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Problema 1
Se dau datele x si y din tabelul de mai jos. Calculati media, dispersia si coe
X Y XY X! Y!
7.81 46.47 "#!.$"%& #%.$$#1 !1'$.(#1
5.67 41.8 !"&.%%# "!.1()$ 1&(&.!(
6.56 35.21 !"%.$&&# (".%""# 1!"$.&((5.74 38.06 !1).(#(( "!.$(&# 1(().'#(
8.96 40.48 "#!.&%%) )%.!)1# 1#").#"
13.07 43.51 '#).#&'& 1&%.)!($ 1)$".1!
8.73 37.78 "!$.)1$( &#.!1!$ 1(!&."!)
7.41 36.98 !&(.%!1) '(.$%)1 1"#&.'!
5.49 38.79 !1!.$'&1 "%.1(%1 1'%(.##(
2.74 48.66 1""."!)( &.'%&# !"#&.&$#
6.82 57.11 ")$.($%! (#.'1!( "!#1.''!
7.59 60.04 (''.&%"# '&.#%)1 "#%(.)%!
*edia &.!1')"" (".&(%)" "1(.#&" '&.&#%1# 1$&1.&%!
+x '.#$1$%) !.")'&&!
+y ').((1!& &.#((#)$
Cx,y- %.$'"'))
rx,y- %.%'!!)(
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cientul de corelatie apoi trasati grafcul datelor. Ce observati?
! ( # ) 1% 1!%
1%
!%
"%
(%
'%
#%
&%
date
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Problema !
Se dau datele de intrare X si iesire Y, de la o statie de epurare, in tabel
/0ati
a- mediile, dispersiile si abaterile medii patratice pentru X si Y
b- corelatia si coefcientul de corelatie dintre X si Y
c- dreapta de regresie a lui y pe x
d- dreapta de regresie a lui x pe ye- trasati grafcul de date X,Y- si cele doua drepte de regresie
x y xy x! y! y2%.(&x1!.!1
71.6 22.65 1#!1.&( '1!#.'# '1".%!!' !1.((!
67.96 24.57 1##$.&&& (#1).'#! #%".#)($ 1$.&"1!
75.29 25.14 1)$!.&$1 '##).')( #"!.%1$# !".1&#"
72.64 14.13 1%!#.(%" '!&#.'& 1$$.#'#$ !1.$"%)
64.66 12.62
)1#.%%$! (1)%.$1# 1'$.!#(( 1).1)%!51.35 9.61 ($".(&"' !#"#.)!" $!."'!1 11.$!('
47.83 10.76 '1(.#'%) !!)&.&%$ 11'.&&&# 1%.!&%1
54.16 11.13 #%!.)%%) !$""."%# 1!".)&#$ 1".!('!
60.03 14.29 )'&.)!)& "#%".#%1 !%(.!%(1 1#.%%(1
57.01 16.54 $(!.$('( "!'%.1( !&".'&1# 1(.')(&
62.47 26.13 1#"!."(1 "$%!.'%1 #)!.&&#$ 1&.1'%$
media #!.!&!&" 1&.%'1)! 1%$&."(! "$'".!%# "!&.!$1#
disp &'."1"&) "#.'!&%$
abaterea ).#&)"'1 #.%("&#(
Cx,y- "'.(&)#(rx,y- %.#&#(!$
Cx,y-3+x %.(&1%&)
Cx,y-3+y %.$&1!$&
dr de regresie a lui y pe x y1&.%'2%.(&x#!.!&-
dr de regresie a lui y pe x x#!.!&2%.$&y1&.%'-
CCO-Mnmg/l -intrare
CCO-Mnmg/l -iesire
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l de mai jos.
x2%.$&y4('.&"
#&.&%%'
#$.'#!$
&%.11')
'$.("#1
'&.$&1(''.%'1&
'#.1#&!
'#.'!#1
'$.'$1"
#1.&&")
&1.%
'( '# ') #% #! #( ## #) &%%
'
1%
1'
!%
!'
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Problema "
Se dau valorile X si Y din tabelul de mai jos. /0ati
a- mediile, dispersiile si abaterile medii patratice pent
b- corelatia si coefcientul de corelatie dintre X si Y. Ce
c- dreapta de regresie a lui y pe x
d- dreapta de regresie a lui x pe y
e- trasati grafcul de date X,Y-5- trasati cele doua drepte de regresie intrun singur g
X Y xy x! y!
11 1! 1"! 1!1 1((
1% 1) 1)% 1%% "!(
1% !( !(% 1%% '&#
$.( "& "(&.) ))."# 1"#$
1%.' '! '(# 11%.!' !&%(
$.& #( #!%.) $(.%$ (%$#
$.( #$ #().# ))."# (
$." )1 &'"." )#.($ #'#1$.$ $) $&%.! $).%1 $#%(
$." 1%1 $"$." )#.($ 1%!%1
$ 1%# $'( )1 11!"#
).# 11$ 1%!".( &".$# 1(1#1
media $.#&' #'.%)""" #1!.$' $(.%%%)" '(&).%)"
dispersia %."$'!%) 1!(!.!("
abat %.#!)#'# "'.!('(&
Cxy 1#.&"1!'
6xy %.&''11"
C3+x (!.""'!&
C3+Y %.%1"(#$
dr de regr y y#'.%)2(!.""x$.#&'-
dr de regr x x$.#&2%.%1y#'.%)-
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u X si Y
observati?
afc
y2(!.""x4(&(.(1x2%.%1"y41%.'1
).&) 1%."'
'1.11 1%.!&
'1.11 1%.1$
&#.'%) 1%.%"
!$.$(' $.)"(
#".)%$ $.#&
&#.'%) $.#1
)%.&(1 $.('''."(" $.!"
)%.&(1 $.1$
$".(( $.1"
11%."&! ).$#
) ).' $%
!%
(%
#%
)%
1%%
1!%
1(%
/xis 7itle
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$.' 1% 1%.' 11 11.'
+atele X,Y-
dr lui y pe x
dr lui x pe y
/xis 7itle
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Problema (
Se da concentratia de nisip in sol la di5erite adancimi, in tabelul de mai jos
Se cer
a- mediile, dispersiile si abaterile medii patratice pentru X si Y
b- corelatia si coefcientul de corelatie dintre X si Y.
c- dreapta de regresie a lui y pe x
d- dreapta de regresie a lui x pe ye- trasati grafcul de date X,Y-. Ce observati?
5- trasati cele doua drepte de regresie intrun singur grafc
xy x! y!
% )%.# % % #($#."#
1'% #" $('% !!'%% "$#$
"%% #(." 1$!$% $%%%% (1"(.($
('% #!.' !)1!' !%!'%% "$%#.!'
#%% '&.' "('%% "#%%%% ""%#.!'&'% '$.! (((%% '#!'%% "'%(.#(
$%% (%.) "#&!% )1%%%% 1##(.#(
1%'% (#.$ ($!(' 11%!'%% !1$$.#1
1!%% "&.# ('1!% 1((%%%% 1(1".&#
'(%% '1!.( !&##$#% !$1#%%%% !#!''".)
media 1%)% 1%!.() "%"")1 ""&'%%% !$"1(.))
dispersia
abaterea
Cxy
6xy
C3+X
C3+Y
/dancimea inmm X
Concentratia denisip 8- Y
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.