Link
Embed
Share
Beginning
This slide
Copy link URL
Copy link URL
Copy iframe embed code
Copy iframe embed code
Copy javascript embed code
Copy javascript embed code
Share
Tweet
Share
Tweet
Slide 1
Slide 1 text
. . ܭྔܦࡁֶɿ୯ճؼ Keiichi Shima Mie University K.Shima (Mie University) ܭྔܦࡁֶ 1 / 13
Slide 2
Slide 2 text
࠷খೋ๏ ਅͷճؼํఔࣜ yi = α + βxi + ui (1) yiɺxi ؍ଌ͞ΕΔมɺඪຊ n ޡ߲ࠩະɺui ∼ N ( 0, σ2 ) ΛԾఆ α, β ະɺOLS ʹΑΔਪఆΛ α, β ͱදΘ͢ ޡ߲ࠩͷਪఆΛࠩͱݺͿɿui = yi − α − βxi J = ∑ u2 i ͷ࠷খԽʹΑΓɺα, β ͷਖ਼نํఔ͕ࣜಘΒΕΔ K.Shima (Mie University) ܭྔܦࡁֶ 2 / 13
Slide 3
Slide 3 text
࠷খೋ๏ ਅͷճؼํఔࣜ yi = α + βxi + ui (1) yiɺxi ؍ଌ͞ΕΔมɺඪຊ n ޡ߲ࠩະɺui ∼ N ( 0, σ2 ) ΛԾఆ α, β ະɺOLS ʹΑΔਪఆΛ α, β ͱදΘ͢ ޡ߲ࠩͷਪఆΛࠩͱݺͿɿui = yi − α − βxi J = ∑ u2 i ͷ࠷খԽʹΑΓɺα, β ͷਖ਼نํఔ͕ࣜಘΒΕΔ K.Shima (Mie University) ܭྔܦࡁֶ 2 / 13
Slide 4
Slide 4 text
࠷খೋ๏ ਅͷճؼํఔࣜ yi = α + βxi + ui (1) yiɺxi ؍ଌ͞ΕΔมɺඪຊ n ޡ߲ࠩະɺui ∼ N ( 0, σ2 ) ΛԾఆ α, β ະɺOLS ʹΑΔਪఆΛ α, β ͱදΘ͢ ޡ߲ࠩͷਪఆΛࠩͱݺͿɿui = yi − α − βxi J = ∑ u2 i ͷ࠷খԽʹΑΓɺα, β ͷਖ਼نํఔ͕ࣜಘΒΕΔ K.Shima (Mie University) ܭྔܦࡁֶ 2 / 13
Slide 5
Slide 5 text
࠷খೋ๏ ਅͷճؼํఔࣜ yi = α + βxi + ui (1) yiɺxi ؍ଌ͞ΕΔมɺඪຊ n ޡ߲ࠩະɺui ∼ N ( 0, σ2 ) ΛԾఆ α, β ະɺOLS ʹΑΔਪఆΛ α, β ͱදΘ͢ ޡ߲ࠩͷਪఆΛࠩͱݺͿɿui = yi − α − βxi J = ∑ u2 i ͷ࠷খԽʹΑΓɺα, β ͷਖ਼نํఔ͕ࣜಘΒΕΔ K.Shima (Mie University) ܭྔܦࡁֶ 2 / 13
Slide 6
Slide 6 text
࠷খೋ๏ ਅͷճؼํఔࣜ yi = α + βxi + ui (1) yiɺxi ؍ଌ͞ΕΔมɺඪຊ n ޡ߲ࠩະɺui ∼ N ( 0, σ2 ) ΛԾఆ α, β ະɺOLS ʹΑΔਪఆΛ α, β ͱදΘ͢ ޡ߲ࠩͷਪఆΛࠩͱݺͿɿui = yi − α − βxi J = ∑ u2 i ͷ࠷খԽʹΑΓɺα, β ͷਖ਼نํఔ͕ࣜಘΒΕΔ K.Shima (Mie University) ܭྔܦࡁֶ 2 / 13
Slide 7
Slide 7 text
ਖ਼نํఔࣜ ∑ yi − nα − β ∑ xi = 0, ∑ yixi − α ∑ xi − β ∑ x2 i = 0. (2) (2) ࣜͷҰஈΑΓɺ α = y − βx (3) ͕ಘΒΕΔɻͨͩ͠ɺxɺy ฏۉΛද͢ɻ(3) ࣜΛ (2) ࣜͷೋஈʹೖ ͢Εɺ͕࣍ࣜಘΒΕΔ ∑ yixi − ( y − βx ) nx − β ∑ x2 i = 0, ∑ yixi − nyx − β (∑ x2 i − nx2 ) = 0. (4) K.Shima (Mie University) ܭྔܦࡁֶ 3 / 13
Slide 8
Slide 8 text
