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k "J‡3kBxRx <[sBx[‡ 5y [‡ #-#
"
q
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)87%. #3 , E 6)8 Nu l , 0E > %' /= # UNu l , 0E ? > & ( NkB‡[x "Oy RkH"J‡3kBxRx <[sBx[‡ 5y [‡ #-#n[x<ˆR|[k[jH"J‡<kBx x%#
;
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l[v3kH" #
l[v3kH" ( #
l[v3Hk " ( #
l[v3Hk "-( #
l[v3Hk " x lRs #
l[v3Hk " x [lRs #
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1 )8g& j 7%9 >= ) , 6?# / '
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( > )8 ?# c ' &( > # ! [ ,0/ ' # j %' E )8
c ' '( > # mj %&% %&%' & # > ' |)Rx3ˆrq B‡ :x ‡ s |Rv $x3ˆRkRv
y3vl [v Hk "# C Nu, "E ?y3v3l[v kH"#}l:‡zs "# > 0 c > / lB‡3ˆ:x "
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# Nu, 0E 0d) > 0 ,0 > > & > j >!1 !
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# #Yˆ:x" #
l[v kH" #
j"zkH" #
j"zHk "‰ˆƒy [‡ ˆ #
j"zHk "< sBx ‡ q q q#
Rv k5yzj:‡ s .k ">q[q q #
:‡ s l[v kH" >q q[q#
:v l[v kH" >q q[q#
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a)0?
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# > %&%9 ( # 6% A T )8 N > , =0, 1 %&%9 < )8 ?> V 00,0 6%9 ! %'% ) > 0, &a%9 / a)8#g & &( > # M l sBv:‡ zk > # > ( > 00 %' > 'S
Nu l , 0E ? > ' ( 4 > 1 , % > '' & U)8a) > & m% , % Nu ) 0, & [ l , %9 ' j )8g <> 1! ?# c > %&%9 > 3030 > /= > > 3j?~)0?~) > 'xV
c > %'%' |#a 'T( > 4 > 1 , > 1! >= 0 > A& E?E > )8?#
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‡ ‡B#x : -:
[[vv || ** **
[v | * *
k[lBx < )0a3 > %&% # ( ?# V
L E > > Nu, 0E > ) > / Nu, 0E <
# 7% , A > )8 % i( > 0j& -
g >1! ' & M 00 / 6 > > E S)0?# > %&%' %'#)8 > > %'%' / < > A / *l *<%' > ( > 0 0, 'a )8 ( #) , > # V * *
# ?V * * 0, & 0 %&%'a) > ?V *zv * 0, & , '
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> )8 P 0 /= ?> % > > ( ' ?> #<%. > / > V %' ) 3 > %&% R V *Oˆ * %&% , >1! !
I / c > %&%9<)8?## |
c > %&%96)8
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> 1 ,0 > j %9 &%9 >> g > 1! !
M 9 &A V j %9 > " > % 9 c > %'%'6)8?## [[‡:‡: <<kk ss YYˆRˆR|B|B‡‡
$‡cˆ <k s YˆR|B‡
< k sc ˆR|B‡
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YˆBx "< #
kBx [Hk " [‡ :x#> q q q#
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x "6‡ < #
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x "{j #
‡ #Yˆ:
x " #
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x " q{v :%w #
l:v: |Bv3ˆ" Œq q q#
[x |Rx3#ˆ ." [x3|Bx3ˆ Œq[q q#
kzk#[x"$‡Yˆ #
‡ " x >q q[q #
, 0, ' # ?d)8 #
> / > a >1! & ' , S'*%. > g ><1! ? 0, &~) > '~) > |
0, 1 *%'%' , ' '==, ( ?9 6)8 ?> > '' [‡Bx
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q{vBw '# < 7% > 'a)8
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)0 ( <*%'%' S) > [x3|Bx3ˆ ."Bq q q ( # > 3 m V
[x |Bx3ˆ .":q q q gy3v # > ", '~<# ? 06% > > 0 )0#%'? > &V [x |Rx3ˆ .":q[q q 3k #d%9'#
6)8~
?V
[x |Bx3ˆ .":q q q p # > /= # E?E > )8?#
<# ?V
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#
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% h' > 06 c , '#
E?E > <%'?# E g
j %' E a)8
1 ˆ 0 , '
>1! T, % > ) #g > %. %9 7%. ' )8? /T, %' ] ' , >81 0
% %9 > '~%'?# E > & V #a3 9 > #6)8? /=, %9 1
0 %&% > ! C c > / k[l:x '/ h''d)8 )8#%'? > S 0, '
%'?# E > & #~)8 N > , 1 %&% , >1! HP k[l:x *Oˆ * R F '/ h'' 0< c , &
# E?E > < ( 7)8 "E > , 0, &
)8 1 ') > P \V R V , % > ) g > %9 %' 7%9 & )8 /=, %'V
)87%'? > ) # & #% ! )8 &\ > 3! ( !
