Statistics and Regression

7/22/2019 Statistics and Regression

1/35

"

!"#"$%"$' !!"#$%&% () *+,-.&/-!0"# !!"!! #

!"#$"%!"# %&'(

)* +,-.. /012 3-4 5" 6&('7

!"##$%&

#$%& '()*+,-. /0,&,-.& 1- (2,02%,3 (4 )(++(- &.1.%&.%)15 .((5& 1-' +,.$('& *&,' %- 1-1567%-8

,9/,0%+,-.15 '1.1: ;.1.%&.%)15 .((5& 10, *&,' .$0(*8$(*. .$%& )(*0&, .( 1-1567, 1-' )$101).,0%7, 210%1


2/35

V

.$/0( -) +-*.(*.!

1 %(23(4 -) /$!3+ !.$.3!.3+! 555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555 6

7 +%3.(%3-* )-% ,(.(+.3*8 -".03(%!9430, :-3*.! 3* (;:(%3#(*.$0 ,$.$ 55555555555555555555555555555555555555555555555555555 E#E::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: "O

O:V HB;D>\EK; EL> HB;D>\EK WKX#;::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::: "U

"#$#% &'()*+,(-, .(+ /0,+*-1*'( 2(1,03.45 #################################################################################################################################################### %6

"#$#$ 7814*,05 *( 9:;

O:O KDLBEH HBIHB;;DXL ELEK`;D; #XXK;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: "a

"#"#% ?,@0,55*'( 85*(@ A*-0')1 B9-,4C ############################################################################################################################################################ %D

O:P KDLBEH HBIHB;;DXL \;DLI >E#E #HEL;AXH?E#DXL::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: VS

O:U ?\K#DWKB EL> WXK`LX?DEK HBIHB;;DXL::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: O"

"#E#% /'4;('F*.4 ?,@0,55*'( ############################################################################################################################################################################### "%

"#E#$ A841*G4, ?,@0,55*'( ##################################################################################################################################################################################### "H


3/35

O

" #$%&$' () *+,&- ./+/&,/&-,

E ?@A 1 />BCD !E>ECBECD>@ ,AFCGCECHGB >GI .AJKB

.AJK ,ABDJCLECHG (MN>ECHG (ODA@ )NGDECHGPCF >GQR

L ;1+/5, ;%7, c[X\L#YZ

;1+/5, ?,1-d .$, &*+ (4 +,1&*0,+,-.

215*,& '%2%',' ,2%1.%(-d D-'%)1.,&

&)1..,0 (4 '1.1 10(*-' .$, +,1-: #$,

&+155,0 .$, &.1-'10' ',2%1.%(- .$, +(0,

/0,)%&, .$, '1.1:

c;#>B]YZ

>XA@ # >,80,,& (4 A0,,'(+ %- .$, >1.1 ;,.@ LN" LN"

sx

;.1-'10' >,2%1.%(- (4 .$, ?,1-d #$,

&.1-'10' ',2%1.%(- (4 .$, +,1- /0(2%',&

%-&%8$. 1& .( $(3 8((' Y(0 /0,)%&,Z .$,

10%.$+,.%) +,1- %& 4(0 1 &,. (4 0,1'%-8&:

[ [(-4%',-), 5,2,5d ;(+,.%+,& )155,' .$,

',80,, (4 )(-4%',-), %& .$, /0(


4/35

P

.AJK ,ABDJCLECHG (MN>ECHG (ODA@ )NGDECHGPCF >GQR

$ $%& .$, /0(


5/35

U

#1?@A 7 .SHTBCIAI BENIAGEUB ETV>@NA >B > FNGDECHG HF$ PHJ +R >GI # PHJ ,-)R5


6/35

T

0 12&/$2&(3 )(2 4$/$-/&35 67/8&$2,9:&8; ?$2&@$3/+8 4+/+

;(+,.%+,& .$,0, 10, (


7/35

S

.>?@A 6 2>@NAB HF .WHKLBHGUB DJCEAJCHG >B > FNGDECHG HF B>KL@A BCXA

*NK?AJ HF %A>ICGYB

P*R

%>ECH HF #>OCKNK $DDALE>?@A

,AVC>ECHG EH :JADCBCHG 3GIAO

PIK>O9BOR

*NK?AJ HF %A>ICGYB

P*R

%>ECH HF #>OCKNK

$DDALE>?@A ,AVC>ECHG EH

:JADCBCHG 3GIAO

PIK>O9BOR

O ":"UM VU ":aMV

P ":OaO VT ":aMP

U ":USV VS ":aMT

T ":TUT VQ ":aMQ

S ":S"" Va ":a"M

Q ":SPa OM ":a""