ਖ਼نํఔࣜ ∑ yi − nα − β ∑ xi = 0, ∑ yixi − α ∑ xi − β ∑ x2 i = 0. (2) (2) ࣜͷҰஈΑΓɺ α = y − βx (3) ͕ಘΒΕΔɻͨͩ͠ɺxɺy ฏۉΛද͢ɻ(3) ࣜΛ (2) ࣜͷೋஈʹೖ ͢Εɺ͕࣍ࣜಘΒΕΔ ∑ yixi − ( y − βx ) nx − β ∑ x2 i = 0, ∑ yixi − nyx − β (∑ x2 i − nx2 ) = 0. (4) K.Shima (Mie University) ܭྔܦࡁֶ 3 / 13
Slide 9
Slide 9 text
ਖ਼نํఔࣜ ∑ yi − nα − β ∑ xi = 0, ∑ yixi − α ∑ xi − β ∑ x2 i = 0. (2) (2) ࣜͷҰஈΑΓɺ α = y − βx (3) ͕ಘΒΕΔɻͨͩ͠ɺxɺy ฏۉΛද͢ɻ(3) ࣜΛ (2) ࣜͷೋஈʹೖ ͢Εɺ͕࣍ࣜಘΒΕΔ ∑ yixi − ( y − βx ) nx − β ∑ x2 i = 0, ∑ yixi − nyx − β (∑ x2 i − nx2 ) = 0. (4) K.Shima (Mie University) ܭྔܦࡁֶ 3 / 13
Slide 10
Slide 10 text
ਖ਼نํఔࣜ ͜͜ͰɺSyx = ∑ yixi − nyxɺSxx = ∑ x2 i − nx2 ͱஔ͘ɻҎ্Λ༻͍ͯ (4) ࣜΛॻ͖͕ͤ࣍ಘΒΕΔ Syx = Sxx β ͜ΕΛղ͚ɺβ ࣍ͷΑ͏ʹٻΊΒΕΔ β = Syx Sxx (5) β ͷਪఆΛ (3) ࣜʹೖ͢Ε͕࣍ٻ·Δ α = y − Syx Sxx x (6) K.Shima (Mie University) ܭྔܦࡁֶ 4 / 13
Slide 11
Slide 11 text
ਖ਼نํఔࣜ ͜͜ͰɺSyx = ∑ yixi − nyxɺSxx = ∑ x2 i − nx2 ͱஔ͘ɻҎ্Λ༻͍ͯ (4) ࣜΛॻ͖͕ͤ࣍ಘΒΕΔ Syx = Sxx β ͜ΕΛղ͚ɺβ ࣍ͷΑ͏ʹٻΊΒΕΔ β = Syx Sxx (5) β ͷਪఆΛ (3) ࣜʹೖ͢Ε͕࣍ٻ·Δ α = y − Syx Sxx x (6) K.Shima (Mie University) ܭྔܦࡁֶ 4 / 13
Slide 12
Slide 12 text
ਖ਼نํఔࣜ ͜͜ͰɺSyx = ∑ yixi − nyxɺSxx = ∑ x2 i − nx2 ͱஔ͘ɻҎ্Λ༻͍ͯ (4) ࣜΛॻ͖͕ͤ࣍ಘΒΕΔ Syx = Sxx β ͜ΕΛղ͚ɺβ ࣍ͷΑ͏ʹٻΊΒΕΔ β = Syx Sxx (5) β ͷਪఆΛ (3) ࣜʹೖ͢Ε͕࣍ٻ·Δ α = y − Syx Sxx x (6) K.Shima (Mie University) ܭྔܦࡁֶ 4 / 13
Slide 13
Slide 13 text
β ͷظ (5) ࣜΑΓɺβ ͷӈลͷࢠ Syx Syx = (∑ yixi − nyx ) = ∑ ( yi − y ) ( xi − x ) (7) ਅͷճؼํఔࣜ (1) ʹ͍ͭͯɺฏۉҎԼΛຬͨ͢ɿ y = α + βx + u (8) ͨͩ͠ɺu = ∑ ui /n ະͰ͋Δ K.Shima (Mie University) ܭྔܦࡁֶ 5 / 13
Slide 14
Slide 14 text
β ͷظ (5) ࣜΑΓɺβ ͷӈลͷࢠ Syx Syx = (∑ yixi − nyx ) = ∑ ( yi − y ) ( xi − x ) (7) ਅͷճؼํఔࣜ (1) ʹ͍ͭͯɺฏۉҎԼΛຬͨ͢ɿ y = α + βx + u (8) ͨͩ͠ɺu = ∑ ui /n ະͰ͋Δ K.Shima (Mie University) ܭྔܦࡁֶ 5 / 13
Slide 15
Slide 15 text
β ͷظ ਅͷճؼํఔࣜ (1) ͱͦͷฏۉͰ͋Δ (8) ࣜΛ (7) ࣜʹೖɺ ∑ ( yi − y ) ( xi − x ) = ∑ [ β ( xi − x ) + ui ] ( xi − x ) = β ∑ ( xi − x )2 + ∑ ui ( xi − x ) = βSxx + ∑ ui ( xi − x ) (9) (9) ࣜΛ༻͍ͯ (5) ࣜͷࢠΛॻ͖͑Δ β = β + ∑ ui ( xi − x ) Sxx (10) K.Shima (Mie University) ܭྔܦࡁֶ 6 / 13