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%* %$ 1
$ 3 * %* $
%
3
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l:‡ s."# l , *%. / > ) %' j %&% 1 ," > # ?> > 9' %9' 0 )8 , ><1! > %'% > ) / > / ƒ, , 1 )8 ! %'%'
3"
# > > / h 0 %9 ( # 1 ,0 > ) %' /= V %9w%92)8%'#)0 > )8 ( 7)8 | >^1 *%. > >1!?> l , > ' &
> &" /T ) > #U) > j & > 00 %' > ' /Tj > > / & l , > ' & ><1!
# / > ) ) > , &
# EE > 1
Œl:‡ sH" ([sBv3p :y " #-#
F > ( , ?# /= #h )8? > > / h >1! 0 1 j %&%'
30## 1 ,0 > 1 3j % , A > 6 c 0? > -+-, ! %'%' > /= )8 "
/ > ) l:‡ Hs "# d
;
> # ?> > '' 7%.& " 0 j %&% %&%9 & # > ' > 3030 > /= ' j )8 > %'%' "
%' ( # , '#
E?E > V0# Nu Ud# <)0?#
6?' 0h'' 0 %9'
, 7% # / )8# > %&%9 #g'
)8a ><1! V c > > >1! % , , ( #% , > # E?E > S#a ><1! V -$).0/! ! * 3 I ~%'? , ' > > > Nu}( & > 0 )0% A'' > , g%' /= ~)0g ><1! > ' (
/ > )8g 06 > 0 =0& ) ' "
M ,0"! ) )8 > ( , ( ?9 n , ( h' jVg > ' ?> % , > / &T) >
, > &/ > U%9 > ) > )8 E?E > > V%' ! %'% > ( 5"%9 , '0 >1! P #"%9# 1!> )8
> Nu, 0E s ˆ:v s "#6%' ( *) > "' %'%' /= ?> A R
uNs[ˆ:v3s " # #
Œl[v kH" #
;
;
< −3
−2
−1
x
0
1
2
0
20
uNs[ˆ:v3s " # #
Œl[v kH" #
;
;
40
60
Index
80
100
< "s
−2
−1
0
y
1
2
3
−2
−1
0
1
2
x
k M=%9 (,0 > 00 %' > , > %' T%. > 307% > 0 / >D> ( , h9 uNs[ˆ:v3s " # #
?qtk [u[‡Tqtk " #
;Œl[v kH" ?qtk A#
;
;
< $
−2
−1
0
x.ts
1
2
0
20
40
60
80
Time
100
MB% > ?303j 9 & , D, >1! 9% / # , '## EE > ) )0 h' > / &=
( h' j V
%'h9 > ) ? / > ) l [v k." #6 c E k[l:x
uNs[ˆ:v3s " # #
Œl[v kH" Ek[l:x * *#
;
;
< −2
−1
x
0
1
2
0
20
40
60
80
100
Index
%97)8 > /=m >D> , B%9 /T *%9 /T > ' ( > ><1! >D 7%. > /=/ 4S" )8 > /= > ' > n#<%' /= ( #%9'< 0 )8
%'U% & ) ''D
n)87%. #3 , E U)8 Nu l , 0E > f %97)8 > /= #
)87%. #3 , E 6)8 Nu l , 0E > _, > ( > > 30## l , > > '
' ( >
0 0E >l , >
?> % )8
> )
, >
y3v[v sRx uBy "{sBx3l"Oy ")*Bxs x * *c|‡ [v * *OsBvv *$# # sRx3l "Oy ">*z‡ s sBv * * <v ‡ *!# # ‰sBxHl ")*| <‡ v * # sRx3l ")*csRv 3v *8 # >*c‡ Rs[sBv * >*c‡ s[sBv * ‰sBxHl ")*c‡ sB‡ˆƒyv<ˆ:x *8 %# >*| s Y|<v *!#
; y3v [v sR
x u #‡ Tq (R‡:yzkBv Hs "Oyv [v sBx #
;NkB‡ [x "Oy3v [v3sBx #
y3v v sBx
‡ sB‡ˆ$y v3ˆBx ‡ Rs sRv | ‡ v |[s z| v sRv 3v Bx3s Rx v [‡
#
#
#
; [x Bx "Oy3v v sBx #+ %u *z‡3sR‡3ˆƒyTq *
; [x Bx "Oy3v v sBx #+ %u *z‡ q *
;Œl [v H
k "y3v [v sRx #
;
< 0
2
4
6
8
10
12
14
aranc.
