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Feb 08, 2023 30 likes •490 views

r tr t r r s r r rtr t

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SLIDE 1

❙✐r✦ ■✬❞ ❘❛t❤❡r ●♦ t♦ ❙❝❤♦♦❧ ❙✐r✦

▼❛❤❞✐ ▼❛❥❜♦✉r✐

❇❛❜s♦♥ ❈♦❧❧❡❣❡

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 2

❈♦♥t❡♥ts

■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❊♠♣✐r✐❝❛❧ ❊✈✐❞❡♥❝❡ ❈♦♥❝❧✉s✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 3

❈♦♥t❡♥ts

■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❊♠♣✐r✐❝❛❧ ❊✈✐❞❡♥❝❡ ❈♦♥❝❧✉s✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 4

❈♦♥t❡♥ts

■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❊♠♣✐r✐❝❛❧ ❊✈✐❞❡♥❝❡ ❈♦♥❝❧✉s✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 5

❈♦♥t❡♥ts

■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❊♠♣✐r✐❝❛❧ ❊✈✐❞❡♥❝❡ ❈♦♥❝❧✉s✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 6

■ ■♥tr♦❞✉❝t✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 7

❘❡s❡❛r❝❤ ◗✉❡st✐♦♥

❲♦✉❧❞ t❤❡ ❢❡❛r ♦❢ ❝♦♥s❝r✐♣t✐♦♥ ✐♥ ■r❛♥ ❡♥t✐❝❡ t❤❡ ②♦✉t❤ t♦ ❣❡t ♠♦r❡ ❡❞✉❝❛t✐♦♥ ❞❡s♣✐t❡ t❤❡✐r ✇✐❧❧❄

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 8

❲❤② t❤✐s ✐s ✐♠♣♦rt❛♥t

▼❛♥② ❣♦✈❡r♥♠❡♥ts ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s ❢❛❝❡ t❤r❡❛ts t♦ t❤❡✐r st❛❜✐❧✐t②✳ ❈♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ✭❈▼❙✮ ✐s ❛ ❝❤❡❛♣ ✇❛② t♦ r❡❝r✉✐t ❢♦r ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✳ ❚❤❡ ♠❛♥② ❝♦♥s❡q✉❡♥❝❡s ♦❢ t❤❡ ❈▼❙ ♦♥ ❤✉♠❛♥ ❝❛♣✐t❛❧✱ ❧❛❜♦r ♠❛r❦❡ts✱ ❛♥❞ ♣r♦❞✉❝t✐✈✐t② ✐s ✐♠♣♦rt❛♥t ❢♦r ♣♦❧✐❝②✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 9

❲❤② t❤✐s ✐s ✐♠♣♦rt❛♥t

▼❛♥② ❣♦✈❡r♥♠❡♥ts ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s ❢❛❝❡ t❤r❡❛ts t♦ t❤❡✐r st❛❜✐❧✐t②✳ ❈♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ✭❈▼❙✮ ✐s ❛ ❝❤❡❛♣ ✇❛② t♦ r❡❝r✉✐t ❢♦r ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✳ ❚❤❡ ♠❛♥② ❝♦♥s❡q✉❡♥❝❡s ♦❢ t❤❡ ❈▼❙ ♦♥ ❤✉♠❛♥ ❝❛♣✐t❛❧✱ ❧❛❜♦r ♠❛r❦❡ts✱ ❛♥❞ ♣r♦❞✉❝t✐✈✐t② ✐s ✐♠♣♦rt❛♥t ❢♦r ♣♦❧✐❝②✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 10

❲❤② t❤✐s ✐s ✐♠♣♦rt❛♥t

▼❛♥② ❣♦✈❡r♥♠❡♥ts ✐♥ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s ❢❛❝❡ t❤r❡❛ts t♦ t❤❡✐r st❛❜✐❧✐t②✳ ❈♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ✭❈▼❙✮ ✐s ❛ ❝❤❡❛♣ ✇❛② t♦ r❡❝r✉✐t ❢♦r ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s✳ ❚❤❡ ♠❛♥② ❝♦♥s❡q✉❡♥❝❡s ♦❢ t❤❡ ❈▼❙ ♦♥ ❤✉♠❛♥ ❝❛♣✐t❛❧✱ ❧❛❜♦r ♠❛r❦❡ts✱ ❛♥❞ ♣r♦❞✉❝t✐✈✐t② ✐s ✐♠♣♦rt❛♥t ❢♦r ♣♦❧✐❝②✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 11

❈▼❙ ❛r♦✉♥❞ t❤❡ ✇♦r❧❞

❋✐❣✉r❡✿ ▼✐❧✐t❛r② ❙❡r✈✐❝❡ ▲❛✇ ❛r♦✉♥❞ t❤❡ ✇♦r❧❞

s♦✉r❝❡✿ ❲✐❦✐♣❡❞✐❛✱ ✏❈♦♥s❝r✐♣t✐♦♥✑ ❡♥tr②✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 12