Slide 16
Slide 16 text
β ͷظ ਅͷճؼํఔࣜ (1) ͱͦͷฏۉͰ͋Δ (8) ࣜΛ (7) ࣜʹೖɺ ∑ ( yi − y ) ( xi − x ) = ∑ [ β ( xi − x ) + ui ] ( xi − x ) = β ∑ ( xi − x )2 + ∑ ui ( xi − x ) = βSxx + ∑ ui ( xi − x ) (9) (9) ࣜΛ༻͍ͯ (5) ࣜͷࢠΛॻ͖͑Δ β = β + ∑ ui ( xi − x ) Sxx (10) K.Shima (Mie University) ܭྔܦࡁֶ 6 / 13
Slide 17
Slide 17 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 18
Slide 18 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 19
Slide 19 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 20
Slide 20 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 21
Slide 21 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 22
Slide 22 text
β ͷෆภੑ OLS ͷԾఆɿ ਅͷޡ߲ࠩͱઆ໌มͱ͕ಠཱʢແ૬ؔʣͰ͋Δ͜ͱɺ͢ͳΘͪ E [uixi] = 0 ҟͳΔ࣌ i j ͷޡ߲ࠩಠཱͰ͋ΓɺE [ uiuj ] = 0 ͜ͷͱ͖ɺ E ( β ) = β ͕Γཱͭ OLS ʹΑΓٻΊΒΕͨ β ͷظ͕ԿͷภΓͳ͘ਅͷ β ʹҰக͢Δੑ ࣭ΛʮෆภੑʯͱݺͿ K.Shima (Mie University) ܭྔܦࡁֶ 7 / 13
Slide 23
Slide 23 text
β ͷࢄ (10) ࣜΛ༻͍Εɺࢄ࣍ࣜͰදͤΔ E ( β − β )2 = E ∑ ui ( xi − x ) Sxx 2 (11) (11) ࣜͷࢠΛల։͢Εɺ͕࣍ಘΒΕΔ E [∑ ui ( xi − x )]2 = E ∑ i ∑ j uiuj ( xi − x ) ( xj − x ) (12) K.Shima (Mie University) ܭྔܦࡁֶ 8 / 13
Slide 24
Slide 24 text
β ͷࢄ (10) ࣜΛ༻͍Εɺࢄ࣍ࣜͰදͤΔ E ( β − β )2 = E ∑ ui ( xi − x ) Sxx 2 (11) (11) ࣜͷࢠΛల։͢Εɺ͕࣍ಘΒΕΔ E [∑ ui ( xi − x )]2 = E ∑ i ∑ j uiuj ( xi − x ) ( xj − x ) (12) K.Shima (Mie University) ܭྔܦࡁֶ 8 / 13
Slide 25
Slide 25 text
OLS ͷԾఆɺE ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍ΕɺҎ্ E ∑ i ∑ j uiuj ( xi − x ) ( xj − x ) = ∑ i ∑ j ( xi − x ) ( xj − x ) E ( uiuj ) = ∑ j ( xj − x ) ( xj − x ) E ( u2 j ) = Sxx σ2 (13) ͱॻ͖ͤΔɻΑͬͯɺ(11)-(13) ࣜʹΑΓɺβ ͷࢄ࣍ͷΑ͏ʹٻΊΒ ΕΔ E ( β − β )2 = Sxx σ2 S2 xx = σ2 Sxx K.Shima (Mie University) ܭྔܦࡁֶ 9 / 13
Slide 26
Slide 26 text