a ":SSS O" ":a"O

"M ":SaQ OV ":a"P

"" ":Q"U OO ":a"T

"V ":QVa OP ":a"S

"O ":QPM OU ":a"a

"P ":QPa OT ":aVM

"U ":QUQ OS ":aV"

"T ":QTU OQ ":aVV

"S ":QS" Oa ":aVO

"Q ":QST PM ":aVP

"a ":QQ" UM ":aO"

VM ":QQU TM ":aOT

V" ":QQa SM ":aP

VV ":QaO QM ":aPV

VO ":QaT aM ":aPP

VP ":Qaa "MM ":aPT

VU ":aMV % ":aT


8/35

Q

0AH 1C+7%$3$/I, 12&/$2&+ EF.J#F= D$/C(;G

E- 15.,0-1.%2, +,.$(' )(++(-56 *&,' .( %',-.%46 (*.5%,0& %& .$, [$1*2,-,.^& )0%.,0%1: #$%& +,.$(' %&

0,)(++,-','


9/35

a

(O>KL@A 1 D- .$%& ,91+/5, "M 0,1'%-8& 10, .1f,- *&%-8 1 5,-8.$ +,1&*0%-8 ',2%),: #$, +,.$('(5(86

(*.5%-,' 4(0 .$, #$(+/&(- !+,.$(' %& 4(55(3,' .( ',.,0+%-, %4 1-6 (4 .$, '1.1 )1-


10/35

"M

H #$52$,,&(3 F3+8K,&,

D- ,9/,0%+,-.15 3(0f@ .$,0, %& (4.,- 1 -,,' .( ,&.1 JAYJABBCHG L@HE5

#$, ,00(0 (0 0,&%'*15 4(0 1 0,80,&&%(- 1-156&%& %& ',4%-,' 1& .$, (


11/35

""

G$,- *&%-8 1 0,80,&&%(- +(',5 4(0 /0,'%).%(- /*0/(&,&@ %. %& %+/(0.1-. .$1. 6(* )(-&%',0 (-56 .$, 0,5,21-.

01-8, (4 .$, %-',/,-',-. 210%1


12/35

"V

;(+, (4 .$, )(++(- .,0+& 6(* &$(*5' GI .AJKB

#,0+ >,&)0%/.%(- Bj*1.%(- B9),5]A*-).%(-

Y%4 1-6Z

K HJ >1 ;5(/, c ;KXWBY6^&@ 9^&Z

&K HJ&>1

\-),0.1%-.6 %- .$, &5(/, 215*, t!,"#

&.1-'10' ,00(0 (4 &5(/,

? HJ >= D-.,0),/. cDL#BH[BW#Y6^&@ 9^&Z

&? HJ&>=

\-),0.1%-.6 %- .$, %-.,0),/. 215*, t!,"

# &.1-'10' ,00(0 (4

%-.,0),/.

% [(00,51.%(- [(,44%)%,-. c[XHHBKY6^&@ 9^&Z

%7 #$%& f-(3- 1& .$, )(,44%)%,-. (4

',.,0+%-1.%(-: HV+,1&*0,& .$,

/0(/(0.%(- (4 210%1


13/35

"O

HA" 1(22$8+/&(3 () =>?$2&@$3/+8 4+/+

;(+, 5,2,5 (4 &)1..,0 '*, .( 01-'(+ ,00(0& %& )(++(- %- 2%0.*1556 155 +,1&*0,+,-. &6&.,+&: D- &(+, )1&,&

.$, &)1..,0 +16


14/35

"P

.>?@A < +JCECD>@ V>@NAB HF EWA DHJJA@>ECHG DHAFFCDCAGE >B > FNGDECHG HF B>KL@A BCXA FHJ $`=5=\N Rcritical

(@ 95% Confidence Level)