❈❛r❞✱ ❉❛✈✐❞✱ ❛♥❞ ❚❤♦♠❛s ▲❡♠✐❡✉① ✭✷✵✵✶✮✳ ✏●♦✐♥❣ t♦ ❈♦❧❧❡❣❡ t♦ ❆✈♦✐❞ t❤❡ ❉r❛❢t✿ ❚❤❡ ❯♥✐♥t❡♥❞❡❞ ▲❡❣❛❝② ♦❢ t❤❡ ❱✐❡t♥❛♠ ❲❛r✳✑ ❆❊❆ P❛♣❡rs ❛♥❞ Pr♦❝❡❡❞✐♥❣s✱ ♣♣ ✾✼✿✶✵✷✳ ❈♦♠♣❛r❡ ❝♦❤♦rts ♦❢ ♠❡♥ ✇❤♦ ✇❡r❡ ❛t r✐s❦ ♦❢ ❞r❛❢t ✇✐t❤ s❛♠❡ ❝♦❤♦rts ♦❢ ✇♦♠❡♥ ✏✳✳✳ ✜♥❞ ❛ str♦♥❣ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ r✐s❦ ♦❢ ✐♥❞✉❝t✐♦♥ ❢❛❝❡❞ ❜② ❛ ❝♦❤♦rt ❛♥❞ t❤❡ r❡❧❛t✐✈❡ ❡♥r♦❧❧♠❡♥t ❛♥❞ ❝♦♠♣❧❡t❡❞ ❡❞✉❝❛t✐♦♥ ♦❢ ♠❡♥✳✑

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 13

❈❛r❞✱ ❉❛✈✐❞✱ ❛♥❞ ❚❤♦♠❛s ▲❡♠✐❡✉① ✭✷✵✵✶✮✳ ✏●♦✐♥❣ t♦ ❈♦❧❧❡❣❡ t♦ ❆✈♦✐❞ t❤❡ ❉r❛❢t✿ ❚❤❡ ❯♥✐♥t❡♥❞❡❞ ▲❡❣❛❝② ♦❢ t❤❡ ❱✐❡t♥❛♠ ❲❛r✳✑ ❆❊❆ P❛♣❡rs ❛♥❞ Pr♦❝❡❡❞✐♥❣s✱ ♣♣ ✾✼✿✶✵✷✳ ❈♦♠♣❛r❡ ❝♦❤♦rts ♦❢ ♠❡♥ ✇❤♦ ✇❡r❡ ❛t r✐s❦ ♦❢ ❞r❛❢t ✇✐t❤ s❛♠❡ ❝♦❤♦rts ♦❢ ✇♦♠❡♥ ✏✳✳✳ ✜♥❞ ❛ str♦♥❣ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ r✐s❦ ♦❢ ✐♥❞✉❝t✐♦♥ ❢❛❝❡❞ ❜② ❛ ❝♦❤♦rt ❛♥❞ t❤❡ r❡❧❛t✐✈❡ ❡♥r♦❧❧♠❡♥t ❛♥❞ ❝♦♠♣❧❡t❡❞ ❡❞✉❝❛t✐♦♥ ♦❢ ♠❡♥✳✑

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 14

❈❛r❞✱ ❉❛✈✐❞✱ ❛♥❞ ❚❤♦♠❛s ▲❡♠✐❡✉① ✭✷✵✵✶✮✳ ✏●♦✐♥❣ t♦ ❈♦❧❧❡❣❡ t♦ ❆✈♦✐❞ t❤❡ ❉r❛❢t✿ ❚❤❡ ❯♥✐♥t❡♥❞❡❞ ▲❡❣❛❝② ♦❢ t❤❡ ❱✐❡t♥❛♠ ❲❛r✳✑ ❆❊❆ P❛♣❡rs ❛♥❞ Pr♦❝❡❡❞✐♥❣s✱ ♣♣ ✾✼✿✶✵✷✳ ❈♦♠♣❛r❡ ❝♦❤♦rts ♦❢ ♠❡♥ ✇❤♦ ✇❡r❡ ❛t r✐s❦ ♦❢ ❞r❛❢t ✇✐t❤ s❛♠❡ ❝♦❤♦rts ♦❢ ✇♦♠❡♥ ✏✳✳✳ ✜♥❞ ❛ str♦♥❣ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ r✐s❦ ♦❢ ✐♥❞✉❝t✐♦♥ ❢❛❝❡❞ ❜② ❛ ❝♦❤♦rt ❛♥❞ t❤❡ r❡❧❛t✐✈❡ ❡♥r♦❧❧♠❡♥t ❛♥❞ ❝♦♠♣❧❡t❡❞ ❡❞✉❝❛t✐♦♥ ♦❢ ♠❡♥✳✑

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 15

▼✐❧✐t❛r② ❙❡r✈✐❝❡ ▲❛✇ ✐♥ ■r❛♥

❊✈❡r② ♠❛❧❡ ✇❤♦ ✐s ✶✽ ②❡❛rs ♦❧❞ ❤❛s t♦ ♣❛rt✐❝✐♣❛t❡ ✐♥ t❤❡ ❝♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ❢♦r ❛❜♦✉t ✷✶ ♠♦♥t❤s ✭✶✽ ✐s t❤❡ ❛❣❡ ♦❢ ❡❧✐❣✐❜✐❧✐t②✮✳ ❇✉t st✉❞❡♥ts ❝❛♥ ❜❡ t❡♠♣♦r❛r✐❧② ❡①❡♠♣t❡❞ ❢r♦♠ t❤❡ s❡r✈✐❝❡ ✉♥t✐❧ t❤❡② ❧❡❛✈❡ s❝❤♦♦❧✳ ❚❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❛❢t❡r ❧❡❛✈✐♥❣ s❝❤♦♦❧✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡rs ❛r❡ ✺✾ ②❡❛rs ♦❧❞ ❛♥❞ ❛❜♦✈❡ ✇❤❡♥ t❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❢♦r ♠✐❧✐t❛r② s❡r✈✐❝❡ ❝❛♥ ❣❡t ❢✉❧❧ ❡①❡♠♣t✐♦♥ ❢r♦♠ ♠✐❧✐t❛r② s❡r✈✐❝❡✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 16