F
Nu E >
E>
)8 S '' =
l , *%. > ( > )87%9 > > 3"
#
azz.
giallo
grigio
> 1! >w 0 > 3"
# > )D%&%' , , ><1! >‚ rosso
verde
viola
> ( > > 30##‚y3v [v3sBxw%9 1 0
N > ' C~> %9'*%'% > 0 & ) ," > %'
" > > & |) > , > ( > > 30#
/ > ) i(, 0, 1 , '#
E @
,l > > ' ( >
NkzkBv v q <k v uRy "{sBx<l"y ")* Ol[v $‡ * * [‡ RsRx ‡ *$# # # sRx3l")*OˆBx ˆBv * # sBx3l")*Yx[x $xˆRkB‡ sBx * %# ‰sBx<l")* $x <‡ * # {sRxl"* cl v 5‡ * %# #
;NkzkBv v q <k v u$(R‡By<k v s."{kYkBv[v q <k #<v
[x Bx:5y ")*ˆ:x ˆ:v *8>*Yx 3x $x<ˆRkR‡ sRx * * ƒx <‡ * >* cl [v $‡ *8* [‡[sBx[‡ *# #
;NkB‡ [x "ok zkBv [v q <k #v #
kzkRv [v q zk # v
ˆ:x ˆ:vNx x $x3ˆRkR‡ sBx
$x ‡ cl [v $ ‡ [‡ RsBx[#‡
;Œl [v H
k "{k zkBv v q <k <v ‡ * zkBv [v k #v l:v x RkBv *#
;
< q
0
5
10
15
20
nessuno
elementare
media
diploma
laurea
Titolo di Studio posseduto
I ?> % , a%9g > , > ( > > 30## l , > &A > & ( =
> > # > %9a)0 ( N > % > )
, 7%. > /=/ >
‡ 3kBx Rx u3s ˆ:v s " # # #
Œj"<kH"J‡3kBxRx ‡ * sRx Bx3ˆRx * !ƒ‡cˆ * ? zkBv3|[sB‡ $‡ Rx x>‡3kBxRx *#
;
;
< o
10
0
5
Frequenze
15
Istogramma delle altezze
140
150
160
170
180
190
altezze
1 9% > > )8?' '/ > >
[ l , %9 ? > % c > /T E?E > )8?#
> %&%9 ? # c 7%. > /=/ > m
c
/
1
j
1
,
) > V > 6) > > > &% %'
30##A >T> ' & d)8 1 &% % > y [‡ u # " Dm #
Œj"<kH"J‡3kBxRBx<RsRx ‡ -5y ‡ 3‡ * [sBx Bx3ˆ x * !$‡cˆ * ? <kRv3|[sB‡ $‡ Rx x>‡3kBxRx *#
;
;
< p
0
5
10
15
20
Frequenze
25
30
35
Istogramma delle altezze
140
150
160
170
180
altezze
190
200
210
W c ) > > / 2 l , %9 c , ' / > > 0" *%9 > E B ><1j?>U> , 0) > ' %9 > %9 > & ( #% , > E?E > 'xV >?> , % > )8
> % ?
> )8?
~%9 / a)8?## > %&%9 Mm%' ($," # %. ', , 3 > > & m) > , > ( > > 30## l , > '
> ' ( > 9%
j %&% , '#
E?E > S %9 , & / > )8
;
;
!
‡3kBxRx u3s ˆ:v s " # # #
:v [l v kH"6‡kBxRx #[‡ *:3kBxRx *#
< 150
160
170
180
190
Altezze
F &% %' > /T
E E > > '% > ( )8 ( %'\3 8
) ~
( #a)8 , N >
5, > %9'%&% > ( > > 30#
l , > '
> ' ( > > ' @
9 3x 3v u (R‡:yzkBv Hs "Oy "osRx3.l ")*ƒ‡[yzj * %# sBxl")*>(Rx Yˆ:x * #-#-#
Œl[v kH"3x3v J‡3kBx x #
;
;
< t
150
160
170
180
190
femmine
n
% #A > /
A 6, '#
j% / >
' , &
# E?E > ' > %'%'#
)8")8!3 > %&% / > / > Œl:x [u3s[ˆ:v s " # #
;Œl[v kH"‰l:x-#
; Yˆ:x "{l:x #
;
maschi
# ( ?# l:v YˆRk "#5
) l [v3kH"#
YˆBx "#V 0 ( < 65
70
pesi
75
80
85
0
20
40
60
80
100
Index
Z > 00 %' ' > /== > , .% &%&% > 1! # }) , ( > > 3"
# m
jV! )8 > ) #
) , d%9 / 3 #a)8 ( %'g6 %9 ) T
, > #? ) >
uNs[ˆ:v3s " # #
uNs[ˆ:v3s " # #
;Œl[v kH" ‚l$yzj * B * # 5y "u q q%# <#[‡ * R‡3sz‡" #A*#
;Œl:vYˆRk "(lƒyzj * *#
; [x |Bx3ˆ ." q y ")* * >* *# ‰l5yzj By ">* B *8>* %*$# | *c| sR‡ *#
;
;
< s
+
3
2
+*
*
*
+
+
** * *
+ +*
+
1
0
−1
+
−3
−2
x
y
*
*
*
* *
* + *
+++
*
* +* *
+
*
+
** +
++ * +
+
*
+
+
* ** + +
**
+ + +
+
*
* * +*
+ + + + * + * * +* ** *++ ++ *
++
+
+
+
+
+
+
+
*
+
* +***
+ + +*
+ ***+* * * *+ +
++* *
+ *+
* +
*
+ *+ ** *** *
*
+
+
+
+
* +
+
*
++ + +* +
*+ +* + * + * *
++
+
* *
* * + ++ +
+* * ++++
*
* * *+
*
**
++
+ *
* *
+ * ++
*
+
*
*
+
+
*
*
*
*
Variabili
*
*
0
20
40
60
80
100
Index
M}%'~ >|>| 0 N > , ) > > uN > / 0, 1 * %'%' , '## > ( , > / > })8
><1j
!
