Una Guida all`utilizzo dell`Ambiente Statistico R Angelo M

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l[v3Hk " x [lRs #
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%* %$ 1
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3
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l: s."# l , *%. / > ) %' j %&% 1 ," > # ?> > 9' %9' 0 )8 , ><1! > %'% > ) / > / , , 1 )8 ! %'%'
3"
# > > / h 0 %9 ( # 1 ,0 > ) %' /= V %9w%92)8%'#)0 > )8 ( 7)8 | >^1 *%. > >1!?> l , > ' &
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# / > ) ) > , &
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l: sH" ([sBv3p :y " #-#
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;
> # ?> > '' 7%.& " 0 j %&% %&%9 & # > ' > 3030 > /= ' j )8 > %'%' "
%' ( # , '#
E?E > V0# Nu Ud# <)0?#
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/ > )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 :v s "#6%' ( *) > "' %'%' /= ?> A R
uNs[:v3s " # #
l[v kH" #
;
;
< −3
−2
−1
x
0
1
2
0
20
uNs[:v3s " # #
l[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[:v3s " # #
?qtk [u[Tqtk " #
;l[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[:v3s " # #
l[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 *$# # sRx3l "Oy ">*z s sBv * * <v *!# # sBxHl ")*| < v * # sRx3l ")*csRv 3v *8 # >*c Rs[sBv * >*c s[sBv * sBxHl ")*c sByv<:x *8 %# >*| s Y|<v *!#
; y3v [v sR
x u # Tq (R:yzkBv Hs "Oyv [v sBx #
;NkB [x "Oy3v [v3sBx #
y3v v sBx
sB$y v3Bx Rs sRv | v |[s z| v sRv 3v Bx3s Rx v [
#
#
#
; [x Bx "Oy3v v sBx #+ %u *z3sR3yTq *
; [x Bx "Oy3v v sBx #+ %u *z q *
;l [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")*OBx Bv * # sBx3l")*Yx[x $xRkB sBx * %# sBx<l")* $x < * # {sRxl"* cl v 5 * %# #
;NkzkBv v q <k v u$(RBy<k v s."{kYkBv[v q <k #<v
[x Bx:5y ")*:x :v *8>*Yx 3x $x<RkR sRx * * x < * >* cl [v $ *8* [[sBx[ *# #
;NkB [x "ok zkBv [v q <k #v #
kzkRv [v q zk # v
$x cl [v $ [ RsBx[#
;l [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 :v s " # # #
j"<kH"J3kBxRx * sRx Bx3Rx * !c * ? 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 #
j"<kH"J3kBxRBx<RsRx -5y 3 * [sBx Bx3 x * !$c * ? <kRv3|[sB $ Rx x>3kBxRx *#
;
;
 > / 2 l , %9 c , ' / > > 0" *%9 > E B ><1j?>U> , 0) > ' %9 > %9 > & ( #% , > E?E > 'xV >?> , % > )8
> % ?
> )8?
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> ' ( > 9%
j %&% , '#
E?E > S %9 , & / > )8
;
;
!
3kBxRx u3s :v s " # # #
:v [l v kH"6kBxRx #[ *: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 ")*[yzj * %# sBxl")*>(Rx Y:x * #-#-#
l[v kH"3x3v J3kBx x #
;
;
< t
150
160
170
180
190
femmine
n
% #A > /
A 6, '#
j% / >
' , &
# E?E > ' > %'%'#
)8")8!3 > %&% / > / > l:x [u3s[:v s " # #
;l[v kH"l:x-#
; Y:x "{l:x #
;
maschi
# ( ?# l:v YRk "#5
) l [v3kH"#
YBx "#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[:v3s " # #
uNs[:v3s " # #
;l[v kH" l$yzj * B * # 5y "u q q%# <#[ * R3sz" #A*#
;l:vYRk "(lyzj * *#
; [x |Bx3 ." q y ")* * >* *# l5yzj By ">* B *8>* %*$# | *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 :v s " # # #
;l:x [u3s[:v s " # #
; u Dm ; x kB u3 : l x" {s x3l :yx #
; R k [u R kBDq([sB x"J< kBxRx lRx Jx3kB%#
;l: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 :v s " # # #
; $x Dq{3kBxRx u $ x[3."6kBx[x #
; q{kBxRx u# ."JkBx x%#
; Yrq{3kBx x u c "J< kBxRx%#
; $?q{3kBx x u $ H"J< kBxRx%#
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0.01
Densità
0.03
0.04
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160
170
180
190
altezze
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0.2
0.4
F(x)
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Funzione di ripartizione teorica ed empirica
140
150
160
170
180
190
200
x
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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
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y
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6
3
2
1
0
6
−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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g <> 1j ( #% , > # E?E > ' a) > 0 Nu&/ > E g% , g '& >? #)0 > ? > ' ( > / &
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j &%'$)03 > %9 N > 9&% , # '& >? 7)8 > # Fitted values
Obs. number
J $ 2 a 2 'O
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q x q q lR= s =
x [l s =
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# EE > H# > > E > ! \V; \V \V* ;\V0
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