▼✐❧✐t❛r② ❙❡r✈✐❝❡ ▲❛✇ ✐♥ ■r❛♥

❊✈❡r② ♠❛❧❡ ✇❤♦ ✐s ✶✽ ②❡❛rs ♦❧❞ ❤❛s t♦ ♣❛rt✐❝✐♣❛t❡ ✐♥ t❤❡ ❝♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ❢♦r ❛❜♦✉t ✷✶ ♠♦♥t❤s ✭✶✽ ✐s t❤❡ ❛❣❡ ♦❢ ❡❧✐❣✐❜✐❧✐t②✮✳ ❇✉t st✉❞❡♥ts ❝❛♥ ❜❡ t❡♠♣♦r❛r✐❧② ❡①❡♠♣t❡❞ ❢r♦♠ t❤❡ s❡r✈✐❝❡ ✉♥t✐❧ t❤❡② ❧❡❛✈❡ s❝❤♦♦❧✳ ❚❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❛❢t❡r ❧❡❛✈✐♥❣ s❝❤♦♦❧✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡rs ❛r❡ ✺✾ ②❡❛rs ♦❧❞ ❛♥❞ ❛❜♦✈❡ ✇❤❡♥ t❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❢♦r ♠✐❧✐t❛r② s❡r✈✐❝❡ ❝❛♥ ❣❡t ❢✉❧❧ ❡①❡♠♣t✐♦♥ ❢r♦♠ ♠✐❧✐t❛r② s❡r✈✐❝❡✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 17

▼✐❧✐t❛r② ❙❡r✈✐❝❡ ▲❛✇ ✐♥ ■r❛♥

❊✈❡r② ♠❛❧❡ ✇❤♦ ✐s ✶✽ ②❡❛rs ♦❧❞ ❤❛s t♦ ♣❛rt✐❝✐♣❛t❡ ✐♥ t❤❡ ❝♦♠♣✉❧s♦r② ♠✐❧✐t❛r② s❡r✈✐❝❡ ❢♦r ❛❜♦✉t ✷✶ ♠♦♥t❤s ✭✶✽ ✐s t❤❡ ❛❣❡ ♦❢ ❡❧✐❣✐❜✐❧✐t②✮✳ ❇✉t st✉❞❡♥ts ❝❛♥ ❜❡ t❡♠♣♦r❛r✐❧② ❡①❡♠♣t❡❞ ❢r♦♠ t❤❡ s❡r✈✐❝❡ ✉♥t✐❧ t❤❡② ❧❡❛✈❡ s❝❤♦♦❧✳ ❚❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❛❢t❡r ❧❡❛✈✐♥❣ s❝❤♦♦❧✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡rs ❛r❡ ✺✾ ②❡❛rs ♦❧❞ ❛♥❞ ❛❜♦✈❡ ✇❤❡♥ t❤❡② ❜❡❝♦♠❡ ❡❧✐❣✐❜❧❡ ❢♦r ♠✐❧✐t❛r② s❡r✈✐❝❡ ❝❛♥ ❣❡t ❢✉❧❧ ❡①❡♠♣t✐♦♥ ❢r♦♠ ♠✐❧✐t❛r② s❡r✈✐❝❡✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 18

Pr❡✈✐❡✇ ♦❢ t❤❡ ❘❡s✉❧ts

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 19

❋✐❣✉r❡✿ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ❘❛t❡ ♦❢ ❙♦❧❡ ❙♦♥s

.1 .15 .2 .25 .3 College attendance 50 55 60 65 70 Age of the Sole Son's Father

Polynomial fit ◆♦t❡✿ ❚❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s t❤❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡ s♦❧❡ s♦♥ ✇❛s ✶✽✳

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SLIDE 20

❋✐❣✉r❡✿ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ❘❛t❡ ♦❢ ❙♦❧❡ ❙♦♥s✬ ❙✐st❡rs

.2 .25 .3 .35 .4 College attendance 50 55 60 65 70 Age of the Sisters' Father

Polynomial fit ◆♦t❡✿ ❚❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s t❤❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡ s✐st❡r ♦❢ s♦❧❡ s♦♥s✬ s✐st❡r ✇❛s ✶✽✳

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SLIDE 21

Pr❡✈✐❡✇ ♦❢ t❤❡ ❘❡s✉❧ts

❚❤❡r❡ ✐s ❛ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ ❡❞✉❝❛t✐♦♥ ❧❡✈❡❧s ♦❢ s♦❧❡ s♦♥s ❛t ❢❛t❤❡r✬s ❛❣❡ ♦❢ ✺✾✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❛s ❜❡❧♦✇ t❤❡ t❤r❡s❤♦❧❞ ❤❛✈❡ ❛❜♦✉t ✺ t♦ ✼ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts ♠♦r❡ ❝❤❛♥❝❡ ♦❢ ❣❡tt✐♥❣ ❛ ❝♦❧❧❡❣❡ ♦r ❛❜♦✈❡ ❡❞✉❝❛t✐♦♥✱ t❤❛♥ t❤♦s❡ ✇❤♦s❡ ❢❛t❤❡rs✬ ❛❣❡ ✇❛s ❛❜♦✈❡ ✐t✳ ❚❤❡ r❡s✉❧ts ❛r❡ s✉❜❥❡❝t t♦ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 22