; ‡3kBxRx u3s ˆ:v s " # # #
;Œl:x [u3s[ˆ:v s " # #
; u Dm ; x kB‡ u3 ‡ : l x" {s x3l ‡:yx #
; R ‡ k [u R ‡ kB‡Dq([sB‡ ƒ x"J‡< kBxRx ‰lRx Jx3kB‡%#
;Œl:‡zs "R‡ k #
< 70
75
80
85
180
190
65
80
85
160
170
altezze
50
60
70
65
70
75
pesi
20
30
40
eta
160
170
180
190
20
30
40
50
60
70
[ / > ) 3‡ :l x"#V , '#
E?E > % 0 > V 0 )8 , ?> /= 5)0 > /= # EE > s
9% & > % > #\?# / &a)8? ( h' \V0% ,00j ) 0S , 9'~#j
/ '
)8 > 3003 > > %.&%&% > 0& 3 > 30#
> 1 )8a*%'%' S%9 > 9& / =%' /= 1 > #])8 l , %9 > %' E =%' %'#)0 > % )8]) i( %. ', , > 1! , 2%'% i( > 0! D, 7%. > /=/ >H %. ', % , , %'# / m)8
) > ' > )8#%9 #3 , E '/ > #)0 > > / h ~ > / *)8 > > ( > > 0E >?> > '
)8 ?9 > / '6% , ~) > '
!
; ‡3kBxRx u3s ˆ:v s " # # #
; $x ‡Dq{‡3kBxRx u $ x[‡3ˆ."6‡kBx[x #
; q{‡kBxRx u# ."J‡kBx x%#
; Yˆrq{‡3kBx x u c ˆ"J‡< kBxRx%#
; $‡?q{‡3kBx x u $ ‡H"J‡< kBxRx%#
;Œj"<kH"J‡3kBxRx ([sRx :
<3‡ * Rx3ˆ zk ‡ *8!ƒ‡Yˆ * ? zkRv | sB‡ ƒ‡ x[x ‡3kRxRx *$#
;Œl[ v kH" ( ˆ$y<k v3ˆ" # 3 ˆ:v s c ˆrq{‡3 kRxRxRu " ƒ !$‡?xq{‡ ‡ kBq{x‡ RkRxxBRx J‡ q{‡3 kBx# x # < 0.02
0.00
0.01
Densità
0.03
0.04
Istogramma delle altezze
150
160
170
180
190
altezze
M ,0"! > /= > )8 ( # > & E ] /T >- %9 &, > % ,
' > 4 %'7%.& , , / > )
Nu, 0E )0 > & E Q /T %9 &, , >1! 0 '# } > Nu, 0E )8 A@
8) > ' >S & #% ! )8 & Nu, 0E 5)8 > & E 0 '/ h''6)8 > 00 %' > U ><1!> / & >
> l , *%. / > ) Y 1 & , ? >62i> <kBxl ( ˆ"
; ? RsB‡3sH" <kRx3l ( ˆ #
; ‡3 kBxRx u3s ˆ:v s " # # #
;Œl[v kH" ( ˆ$y<k v3ˆ" # l[ˆ:v s " # # # [‡: * H" # * $ ‡Y ˆ * ˆ vˆ:x sc l:‡ s k- v3ˆ:x€kBx v s [y3‡Nx x :lzs[y3‡ *#
;Œl[ v kH"Jx:y - (."J‡3 kBxRx%# Bx3s[k y3‡#: Rvq_lBvcˆ k - -: {‡ #
< 0.0
0.2
0.4
F(x)
0.6
0.8
1.0
Funzione di ripartizione teorica ed empirica
140
150
160
170
180
190
200
x
1
/ $ 1 %21
++ ! % *3+ - 2 U 0- l , *%. > % 9% g) >
1 l , > 0-%' /= # %'## , '#
l , > ) %'!Oj?9 , > )8a <> 1! \ % 9 > / 30# & *h ! b` @B \cdBA€@R@R9<;f 5'85f*@R9<; + i:9<@TZ3 Z 5A€; #&;[\c@ d*; fT+h\O\Y5!c\c ZzUh; Z 5A€;
4 ! > ( "' ) 9 , ><1! V %' ! ?303j > ww # > w
><!1 ? 0' %&% )8'*%.& , &
# EE > P % > / '( :9< R [ l , *%. 1 +O‘ Ž )JI 0 7% , A > 7) ‚ ?> % # Nu&/ > ><!1 n, '#
E?E > w
> ) > 9 > / ' )8 >!1 )Q A 0 )8 /= > / /= > / > ' ?
