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Problema 1 Se dau datele x si y din tabelul de mai jo s. 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""."!)( &.'%&# !"#&.&$# 6.82 57.1 1 ")$.($%! (#.'1!( "!#1.''! 7.59 60.04 (''.&%"# '&.#%)1 "#%(.)%! *edia &.!1')"" (".&(%)" "1(.#&" '&.&#%1# 1$&1.&%! +x '.#$1$%) !.")'&&! +y ').((1!& &.#((#)$ Cx,y- %.$'"')) rx,y- %.%'!!)(

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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%

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%# $'( )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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