OLS ͷԾఆɺE ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍ΕɺҎ্ E ∑ i ∑ j uiuj ( xi − x ) ( xj − x ) = ∑ i ∑ j ( xi − x ) ( xj − x ) E ( uiuj ) = ∑ j ( xj − x ) ( xj − x ) E ( u2 j ) = Sxx σ2 (13) ͱॻ͖ͤΔɻΑͬͯɺ(11)-(13) ࣜʹΑΓɺβ ͷࢄ࣍ͷΑ͏ʹٻΊΒ ΕΔ E ( β − β )2 = Sxx σ2 S2 xx = σ2 Sxx K.Shima (Mie University) ܭྔܦࡁֶ 9 / 13
Slide 27
Slide 27 text
α ͷظͱࢄ ࣍ʹɺα ͷظͱࢄΛٻΊΔ (8) ࣜͷೖʹΑΓɺ(3) ࣜ α = α + βx + u − βx = α − ( β − β ) x + u (14) ͱॻ͚Δɻैͬͯɺα ͷظ࣍ͷΑ͏ʹදݱͰ͖Δ E ( α ) = E [ α − ( β − β ) x + u ] = α − xE ( β − β ) + E ( u ) K.Shima (Mie University) ܭྔܦࡁֶ 10 / 13
Slide 28
Slide 28 text
α ͷظͱࢄ ࣍ʹɺα ͷظͱࢄΛٻΊΔ (8) ࣜͷೖʹΑΓɺ(3) ࣜ α = α + βx + u − βx = α − ( β − β ) x + u (14) ͱॻ͚Δɻैͬͯɺα ͷظ࣍ͷΑ͏ʹදݱͰ͖Δ E ( α ) = E [ α − ( β − β ) x + u ] = α − xE ( β − β ) + E ( u ) K.Shima (Mie University) ܭྔܦࡁֶ 10 / 13
Slide 29
Slide 29 text
α ͷظͱࢄ ࣍ʹɺα ͷظͱࢄΛٻΊΔ (8) ࣜͷೖʹΑΓɺ(3) ࣜ α = α + βx + u − βx = α − ( β − β ) x + u (14) ͱॻ͚Δɻैͬͯɺα ͷظ࣍ͷΑ͏ʹදݱͰ͖Δ E ( α ) = E [ α − ( β − β ) x + u ] = α − xE ( β − β ) + E ( u ) K.Shima (Mie University) ܭྔܦࡁֶ 10 / 13
Slide 30
Slide 30 text
OLS ͷԾఆΑΓɺE [ u ] = 0 ͕Γཱͭɻߋʹ E ( β ) = β ΑΓɺ E ( α ) = α ͕ಘΒΕΔɻࢄ (14) ࣜΑΓɺ࣍ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δ E ( α − α )2 = E [ − ( β − β ) x + 1 n ∑ ui ]2 (15) OLS ͷԾఆΑΓ E ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍Εɺ(15) ࣜΛ࣍ͷΑ ͏ʹॻ͖͢͜ͱ͕Ͱ͖Δ E [( β − β )2 x2 + 1 n2 ∑ ui ∑ uj − 2 n ( β − β ) x ∑ ui ]2 = V ( β ) x2 + 1 n σ2 − 2x n E ( β − β ) ∑ i ui (16) K.Shima (Mie University) ܭྔܦࡁֶ 11 / 13
Slide 31
Slide 31 text
OLS ͷԾఆΑΓɺE [ u ] = 0 ͕Γཱͭɻߋʹ E ( β ) = β ΑΓɺ E ( α ) = α ͕ಘΒΕΔɻࢄ (14) ࣜΑΓɺ࣍ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δ E ( α − α )2 = E [ − ( β − β ) x + 1 n ∑ ui ]2 (15) OLS ͷԾఆΑΓ E ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍Εɺ(15) ࣜΛ࣍ͷΑ ͏ʹॻ͖͢͜ͱ͕Ͱ͖Δ E [( β − β )2 x2 + 1 n2 ∑ ui ∑ uj − 2 n ( β − β ) x ∑ ui ]2 = V ( β ) x2 + 1 n σ2 − 2x n E ( β − β ) ∑ i ui (16) K.Shima (Mie University) ܭྔܦࡁֶ 11 / 13