> 00, & 4 c > A ' )8V$" >!1 " Nu'/ > D‹ > 0 l , > #A > 1
/T A % ?> % > % 17 %9 %'
> g ><j1 j Nu&/ > KŽ5) %KV %97)8 > 0 ( 1 > 0]# ( > > 0 l , %9' ><j1 ,0 > U/ % > E #% ?9 K > 2 ><!1 ] Nu&/ > +O‘ Ž )JI F > , 1 #m Nu'/ > KŽ5) %D
:9< 1 j %&%'
30## , &
# E?E > # 0j , / , 1 DN > > E -)8
> > :i # > `b @BdB@R59<9<;a] V i51 9<, @ T> Z3r3 h,0; d > .9<#)8Fƒ ;> %' > ( +-> , > # ) 1 w%' % , , > %:; ' 5% . > > ,> ( > > !1 ) D /=) > A % %&% j %&%9#30# / &d% , ~) ( m P > )D*%9 /T % , .4 % 2 R M8d%9g& >
(
/
,
0
!
(
)8-% > > )8 h9 > &‚% /
VU%9 ?303j !1 > , 30 ? )8?
0' > /=/ > V )8 ) l , *%. /T ) , ' #~ > ('! J > )0?#
C ?a)8
n,0& )8 0 % )eIƒQoG +]) +‘&%‘ Ž )
S BK…PRL S6G IƒPRŽtKQeM‘ +"%GcS6S ‘  9‘ 8zKOL:Ž5)(MK IƒQoK

Iƒ‘ P ) % Ž5).) %&% !) 88Y‘SO‘ L )<Q6M‘ K"%&% )DL$K  K"% % ) 8<G<QoG V l , )8 %' 0)0 ( A > )8
)8 <#g > (&dN > 9 V"% > ( > ) % %&% % , )87% 1 %'% "
2
c a 2 H [ l , *%. > > > Nu6( ) /= > , <)8
# Nu, 0E " &/ h9 # > )8?
, 1 /=! > '\ )8 a)8*% 9& ( 303" > /T > 1 ( 7%9 , 0 *)8 ' > > > Nu
# Nu, 0E $x[‡3ˆ"#< B‡ sH"#  > ' > V
> Nu, 0E $x[‡3ˆ"# > > > / )8 >> / ?' ?> )0 , ( h' ])0 %'%' &( > E 00," V0% 1!> ) c > / k s ~V , > / *)8 > @x /=/ ) 4
> Nu, 0E B‡3sH"# ?> > > ( > > 0E >S?> /T > > )8 , ( h9 _)8 %&%9 '( > @
E xV%' / > / )8
> Nu, 0E ( > %&% > > 00, 6, ( h' 4
B‡3sH"# _1 > Nu, 0E y3vH"# ~%' / > / ' l , h@
##? > ><> # > Nu, 0E <
%.&d) , Nu, "E a > 0 ) , ( ?9 m > # > V , '#
E?E > ) , > )8
#d) , Nu, 0E V ( # %9'
, A > > i( > > 0E > )8 m 4 %9V0 ( V8 c > / )8
R‡ sH"#… yvH"# 1 , > / > \V%9 > (;> 1 # ?> )8?# > / > -)0 ( > > 0E >
i( > > 0E > V %97)8 > ) / ( > > 30## 0 |)0?# > / > 4 %'V
( V > / &a)8 B‡ sH"#}"
yvH"#d% ) , / > m \V"%' > (;> 1 # ?> A@
)0?# > / > S)0 ( > > 0E > i( > > 0E > > # 0 S)81=-# 0 )8 4
> Nu, 0E y3v3sH"# '/ ?9'U)0 ?> > ]# &_)8 ' ? > E ]# > @
T) > , , &
# EE %' / #
>Hl , ?# )0?# > Nu, 0E ^
y3v$H"# - > ' > V
yv sH"# > > # ')8 ' ? > E )0 ) , ( h' n \Va%9 > @
/ ' )8 l , %9 > Nu, 0E T% l , *%.& ) , ( h' 4 %9Vg ( Vj c > / )8 y3v sH"# 1 , > / > $
jV\%' > (i> 1 ?> )8?# > / > })0 & > E V
%97)8 > ) / ( > > 30##B
0 |)8
> / > 4 %9V ( V > @
/ ' )8 y3v sH"#% ) , / > H$
\V\%9 > (;> 1 # > )0?# > / > })8
& ? > E U > 0 6)8|6
0 6)8 4
%9_%' (,0 # ?> > 2 % > l , > ) > & -/ )0 % ,=, ?> /= 5)0 %&%9 '( > @