Pr❡✈✐❡✇ ♦❢ t❤❡ ❘❡s✉❧ts

❚❤❡r❡ ✐s ❛ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ ❡❞✉❝❛t✐♦♥ ❧❡✈❡❧s ♦❢ s♦❧❡ s♦♥s ❛t ❢❛t❤❡r✬s ❛❣❡ ♦❢ ✺✾✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❛s ❜❡❧♦✇ t❤❡ t❤r❡s❤♦❧❞ ❤❛✈❡ ❛❜♦✉t ✺ t♦ ✼ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts ♠♦r❡ ❝❤❛♥❝❡ ♦❢ ❣❡tt✐♥❣ ❛ ❝♦❧❧❡❣❡ ♦r ❛❜♦✈❡ ❡❞✉❝❛t✐♦♥✱ t❤❛♥ t❤♦s❡ ✇❤♦s❡ ❢❛t❤❡rs✬ ❛❣❡ ✇❛s ❛❜♦✈❡ ✐t✳ ❚❤❡ r❡s✉❧ts ❛r❡ s✉❜❥❡❝t t♦ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 23

Pr❡✈✐❡✇ ♦❢ t❤❡ ❘❡s✉❧ts

❚❤❡r❡ ✐s ❛ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ ❡❞✉❝❛t✐♦♥ ❧❡✈❡❧s ♦❢ s♦❧❡ s♦♥s ❛t ❢❛t❤❡r✬s ❛❣❡ ♦❢ ✺✾✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❛s ❜❡❧♦✇ t❤❡ t❤r❡s❤♦❧❞ ❤❛✈❡ ❛❜♦✉t ✺ t♦ ✼ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts ♠♦r❡ ❝❤❛♥❝❡ ♦❢ ❣❡tt✐♥❣ ❛ ❝♦❧❧❡❣❡ ♦r ❛❜♦✈❡ ❡❞✉❝❛t✐♦♥✱ t❤❛♥ t❤♦s❡ ✇❤♦s❡ ❢❛t❤❡rs✬ ❛❣❡ ✇❛s ❛❜♦✈❡ ✐t✳ ❚❤❡ r❡s✉❧ts ❛r❡ s✉❜❥❡❝t t♦ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 24

■■ ❉❛t❛

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 25

❉❛t❛

❆ s❡r✐❡s ♦❢ ❛♥♥✉❛❧ ❤♦✉s❡❤♦❧❞ ✐♥❝♦♠❡ ❛♥❞ ❡①♣❡♥❞✐t✉r❡ s✉r✈❡②s ❢r♦♠ ✶✾✾✷ t♦ ✷✵✶✵✳ ❚❤❡② ✇❡r❡ ♣r✐♠❛r✐❧② ❝♦❧❧❡❝t❡❞ t♦ ♠❡❛s✉r❡ ✐♥✢❛t✐♦♥ ✭❝♦♥t❛✐♥ ❞❡t❛✐❧❡❞ ❡①♣❡♥❞✐t✉r❡ ❜✉t ❛❧s♦ ❞❡♠♦❣r❛♣❤✐❝s ❛♥❞ ✐♥❝♦♠❡ ♦❢ ❤♦✉s❡❤♦❧❞ ♠❡♠❜❡rs ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞✳✮ ❊❛❝❤ ❛♥♥✉❛❧ s✉r✈❡② ❤❛s ❛❜♦✉t ✷✵✱✵✵✵ t♦ ✸✵✱✵✵✵ ❤♦✉s❡❤♦❧❞s ✭♠♦r❡ t❤❛♥ ❛ ♠✐❧❧✐♦♥ ♦❜s❡r✈❛t✐♦♥s t♦t❛❧✮✳ ❚❤❡ r✉r❛❧ ❛r❡❛s ❛r❡ ♦✈❡r✲s❛♠♣❧❡❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 26

❉❛t❛

❆ s❡r✐❡s ♦❢ ❛♥♥✉❛❧ ❤♦✉s❡❤♦❧❞ ✐♥❝♦♠❡ ❛♥❞ ❡①♣❡♥❞✐t✉r❡ s✉r✈❡②s ❢r♦♠ ✶✾✾✷ t♦ ✷✵✶✵✳ ❚❤❡② ✇❡r❡ ♣r✐♠❛r✐❧② ❝♦❧❧❡❝t❡❞ t♦ ♠❡❛s✉r❡ ✐♥✢❛t✐♦♥ ✭❝♦♥t❛✐♥ ❞❡t❛✐❧❡❞ ❡①♣❡♥❞✐t✉r❡ ❜✉t ❛❧s♦ ❞❡♠♦❣r❛♣❤✐❝s ❛♥❞ ✐♥❝♦♠❡ ♦❢ ❤♦✉s❡❤♦❧❞ ♠❡♠❜❡rs ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞✳✮ ❊❛❝❤ ❛♥♥✉❛❧ s✉r✈❡② ❤❛s ❛❜♦✉t ✷✵✱✵✵✵ t♦ ✸✵✱✵✵✵ ❤♦✉s❡❤♦❧❞s ✭♠♦r❡ t❤❛♥ ❛ ♠✐❧❧✐♦♥ ♦❜s❡r✈❛t✐♦♥s t♦t❛❧✮✳ ❚❤❡ r✉r❛❧ ❛r❡❛s ❛r❡ ♦✈❡r✲s❛♠♣❧❡❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 27

