Transcript
Page 1: Regressions and Refutations: On the Logic of Model Discovery

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Regressions &

RefutationsON THE LOGIC OF MODEL DISCOVERY

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Inspiration. . . .

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roof & Refutations

!"p#a$ %eta$ Gaa$ De"ta$ et'.

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roof & Refutations

V  ( ) * ) ( +,

E ( +- * +- ( -

F  ( , * , ( +-

  V  – E + F ( +, / - * +- (

0t1i'e Eu"er2s foru"a3

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roof & Refutations

V  ( * - ( ,

E ( , * 4 ( ++

F  ( * ( )

  V  – E + F ( , / ++ * ) ( 5

0+467 of Eu"er2s foru"a3

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roof & Refutations

V  ( * 5 ( 8

E ( , * , ( +-

F  ( * ( )

  V  – E + F ( 8 / +- * ) ( 5

0+467 of Eu"er2s foru"a3

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roof & Refutations

9it# apo"ogies to Ire La:atos$ se;era" note1ort#< =ata sets 1i"" >'onsi=ere= for #o1 t#e< 'an support a stu=ent2s un=erstan=ing ofo=e" >ui"=ing 0'on?e'tures3.

 @a'Aues C#ar"es2 an= Ro>ert %o<"e2s =ata on t#e teperature$pressure$ an= ;o"ue of an i=ea" gas

E=1in Hu>>"e2s =ata on ga"aB< ;e"o'it< an= =istan'e

a;e" Ya:o;"e;2s an= 9a"ter Guessfor=2s =ata 'onne'ting po"iti'san= a"'o#o" 'onsuption

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C#ar"es2s La1$ '. +8)6s

p.

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C#ar"es2s La1$ '. +8)6s

p.

Superfuidity 

LiAui= #e"iu at - 0an= a >it 'o"=e!ppears to =rip t#roug# a so"i= >ea:!ppears to =ef< gra;it<

%e<on= i=ea" gas eBperien'e

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C#ar"es2s La1$ '. +8)6s

p.

Negative Kelvin

Nature 0@an. 5$ -6+53uantu gas goes >e"o1 a>so"ute "tra'o"= atos pa;e 1a< for negatateria"s.

%e<on= i=ea" gas eBperien'e

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%o<"e2s La1 on air$ +,,6

 @. %. Conant. H

Case Histories Experimental S$ Har;ar= ni;ress. Ca>ri=+48. Vo". +. p

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%o<"e2s La1 on air$ +,,6

-6 6 ,6 )6 +66 +-6 +66

+6

-6

56

6

46

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Vo"ue 0ar>itrar< units3

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6.6

6.64

6.6,

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6.6)

6.6

%o<"e2s =ata$ re'ipro'ate=

0in. Hg3

+JVo"ue 0ar>itrar< units3

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%o<"e2s La1 on air$ +,,6

Linear regressionK +JV  ( –0.000135 * 6.6668+5 P

%o<"eK ran o=e" t#roug# t#e origin$ P ( 6 in. Hg

rett< '"ose to =ire't ;ariation

Doesn2t see to 'onsi=er V  ( 6 or super 'o"= T $ as in C#ar"es2o=e".

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Hu>>"e2s =ata

Proceedings of the National cadem! of Sciences

Vo"ue +4 K Mar'# +4$ +- KNu>er 5

! re"ation >et1een =istan'e an=ra=ia" ;e"o'it< aong eBtra

ga"a'ti' ne>u"ae

Sour'e of t#e Hu>>"e Constant$H6.

0T1o uses of H63

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Hu>>"e2s =ata

For Figure + 0origina"3

v  ( /6.) * 4 r 

H6K "6 ( 6

P ( 6.,56 0P  6.64 or$ t#epro>a>i"it< of a T<pe I error is6.,56.3

RSA0a=?3 ( ,6.,7 v K :Jse'. r K egaparse's

F"ip H6 to get se'on=s$ or >i""ion

<ears

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Hu>>"e2s =ata

sua" ;a"ue to=a<K H6 ( 8+

or +5.,,, >i""ion <ears

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Hu>>"e2s =ata

Su'# as t#ese =ata

S"opeK ,,.,

Inter'ept noneroK 584.-)

RsAK 6.4,4

 T#is is t#e :in= of 'orre"ationfoun= in t#e so'ia" s'ien'es. It

sees at<pi'a" for t#e #ar=s'ien'es.

On t#e #<pot#esis H6K "6 ( 6$ 1

#a;e P ( 6.666. T#e pro>a>i"itof a T<pe I error is inis'u"e. It2sa"ost 'ertain t#at t#e nu""#<pot#esis is fa"se.

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 Ya:o;"e; & Guessfor=

!"'o#o" Consuption an=o"iti'a" I=eo"og<K 9#at2s art<Got to Do 1it# It

 @ourna" of 9ine E'onoi's$Vo"ue )$ Nu>er 5$ -6+5$ages 554/54

Data pointsK a"" 46 states in t#e

S! 0no possessions$ territoriesor =istri'ts3

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 Ya:o;"e; & Guessfor=

>eer 0ga""ons per 'apita3 (-+.)+)558 * 6.6+654,5+i=eo"og<

RsA ( 6.66+)4)-,+

P;a"ue on s"opeK 6.8,8

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 Ya:o;"e; & Guessfor=

1ine 0ga""ons per 'apita3 (6.54-65-8+ * 6.6-8)i=eo"og<

RsA ( 6.-5,-6+

P;a"ue on s"opeK 6.666

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 Ya:o;"e; & Guessfor=

spirits 0ga""ons per 'apita3 (+.-48)464 * 6.668,+8-48i=eo"og<

RsA ( 6.65--)6,

;a"ue on t#e s"opeK 6.-++)

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Regressions & Refutations

Espe'ia""< for #istori'a" =ata$ s#o1 t#e rea" =ata to our stu=ents.

eBtensions to t#e o=e"s

1#at #appens if t#e inter'ept =rops

t#e RsA

t#e resi=ua"s p"ots

ot#er =iagnosti's$ et'.

uniforitarian assuptions


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