E ' , ' ( h9 D
1 , '#
E?E > _ > Nu, 0E ."# 4 %'V ( V
\V%' 0, 6
/ > / )0 ."#S%9 , '## EE > , > / > d, ) > > Nu > / %' '' 'i> 1
( h' })0% ?> & l , > ) > ' / )0)8
# 0 })8?# > / > )0? ) > >
Nu > / !
"
q
> <
o
> > Nu, 0E /= A w, &
# E?E > > 1 $x <‡3ˆ"#V 0 *%.&A , #% > / )8 > > )8
, ( h' 4
%9<)8 , ( ?9 S)8 %&%' &( > E |%' ( ?> > # / /T V0# / > %'%'A@
/T V l , > '#
> / )8 >U> / h& > %9 0, _1 , &
# EE > # / > ) ƒ‡ sH" # 4
?> > S l , > '## %' 0, m
1 , '#
E?E > 6 > Nu, 0E B‡3ˆRk x"# 4 7% , A > '
%9 / # >l , ?#
'' , ' > Nu, 0E B‡3ˆRk x"#B%' > 0 > Nu, 0E ( )Bx3ˆ "#V 0 Nu 7% _ %'#)0)0h9& l , ,0/ j)8 b , 2 V 0 > "0' %'%'
@
/ > ' ( > / ' & 7% ! ) > 8 l , > '## , 1 / /= U
/ > %&%9 /=" b >
1 0 c > & ( > ?> > ' > Nu, "E ( >Bx3ˆ "#S% # l , > '
>T
, '#
E?E > >‚ %9 &, E m)83 8 F }/ > ])8?9 > #% , #
w
# (
)8\ "E ? 7% , A > Q, '## EE > ) :‡3ˆ k [x"#m@
( )Rx3ˆ "#w%9 / > ) >
> # >T % , A > E <)0?# c 0? # > D 8a 7 c 1 j %&%9#30#
> > T > Nu, 0E w)8)8 %'A > 1 )8 0& 3 > 30#
> 1 V~ > Nu, 0E
> & E l , > '#
])0?#
0 > #B)87%. #3 , E B)8 0& 3 > 30#
> 1 W c
j %&9% #30#
< > %&%9 '( > E %9 , ) @ > % , > #g) >=l , %9'd)87%. #3 , E J
1 a%'? , &
)8 #d)87%. #3 , E a)87% j 30## ? >62i> :‡ 3x <
[
47%. #3 , E
3jh >
30 / > #
30 / > # ? > ' ( >
>, "A@ l , > ) > % j 0E > #
L
> /T/ >
/ h ?>
/ h ?>
@ &/ > #
#%9' ?>
'/ > #
F 7%'% )8 M , )8 , Nu&/ y ?#3 , #
yY# I / S nZ
:x kR‡
"cˆ:v ˆ"Yˆ:v y3‡ $yzj yzj x [l
(
|B‡ $‡
|Bx v j l:x s
[ˆBv3|v s ˆ:v s l:v p:x "ˆ k)( "p By3v m)8
?# @
# sB‡3kBx
- ( V#-( !V ˆ$yzl
Yj:‡3l:lRx!sRVv y3‡[x
$v:x[y3‡3‡ ˆk [< VRv v3|jˆgˆgVVV# #y3 ‡v [ | x
$ x ‡ˆgV [‡ 3R‡
- (jV ˆ$yzl
Yj:‡3l:Y ˆ\x!VRVV$ˆ ‡y3‡[x
/ ' > )0)8 E > zjB‡3l:x V zj:‡3lBx !V ˆƒyzl
Rx!V lRsBv
Rx!V lRsBv
v:y3‡ k <v3ˆgV y3‡ [x
-(jV ˆ$yzl
F w '' ‚ > Nu, 0E )8S)0 %'A > 1 VS%9 > ' ! > / )0?# > )8#%9 #3 , E
, > jV > Nu, 0E -)8 > & E , > lgV # l , > &
# , > %&%' &( > E %9 , ) @ ?> % , > # , > s )n%' /= V %9 , & / > ) (
?> > # @ ( > 2% , #_) , )85)8 , > )8#%9 #3 , E ]])8"M , )8 ws q-
)8a##3! > 1 ' #% j )8 0E > )8 0, '~@ ;
zlRkH"6u q -( #
>
# > )0
> + q <
p
#a%9 , & / > ) ( # < ( > > l , > &
#< ' 7% j )0 0E > )8
, > 0& 3 > 30#
> 1 >= ) > % 0, 6)8 , > 0) #%9 3 , E L P Vjp R > > c#s
;-(."