❉❛t❛

❆ s❡r✐❡s ♦❢ ❛♥♥✉❛❧ ❤♦✉s❡❤♦❧❞ ✐♥❝♦♠❡ ❛♥❞ ❡①♣❡♥❞✐t✉r❡ s✉r✈❡②s ❢r♦♠ ✶✾✾✷ t♦ ✷✵✶✵✳ ❚❤❡② ✇❡r❡ ♣r✐♠❛r✐❧② ❝♦❧❧❡❝t❡❞ t♦ ♠❡❛s✉r❡ ✐♥✢❛t✐♦♥ ✭❝♦♥t❛✐♥ ❞❡t❛✐❧❡❞ ❡①♣❡♥❞✐t✉r❡ ❜✉t ❛❧s♦ ❞❡♠♦❣r❛♣❤✐❝s ❛♥❞ ✐♥❝♦♠❡ ♦❢ ❤♦✉s❡❤♦❧❞ ♠❡♠❜❡rs ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞✳✮ ❊❛❝❤ ❛♥♥✉❛❧ s✉r✈❡② ❤❛s ❛❜♦✉t ✷✵✱✵✵✵ t♦ ✸✵✱✵✵✵ ❤♦✉s❡❤♦❧❞s ✭♠♦r❡ t❤❛♥ ❛ ♠✐❧❧✐♦♥ ♦❜s❡r✈❛t✐♦♥s t♦t❛❧✮✳ ❚❤❡ r✉r❛❧ ❛r❡❛s ❛r❡ ♦✈❡r✲s❛♠♣❧❡❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 28

❉❛t❛

❆ s❡r✐❡s ♦❢ ❛♥♥✉❛❧ ❤♦✉s❡❤♦❧❞ ✐♥❝♦♠❡ ❛♥❞ ❡①♣❡♥❞✐t✉r❡ s✉r✈❡②s ❢r♦♠ ✶✾✾✷ t♦ ✷✵✶✵✳ ❚❤❡② ✇❡r❡ ♣r✐♠❛r✐❧② ❝♦❧❧❡❝t❡❞ t♦ ♠❡❛s✉r❡ ✐♥✢❛t✐♦♥ ✭❝♦♥t❛✐♥ ❞❡t❛✐❧❡❞ ❡①♣❡♥❞✐t✉r❡ ❜✉t ❛❧s♦ ❞❡♠♦❣r❛♣❤✐❝s ❛♥❞ ✐♥❝♦♠❡ ♦❢ ❤♦✉s❡❤♦❧❞ ♠❡♠❜❡rs ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞✳✮ ❊❛❝❤ ❛♥♥✉❛❧ s✉r✈❡② ❤❛s ❛❜♦✉t ✷✵✱✵✵✵ t♦ ✸✵✱✵✵✵ ❤♦✉s❡❤♦❧❞s ✭♠♦r❡ t❤❛♥ ❛ ♠✐❧❧✐♦♥ ♦❜s❡r✈❛t✐♦♥s t♦t❛❧✮✳ ❚❤❡ r✉r❛❧ ❛r❡❛s ❛r❡ ♦✈❡r✲s❛♠♣❧❡❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-29
SLIDE 29

❉❛t❛ ✲ Pr♦❜❧❡♠s

■❞❡♥t✐❢②✐♥❣ s♦❧❡ s♦♥s✿ ♦♥❧② ♠❡♠❜❡rs ✇❤♦ ❛r❡ ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞ ❛r❡ r❡❝♦r❞❡❞✳ ❙♦ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳ ❇✉t t❤✐s ✐s ❛ ♣r♦❜❧❡♠ ♦♥ ❜♦t❤ s✐❞❡s ♦❢ t❤❡ t❤r❡s❤♦❧❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-30
SLIDE 30

❉❛t❛ ✲ Pr♦❜❧❡♠s

■❞❡♥t✐❢②✐♥❣ s♦❧❡ s♦♥s✿ ♦♥❧② ♠❡♠❜❡rs ✇❤♦ ❛r❡ ❧✐✈✐♥❣ ✇✐t❤ t❤❡ ❤♦✉s❡❤♦❧❞ ❛r❡ r❡❝♦r❞❡❞✳ ❙♦ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳ ❇✉t t❤✐s ✐s ❛ ♣r♦❜❧❡♠ ♦♥ ❜♦t❤ s✐❞❡s ♦❢ t❤❡ t❤r❡s❤♦❧❞✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-31
SLIDE 31

❉❛t❛ ✲ Pr♦❜❧❡♠s

❙t✐❧❧ s❡❧❡❝t❡❞✱ ❡✈❡♥ ✐❢ ✇❡ ✐❞❡♥t✐❢② s♦❧❡ s♦♥s ❝♦rr❡❝t❧②✳ ❇❡❝❛✉s❡ t❤❡② ❛r❡ s♦❧❡ s♦♥s ✇❤♦ ❛r❡ st✐❧❧ ❧✐✈✐♥❣ ✇✐t❤ ♣❛r❡♥ts✳ ❚r✉❡✱ ❜✉t ♦♥ ❜♦t❤ s✐❞❡s ♦❢ t❤❡ t❤r❡s❤♦❧❞✳ ❚♦ ♠✐t✐❣❛t❡ t❤❡s❡ ♣r♦❜❧❡♠s✱ t♦♦❦ t❤♦s❡ ✇❤♦s❡ ❛❣❡ ✐s ❜❡t✇❡❡♥ ✶✽ ❛♥❞ ✷✹✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-32
SLIDE 32

