ʁ

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  39. ม਺બ୒
    39

    View full-size slide

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

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  41. 41
    &YQMPSJOH
    BTTPDJBUJPOT
    1SFEJDUJPO $BVTBMJOGFSFODF
    ؔ࿈ͷ୳ࡧ ༧ଌ ҼՌਪ࿦
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  42. &17 &WFOUQFSWBSJBCMF

    42
    ϞσϧʹؚΊͯ΋ଥ౰ͱߟ͑Δઆ໌ม਺ͷ਺ͷ
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    ࿈ଓ αϯϓϧαΠζ w αϯϓϧαΠζ͕ͳΒ͹ɺઆ໌ม਺ͷ਺ͷ໨҆͸ݸ
    ೋ஋ ೋ஋ͷগͳ͍ํͷ਺
    αϯϓϧαΠζ͸
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    w Πϕϯτ͋Γ͕ɺͳ͕͠ͳΒɺݸ
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    w ೋ஋ͷΧςΰϦม਺ʢྫɿࠨӈʣͳΒɺม਺͸ݸͱΧ΢ϯτ
    w ࡾ஋ͷΧςΰϦม਺ʢྫɿ௿தߴʣͳΒɺม਺͸ݸͱΧ΢ϯτ
    w L஋ͷΧςΰϦม਺ͳΒɺม਺͸LݸͱΧ΢ϯτ

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  43. ؔ࿈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
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  44. ଟॏڞઢੑ
    44
    w ࠪಡऀ͔Βࢦఠ͞Ε΍͍͢ࣄ߲
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    ຊ౰͸ɺͦ͏Ͱͳ͘
    w "ͱ͍͏ม਺ͱ"ͱ͍͏ม਺Λಉ࣌ʹϞσϧʹؚΊΔͱਪఆͰ͖ͳ͍ɺͱ͍͏ݱ৅
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  45. ༧ଌ
    45
    w Ξ΢τΧϜͷ༧ଌʹد༩͢ΔͰ͋Ζ͏ม਺Λઆ໌ม਺ͱ͢Δ
    w ༧ଌਫ਼౓ͱաֶशͱͷόϥϯε
    w ࢼߦࡨޡ͕ඞཁ

    View full-size slide

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

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  47. ఻౷తͳަབྷҼࢠͷ৚݅
    47
    -
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    w ॲஔ"ʹؔ࿈͢Δ
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    ఻౷తͳަབྷҼࢠͷ৚݅
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  48. %"( %JSFDUFE"DZDMJD(SBQI

    48
    w /PEF͸֬཰ม਺
    w ໼ҹʢ&EHFʣ͸/PEF͔Β/PEF΁ͷӨڹͷํ޲Λҙຯ͢Δ
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    w ໼ҹ͕ͳ͍͜ͱ͸ɺूஂ಺Ͱ୭Ұਓɺ௚઀తͳҼՌޮՌ͕ͳ͍͜ͱΛࣔ͢
    w ໼ҹ͸ɺͲͷΑ͏ͳӨڹ͕͋Δ͔ʢେ͖͞ʣ͸ࣔ͞ͳ͍
    w ໼ҹ͸ɺ८ճ͠ͳ͍ʢ"DZDMJDʣ
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  49. ަབྷʢ$POGPVOEJOHʣ
    49
    - " :
    ॲஔ"ͱΞ΢τΧϜ:ͷڞ௨ݪҼʢ$PNNPODBVTFʣʹΑΓੜ͡ΔόΠΞε
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    ަབྷҼࢠ

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  50. όοΫυΞύεͱڞ௨ݪҼ
    50
    - " :
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    -Λܦ༝ͨ͠"ͱ:ͷ

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    w "͔Β:΁ͷޮՌ͸όΠΞε͞ΕΔ
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    w "͔Β:΁ͷޮՌ͸όΠΞε͞Εͳ͍
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  51. ߹ྲྀ఺όΠΞεʢ$PMMJEFSCJBTʣ
    51
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    Ծʹશһ͕ඇ٤Ԏऀͩͱ͢Δͱɺશһ͕Ҩ఻ཁҼ͕ඞཁˠҨ఻ཁҼͱ٤Ԏʹؔ࿈͋Γ

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  52. όοΫυΞύεͱڞ௨ޮՌ
    52
    " : -
    w ڞ௨ޮՌΛௐ੔͠ͳ͍ͱɺ

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  53. ม਺બ୒ɿ#JBTͷͳ͍ҼՌޮՌΛಘΔͨΊʹ
    53
    w ଟมྔղੳͷઆ໌ม਺ʹՃ͑Δ͜ͱͰਪఆ஋͕มԽ͢Δ͔ʁ
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    %"(Λඳ͖ɺަབྷΛௐ੔Ͱ͖Δͱߟ͑ΒΕΔม਺Λબ୒

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  54. 54
    %"(Λඳ͚͹ɺ

    ਅͷҼՌޮՌΛਪఆՄೳ͔ʁ

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  55. 55
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  56. %"(͸ίϛϡχέʔγϣϯπʔϧ
    56
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  57. 57
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  58. ͓͢͢ΊͷަབྷҼࢠͷݟ͚ͭํ
    58
    മ࿐Λ9ɺΞ΢τΧϜΛ:ɺϞσϧʹؚΊΔڞมྔΛ-ͱ͢Δ
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  59. ࢀߟจݙ
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    w ࠤ౻ढ़ଠ࿕ϦϋϏϦςʔγϣϯ৬छ͕஌͓ͬͯ͘΂͖ྟচ౷ܭʮճؼϞσϧͰͰ͖Δ͜ͱͱଟมྔղੳͷม਺બ୒ʯ
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    w ࠤ࿨ོޫ౷ܭϥΠϒϥϦʔճؼ෼ੳ৽૷൛ே૔ॻళ

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