+ q q #
W c N > ## > 00 %' > >1!?> / ' > Nu, 0E ])8)8 %'
> 1 )8 , > ( > > 30## ?> @
%'#)0 > /T # > % , %9 ( # > _ > 00 %' > > Nu, 0E )0$)8 %'A > 1
% , > # 6 > Nu, 0E d)0 > ' E <)0 , > ( > > 30#
?> % , > # '/ > 6%9 > ) > )8 E?E > >
Œl[v kH" ( ˆ$y<k v3ˆ" # l[ˆ:v s " # u ‡ *-*8
$‡Yˆ * ˆ v3ˆ:x x3ˆzk ‡> x sYlB‡ s k v3ˆ:x ˆ:‡ H" $# *#
;Œl[v kH" ( ˆ$y<k v3ˆ" # 3ˆ:v s " # u Hy3v *csBx * ‡ #
;
0.0
0.2
0.4
0.6
0.8
1.0
Funzione di densità e di ripartizione di una N(0,1)
−3
−2
−1
0
1
2
3
x
10
aO O O
D
/ jV\V "V V !V # )8? ( h9 ,0/ xV , > / > V [ )8 0 > =
/ )8
#
:\VgV V # )8? N > 9 > %9 j 303! ' > ( -~%'? , & T
!
> B B
B ." # B >u
:u
:
: B :
: B
B:
?m Yˆ :
::n ": B B # : u$: m r
m
:- :n
:n
: :
: ," B # <
0) > # /= )0?# )8 ? *%'%' -
> 6%' /= # d)8 m% ,
[ 0 /= > /= # > c ' ?9 > V0#a%9 ) % # A > %&%9 -
> <%' /= # d)8 w% , > 9 > ( % c # V "1 & h' > , # > q
v |H "%&%9#$V8 % , /}<, ' ! > V )8 ? # > ('> > h309 #>#-/= > % #Nu A'/ > > > V
l:v H" # %&%9 ! / > #6)8 D% , m)8a > ) [ 0 /==, % >
! / > xV#~%' ) Tj ' 0E 6*% ' B B ? " #
B l:v H" # %&%9 /}, ' > )8 / > 6)8? /T )8
Nu&/ > > ) > |d) > \' '/ j # / > g 1 > g > ) [v |
u
I ^ > ) , > ( >= > %&%9a)8?' '/ > &<) > : I _^ > %&%'a)8h& &/ > '6) > :| i( > > > /T )8
> )0)8
' ( > ) , N > ' a)8 m% , :| [ 0 / ) , 6% 1j?> > %.&%&% >= > %'%' 1j?> E S ' > > V
~%9 )8a) , d% 1!> > %9'*%'% >= > %&%9 1!> E > " #) > > % / > N > ' , /= )8
0 &
% #g\h'' 0 > g<#6 & > E > ) , N > 9 /T )8
#~)8 %&%9 -
> <%' /= # 6)8 D% , m%' > > '
?a# ( ?##a)8 :\V )0\ ' )0 1!> C c , ' / > Nu&/ > ) > 1 %9' / % 'd)0g > &< ' h''6 )8 0E l , > &~% a# ( ?#
a)8 : C c > 1 , % > )0 1 , /= )8
/= )8?# # > V 1
C > Nu'/ > V _, )8 > sYl:v<kB‡ Nv3l €kBx3s gv3l >kBx s q q q
) i( 8s zlBv<kB‡ 1 , ( h9 D, > / > 0)8 1 #% = > # ( > > 30
# )8 A@
1 c > TA@ %' /T V B u"V "T /= # > c , %9 c % , %9 % ! %. > 4 vl" =
)8 , & &/ /= )8?# !4 kBx s 1 =, ( ?9 =, > / > P /=0 % s R V , N > 9 V , > Nu&/}, > /=0 )8 & N > ' xV ( ?9 / > 0 *%'%' > > C~> Nu, 0E ? "#D l , %9 &%9 ƒ 1 , '## EE > > 3" w c ' @
0 h > E )8 > / B Vhu"V | / > )0?# > Nu&/}, > V / > , &
# EE > # / > > A / h' C~> Nu, "E <3 > %9 > ) > ' > /T )8
#a# > /}, A& # )8 > 1 "#
$vRx[v q{‡ ‡ k kB‡ kRv[u " (Rv s #[‡ R‡ kB‡ R‡ kB‡ q ([sB‡ $x%#
"# -1 c h' d/= )8
> ) > ' > V 0-' ?> / ' %'7%.&-)8 , >
[ ( > -)8 ##%9 > )8 #% , > & )8?# >D > %&%' F \h' , > , ac > > 7%' )0?# > ( > > 0E > %9 0, 1