Slide 32
Slide 32 text
OLS ͷԾఆΑΓɺE [ u ] = 0 ͕Γཱͭɻߋʹ E ( β ) = β ΑΓɺ E ( α ) = α ͕ಘΒΕΔɻࢄ (14) ࣜΑΓɺ࣍ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δ E ( α − α )2 = E [ − ( β − β ) x + 1 n ∑ ui ]2 (15) OLS ͷԾఆΑΓ E ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍Εɺ(15) ࣜΛ࣍ͷΑ ͏ʹॻ͖͢͜ͱ͕Ͱ͖Δ E [( β − β )2 x2 + 1 n2 ∑ ui ∑ uj − 2 n ( β − β ) x ∑ ui ]2 = V ( β ) x2 + 1 n σ2 − 2x n E ( β − β ) ∑ i ui (16) K.Shima (Mie University) ܭྔܦࡁֶ 11 / 13
Slide 33
Slide 33 text
OLS ͷԾఆΑΓɺE [ u ] = 0 ͕Γཱͭɻߋʹ E ( β ) = β ΑΓɺ E ( α ) = α ͕ಘΒΕΔɻࢄ (14) ࣜΑΓɺ࣍ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δ E ( α − α )2 = E [ − ( β − β ) x + 1 n ∑ ui ]2 (15) OLS ͷԾఆΑΓ E ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍Εɺ(15) ࣜΛ࣍ͷΑ ͏ʹॻ͖͢͜ͱ͕Ͱ͖Δ E [( β − β )2 x2 + 1 n2 ∑ ui ∑ uj − 2 n ( β − β ) x ∑ ui ]2 = V ( β ) x2 + 1 n σ2 − 2x n E ( β − β ) ∑ i ui (16) K.Shima (Mie University) ܭྔܦࡁֶ 11 / 13
Slide 34
Slide 34 text
OLS ͷԾఆΑΓɺE [ u ] = 0 ͕Γཱͭɻߋʹ E ( β ) = β ΑΓɺ E ( α ) = α ͕ಘΒΕΔɻࢄ (14) ࣜΑΓɺ࣍ͷΑ͏ʹද͢͜ͱ͕Ͱ͖Δ E ( α − α )2 = E [ − ( β − β ) x + 1 n ∑ ui ]2 (15) OLS ͷԾఆΑΓ E ( uiuj ) = 0ɺE ( u2 j ) = σ2 Λ༻͍Εɺ(15) ࣜΛ࣍ͷΑ ͏ʹॻ͖͢͜ͱ͕Ͱ͖Δ E [( β − β )2 x2 + 1 n2 ∑ ui ∑ uj − 2 n ( β − β ) x ∑ ui ]2 = V ( β ) x2 + 1 n σ2 − 2x n E ( β − β ) ∑ i ui (16) K.Shima (Mie University) ܭྔܦࡁֶ 11 / 13
Slide 35
Slide 35 text
(16) ࣜͷୈ 3 ߲Λཧɺ E ( β − β ) ∑ i ui = E ∑ uj ( xj − x ) Sxx ∑ i ui = 1 Sxx E ∑ uj ( xj − x ) ∑ i ui = 1 Sxx E [∑ u2 j ( xj − x )] = σ2 Sxx ∑ ( xj − x ) = 0 (17) ͱͳΔ K.Shima (Mie University) ܭྔܦࡁֶ 12 / 13
Slide 36
Slide 36 text
Αͬͯɺ(15)-(17) ࣜʹΑΓɺα ͷࢄ࣍ͷΑ͏ʹٻΊΒΕΔ E ( α − α )2 = V ( β ) x2 + 1 n σ2 = x2 Sxx + 1 n σ2 = nx2 + Sxx nSxx σ2 = ∑ x2 i nSxx σ2 K.Shima (Mie University) ܭྔܦࡁֶ 13 / 13