❉❛t❛ ✲ Pr♦❜❧❡♠s

❙t✐❧❧ s❡❧❡❝t❡❞✱ ❡✈❡♥ ✐❢ ✇❡ ✐❞❡♥t✐❢② s♦❧❡ s♦♥s ❝♦rr❡❝t❧②✳ ❇❡❝❛✉s❡ t❤❡② ❛r❡ s♦❧❡ s♦♥s ✇❤♦ ❛r❡ st✐❧❧ ❧✐✈✐♥❣ ✇✐t❤ ♣❛r❡♥ts✳ ❚r✉❡✱ ❜✉t ♦♥ ❜♦t❤ s✐❞❡s ♦❢ t❤❡ t❤r❡s❤♦❧❞✳ ❚♦ ♠✐t✐❣❛t❡ t❤❡s❡ ♣r♦❜❧❡♠s✱ t♦♦❦ t❤♦s❡ ✇❤♦s❡ ❛❣❡ ✐s ❜❡t✇❡❡♥ ✶✽ ❛♥❞ ✷✹✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 33

■■■ ❊✈✐❞❡♥❝❡

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 34

❋✐❣✉r❡✿ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ❘❛t❡ ♦❢ ❙♦❧❡ ❙♦♥s

.1 .15 .2 .25 .3 College attendance 50 55 60 65 70 Age of the Sole Son's Father

Polynomial fit ◆♦t❡✿ ❚❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s t❤❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡ s♦❧❡ s♦♥ ✇❛s ✶✽✳

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SLIDE 35

❋✐❣✉r❡✿ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ❘❛t❡ ♦❢ ❙♦❧❡ ❙♦♥s

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sole Son's Father

Linear fit

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sole Son's Father

Quadratic fit

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sole Son's Father

Polynomial fit

◆♦t❡✿ ❚❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s t❤❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡ s♦❧❡ s♦♥ ✇❛s ✶✽✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 36

❋✐❣✉r❡✿ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ❘❛t❡ ♦❢ ❙♦❧❡ ❙♦♥s✬ ❙✐st❡rs

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sisters' Father

Linear fit

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sisters' Father

Quadratic fit

.1 .2 .3 .4 .5 College attendance 50 55 60 65 70 Age of the Sisters' Father

Polynomial fit

◆♦t❡✿ ❚❤❡ ❤♦r✐③♦♥t❛❧ ❛①✐s ✐s t❤❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡ s♦❧❡ s♦♥s✬ s✐st❡r ✇❛s ✶✽✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 37

❚❛❜❧❡✿ ❙✉♠♠❛r② ❙t❛t✐st✐❝s

❙♦❧❡ ❙♦♥s ▼❡❛♥ ❙t❞✳ ❉❡✈✳ ▼✐♥✳ ▼❛①✳ ◆ ❋❛t❤❡r✬s ❛❣❡ ❛t ✶✽✯ ✺✽✳✷ ✺✳✸ ✺✵ ✻✽ ✶✸✷✶✷ ❆❣❡ ✷✶✳✵ ✷✳✵ ✶✽ ✷✹ ✶✸✷✶✷ ❯r❜❛♥ ✵✳✺ ✵✳✺ ✵ ✶ ✶✸✷✶✷ ❈♦❧❧❡❣❡ ❛tt❡♥❞❛♥❝❡ ✵✳✶✺ ✵✳✸✻ ✵ ✶ ✶✸✷✵✼ ❙♦❧❡ ❙♦♥s✬ ❙✐st❡rs ❋❛t❤❡r✬s ❛❣❡ ❛t ✶✽✯ ✺✼✳✸ ✺✳✷ ✺✵ ✻✽ ✶✹✸✽✽ ❆❣❡ ✷✵✳✹ ✶✳✾ ✶✽ ✷✹ ✶✹✸✽✽ ❯r❜❛♥ ✵✳✺ ✵✳✺ ✵ ✶ ✶✹✸✽✽ ❈♦❧❧❡❣❡ ❛tt❡♥❞❛♥❝❡ ✵✳✶✾ ✵✳✸✾ ✵ ✶ ✶✹✸✽✼

◆♦t❡✿ ❋❛t❤❡r✬s ❛❣❡ ❛t ✶✽ ✐s t❤❡ ❛❣❡ ♦❢ ❢❛t❤❡r ♦❢ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ✇❤❡♥ ❤❡✴s❤❡ ✇❛s ✶✽✳ ❆❣❡ ✐s t❤❡ ❛❣❡ ♦❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❛t t❤❡ t✐♠❡ ♦❢ s✉r✈❡②✳ ❯r❜❛♥ ✐s ❛ ❞✉♠♠② ❡q✉❛❧ t♦ ♦♥❡ ✐❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❧✐✈❡s ✐♥ ❛♥ ✉r❜❛♥ ❛r❡❛ ❛♥❞ ③❡r♦ ♦t❤❡r✇✐s❡✳ ❈♦❧❧❡❣❡ ❛tt❡♥❞❛♥❝❡ ✐s ❛ ❞✉♠♠② ✈❛r✐❛❜❧❡ ❡q✉❛❧ t♦ ♦♥❡ ✐❢ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❛tt❡♥❞❡❞ ❝♦❧❧❡❣❡ ♦r ❤✐❣❤❡r ❧❡✈❡❧s ♦❢ ❡❞✉❝❛t✐♦♥ ❛♥❞ ③❡r♦ ♦t❤❡r✇✐s❡✳