, &
# EE > > 0 > Nu, 0E r‡ v$H" (Rv s [‡ R‡ kB‡R‡ kB‡Dq([sB‡ ƒx # C B Nu&/ > E % , /= )0?# > ) > 9 > Sj %&% %&%9 ( #% , > E?E > ' , &
# EE > ) <0j , Nu, 0E V
?# ?> &6)8~%'? , A ‡ y3v x( x (-(RxBy<k B‡3l l:‡ lRsBx y<k sBx : ‡#
‡< ‡ R x‡ˆ$y3x (R‡ : [ ‡Bx# lRsc ˆRk
< kBxl
‡3ˆ:v$B‡ sBv3l (Rv s #[‡ l v k lRsBv w $‡ s
;
!
[5 / > )8 , 1 /, / ' , '## EE > &~% ~%'? , '
t
< Z %9'
, #% < > > ( > )8 > > ##%'a)8
> ( > > "E > ‡3ˆ:v$B‡"6v |[|Bx k kBv%#
Rx ‡3ˆ$y3x "6v | |Bx3k kBv%#
M /=/ > )8? l , > ) > & %'7) , > V ? > % % > > (Rv s [‡ "Jv | |Bx k[kBv #
W]%9 > S c % 0 %&%9 S)8 /= )8?# !
l[v3Hk "6v | |Rx k kBv #
F & ) , l , > ' & ><1! V , &
# EE > ' c > > ##%'g)8? %'7) , lRsBx [y<Hk "Jv | |Bx k[kBv 8ˆ:x3p# ‡ kB‡ ‡ kB‡ q( sB‡ $x # [ a) > > Nu > / Nu A )0 ( > ( ( > > 30#
% j1 ?> & #d%.&%&%9<h& "h9&d)8?##
Z
,
, ( =, / > > # %9'
#% h9 > > )8 ( > 0 )8?9' 0 & #% ! ) > ( > 06)8h& &/ > ( > > 30#
g R‡3kB‡ q([sR‡ $x M$ > /= > , > ( %' 7% > )8
c h9 "
W]%9 > S > / > 6)8 *%97) , xV ? ?> % T *% > ' lRscˆRkH"6v |[|Bx k kBv%#
sBx :‡ "6v | |Rx k kRv%#
sBx ."6v |[|Bx k kB%v #
<kBxl "6v | |Rx k kBv #
M?# E > , 0j , T/= )8
> , ) ? # / > ) & &/ ~ " *%9 '( > ) > 0# # %9'
, # /= )8?# , 1 > )8
( > S)8 [ P 2i> 2 [ Nu&/ > ' ' R
'' , ?# > ?> %.& O_7%9 M$ > /= > , > /= T > %&% , )8 #% , > &
)8?# c > > ##%'a)8 ? *%'%' $‡ sH"Jv | |Bx k[kBv #
* %$ .0$'1
1
* * - * % C~> Nu, 0E l R‡3kBx"# &/ ?9&D)8 > ) > ' > , /T )8
"w)8j 7% w) > , 0 )8 & / & > ) > ' > = l , > 0S' '/ > , ' (} /T %'% #
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y
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600
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40
60
80
100
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6
3
2
1
0
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−2
−1
0
1
2
Theoretical Quantiles
Scale−Location plot
Cook’s distance plot
1.0
6
9
0.00
0.5
15
0.20
6
23
0.10
15
0.30
Fitted values
Cook’s distance
1.5
23
500
0.0
Standardized residuals
300
15
−1
100
−100
Residuals
23
0 100
q
Normal Q−Q plot
15
Standardized residuals
Residuals vs Fitted
0 100
300
500
0
5
10
15
20
25
30
1 %' &( A m > 00 %' > w l , > ' & ><1!
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Obs. number
‚J $ 2 a 2 'O
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q x q q lR= s =
x [l s ˆ =
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