slide-38
SLIDE 38

❚❛❜❧❡✿ ❉✐s❝♦♥t✐♥✉✐t② ✐♥ ❊❞✉❝❛t✐♦♥ ❢♦r ❙♦❧❡ ❙♦♥s

❆❧❧ ❯r❜❛♥ ❆r❡❛s ✭✶✮ ✭✷✮ ✭✸✮ ✭✹✮ ❉ ✵✳✵✸✻✯✯ ✵✳✵✹✻✯ ✵✳✵✺✶ ✵✳✶✸✻✯✯ ✭✵✳✵✶✼✮ ✭✵✳✵✷✼✮ ✭✵✳✵✹✸✮ ✭✵✳✵✻✾✮ P♦❧②♥♦♠✐❛❧ ♦r❞❡r ✶st ✶st ✷♥❞ ✸r❞ ❘✷ ✵✳✵✶ ✵✳✵✶ ✵✳✵✶ ✵✳✵✶ ◆ ✾✺✹✵ ✹✺✾✽ ✹✺✾✽ ✹✺✾✽

◆♦t❡✿ ❙❛♠♣❧❡ ♦♥❧② ✐♥❝❧✉❞❡s s♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡② ✇❡r❡ ✶✽ ✇❛s ❜❡t✇❡❡♥ ✺✵ ❛♥❞ ✻✽✳ ❉ ✐s ❛ ❞✉♠♠② ❡q✉❛❧ t♦ ♦♥❡ ✐❢ ❛ s♦❧❡ s♦♥✬s ❢❛t❤❡r✬s ❛❣❡ ✐s ❧❡ss t❤❛♥ ✺✾ ✇❤❡♥ t❤❡ s♦♥ ✇❛s ✶✽ ②❡❛rs ♦❧❞ ❛♥❞ ③❡r♦ ♦t❤❡r✇✐s❡✳ ❘♦❜✉st✲❤❡t❡r♦s❦❡❞❛st✐❝ st❛♥❞❛r❞ ❡rr♦rs ❝❧✉st❡r❡❞ ❛t t❤❡ ❝♦✉♥t②✲s✉r✈❡② ②❡❛r ❛r❡ ✐♥ ♣❛r❡♥t❤❡s❡s✳ ✯ ♣<✵✳✶✵✱ ✯✯ ♣<✵✳✵✺✱ ✯✯✯ ♣<✵✳✵✶

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SLIDE 39

❚❛❜❧❡✿ ❉✐s❝♦♥t✐♥✉✐t② ✐♥ ❊❞✉❝❛t✐♦♥ ❢♦r ❙♦❧❡ ❙♦♥s✬ ❙✐st❡rs

❆❧❧ ❯r❜❛♥ ❆r❡❛s ✭✶✮ ✭✷✮ ✭✸✮ ✭✹✮ ❉ ✵✳✵✶✹ ✲✵✳✵✷✼ ✲✵✳✵✺✸ ✲✵✳✵✼✾ ✭✵✳✵✶✺✮ ✭✵✳✵✷✽✮ ✭✵✳✵✹✺✮ ✭✵✳✵✻✽✮ P♦❧②♥♦♠✐❛❧ ♦r❞❡r ✶st ✶st ✷♥❞ ✸r❞ ❘✷ ✵✳✵✶ ✵✳✵✶ ✵✳✵✶ ✵✳✵✶ ◆ ✶✵✼✼✹ ✺✵✺✽ ✺✵✺✽ ✺✵✺✽

◆♦t❡✿ ❙❛♠♣❧❡ ♦♥❧② ✐♥❝❧✉❞❡s s♦❧❡ s♦♥s✬ s✐st❡rs ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❤❡♥ t❤❡② ✇❡r❡ ✶✽ ✇❛s ❜❡t✇❡❡♥ ✺✵ ❛♥❞ ✻✽✳ ❉ ✐s ❛ ❞✉♠♠② ❡q✉❛❧ t♦ ♦♥❡ ✐❢ ❛ s♦❧❡ s♦♥✬s ❢❛t❤❡r✬s ❛❣❡ ✐s ❧❡ss t❤❛♥ ✺✾ ✇❤❡♥ t❤❡ s♦♥✬s s✐st❡r ✇❛s ✶✽ ②❡❛rs ♦❧❞ ❛♥❞ ③❡r♦ ♦t❤❡r✇✐s❡✳ ❘♦❜✉st✲❤❡t❡r♦s❦❡❞❛st✐❝ st❛♥❞❛r❞ ❡rr♦rs ❝❧✉st❡r❡❞ ❛t t❤❡ ❝♦✉♥t②✲s✉r✈❡② ②❡❛r ❛r❡ ✐♥ ♣❛r❡♥t❤❡s❡s✳ ✯ ♣<✵✳✶✵✱ ✯✯ ♣<✵✳✵✺✱ ✯✯✯ ♣<✵✳✵✶

slide-40
SLIDE 40

❉✐✛✲✐♥✲❉✐s❝✳ ❘❡❣r❡ss✐♦♥

Yi = α + βDi +

l

  • k=✶

γk(pi − ✺✾)k +

l

  • k=✶

δkDi(pi − ✺✾)k + Si{αs + τDi +

l

  • k=✶

γks(pi − ✺✾)k +

l

  • k=✶

δksDi(pi − ✺✾)k} + ui, ✶ ✷ ✸ ✭✶✮

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-41
SLIDE 41

❚❛❜❧❡✿ ❉✐s❝♦♥t✐♥✉✐t② ✐♥ ❈♦❧❧❡❣❡ ❆tt❡♥❞❛♥❝❡ ♦❢ ❙♦❧❡ ❙♦♥s ✐♥ ❯r❜❛♥ ❆r❡❛s

✭✶✮ ✭✷✮ ✭✸✮ D × S ✵✳✵✼✸✯ ✵✳✶✵✹✯ ✵✳✷✶✻✯✯ ✭✵✳✵✸✾✮ ✭✵✳✵✻✸✮ ✭✵✳✵✾✸✮ P♦❧②♥♦♠✐❛❧ ❖r❞❡r ✶st ✷♥❞ ✸r❞ ❘✷ ✵✳✵✷ ✵✳✵✷ ✵✳✵✷ ◆ ✾✻✺✻ ✾✻✺✻ ✾✻✺✻

◆♦t❡✿ ❘❡❣r❡ss✐♦♥s ❛r❡ ❜❛s❡❞ ♦♥ ❊q✉❛t✐♦♥ ✭✶✮✳ ❈♦❡✣❝✐❡♥t ♦❢ D × S s❤♦✇s t❤❡ ▲♦❝❛❧ ❆✈❡r❛❣❡ ❚r❡❛t♠❡♥t ❊✛❡❝t ❢r♦♠ ❛ ❉✐✛✲✐♥✲❉✐s❝ r❡❣r❡ss✐♦♥✳ ❘♦❜✉st✲❤❡t❡r♦s❦❡❞❛st✐❝ st❛♥❞❛r❞ ❡rr♦rs ❛r❡ ✐♥ ♣❛r❡♥t❤❡s❡s✳ ✯ ♣<✵✳✶✵✱ ✯✯ ♣<✵✳✵✺✱ ✯✯✯ ♣<✵✳✵✶

slide-42
SLIDE 42

■❱ ❈♦♥❝❧✉s✐♦♥

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-43
SLIDE 43

❈♦♥❝❧✉s✐♦♥

❚❤❡r❡ ✐s ❛ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ ❡❞✉❝❛t✐♦♥ ❧❡✈❡❧s ♦❢ s♦❧❡ s♦♥s ❛t ❢❛t❤❡r✬s ❛❣❡ ♦❢ ✺✾✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❛s ❜❡❧♦✇ t❤❡ t❤r❡s❤♦❧❞ ❤❛✈❡ ❛❜♦✉t ✺ t♦ ✼ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts ♠♦r❡ ❝❤❛♥❝❡ ♦❢ ❣❡tt✐♥❣ ❛ ❝♦❧❧❡❣❡ ♦r ❛❜♦✈❡ ❡❞✉❝❛t✐♦♥✱ t❤❛♥ t❤♦s❡ ✇❤♦s❡ ❢❛t❤❡rs✬ ❛❣❡ ✇❛s ❛❜♦✈❡ ✐t✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-44
SLIDE 44

❈♦♥❝❧✉s✐♦♥

❚❤❡r❡ ✐s ❛ ❞✐s❝♦♥t✐♥✉✐t② ✐♥ ❡❞✉❝❛t✐♦♥ ❧❡✈❡❧s ♦❢ s♦❧❡ s♦♥s ❛t ❢❛t❤❡r✬s ❛❣❡ ♦❢ ✺✾✳ ❙♦❧❡ s♦♥s ✇❤♦s❡ ❢❛t❤❡r✬s ❛❣❡ ✇❛s ❜❡❧♦✇ t❤❡ t❤r❡s❤♦❧❞ ❤❛✈❡ ❛❜♦✉t ✺ t♦ ✼ ♣❡r❝❡♥t❛❣❡ ♣♦✐♥ts ♠♦r❡ ❝❤❛♥❝❡ ♦❢ ❣❡tt✐♥❣ ❛ ❝♦❧❧❡❣❡ ♦r ❛❜♦✈❡ ❡❞✉❝❛t✐♦♥✱ t❤❛♥ t❤♦s❡ ✇❤♦s❡ ❢❛t❤❡rs✬ ❛❣❡ ✇❛s ❛❜♦✈❡ ✐t✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

slide-45
SLIDE 45

❋✉t✉r❡ ❘❡s❡❛r❝❤

❯s✐♥❣ ❉❍❙ ❞❛t❛s❡ts ♦❢ ❞❡✈❡❧♦♣✐♥❣ ❝♦✉♥tr✐❡s t♦ ❛♥s✇❡r t❤❡ r❡s❡❛r❝❤ q✉❡st✐♦♥✳

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦

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SLIDE 46

❚❤❛♥❦ ②♦✉✦

▼❛❤❞✐ ▼❛❥❜♦✉r✐ ❙✐r✦ ■✬❞ r❛t❤❡r ❣♦ t♦ s❝❤♦♦❧✱ ❙✐r✦