Rcritical

(@ 99% Confidence Level)

3 0.997 1.000

4 0.95 0.990

5 0.878 0.959

6 0.811 0.917

7 0.754 0.875

8 0.707 0.834

9 0.666 0.798

10 0.632 0.765

11 0.602 0.735

12 0.576 0.708

13 0.553 0.684

14 0.532 0.661

15 0.514 0.641

16 0.497 0.623

17 0.482 0.606

18 0.468 0.590

19 0.456 0.575

20 0.444 0.561

25 0.396 0.505

30 0.361 0.463

35 0.334 0.430

40 0.312 0.403

45 0.294 0.380

50 0.279 0.361

100 0.197 0.257

200 0.138 0.180


15/35

"U

HA0 #$,&;7+8, +3; #$,&;7+8


16/35

"T

HAH 1(3)&;$3-$ +3; GI LJAICDECHG CGEAJV>@B

.AJK ,AFCGCECHG

[(-4%',-),

D-.,0215

6/0,'%).,'&6[D

[(-4%',-), %-.,0215&@ [D@ Y(0 )(-4%',-),


17/35

"S

E- ,91+/5, (4 1 )*02, 4%. 3%.$ )(-4%',-), 1-' /0,'%).%(- %-.,0215& %& /0,&,-.,' %- A%8*0, O .$0(*8$ A%8*0, U:

L(., $(3 .$, )(-4%',-), 1-' /0,'%).%(- %-.,0215& 4510, (*. (- .$, &%',& (4 .$, /0,'%).,' +(',5:

)CYNJA 6 (O>KL@A HF JAYJABBCHG @CGA SCEW DHGFCIAGDA >GI LJAICDECHG CGEAJV>@B NBCGY (ODA@5

)CYNJA Z (O>KL@A HF JAYJABBCHG @CGA SCEW DHGFCIAGDA >GI LJAICDECHG CGEAJV>@B NBCGY b#:5

)CYNJA \ (O>KL@A HF JAYJABBCHG @CGA SCEW DHGFCIAGDA >GI LJAICDECHG CGEAJV>@B NBCGY #3*3.$/5

y = -0.0049x + 5.4914R!= 0.97545

0

1

2

3

4

5

6

0 200 400 600 800

Torque,N

-m

RPM

RPM (X)

CI+_act

CI-_act

PI+_act


18/35

"Q

)CYNJA < (O>KL@A HF JAYJABBCHG @CGA SCEW DHGFCIAGDA >GI LJAICDECHG CGEAJV>@B NBCGY 0>?2CAS5

HAM 67/8&$2, &3 >NK 4+/+ .$/,

F*&. 1& %- &%-85, /(%-. +,1&*0,+,-. '1.1@ .$,0, %& 1 -,,' .( *-',0&.1-' (0 &.1.%&.%)1556 ',.,0+%-, %4 1 '1.1

/(%-. %- .$, _N` '1.1 %& 1- h(*.5%,0i: #$, +,.$(' .( *&, 4(0 9N6 '1.1 %-2(52,& )(+/*.%-8 .$, 01.%( (4 .$,

0,&%'*15& Y(


19/35

"a

HAO P&3$+2 #$52$,,&(3 F3+8K,&, B((8,

G$%5, .$,0, 10, -*+,0(*& &(4.310, .((5& 121%511.1 %&

)(55,).,' 1-'

,-.,0,' %-.(

B9),5:

V W5(. .$, '1.1

tL(., (-, /(%-. 1. _cTM" +16


20/35

VM

!EAL ,ABDJCLECHG ,AE>C@B HF $G>@QBCB >GI %ABN@EB

O >,.,0+%-,

0,80,&&%(-

)(,44%)%,-.&

1-' (.$,0

&.1.%&.%)15

/101+,.,0&:

W5(. )*02, 4%.:

[(+/10, .$,

1).*15

)(00,51.%(-

)(,44%)%,-. .(

.$, )0%.%)15

)(00,51.%(-

)(,44%)%,-.

40(+ #1


21/35

V"


P E-1567,

&.1-'10'%7,'

0,&%'*15& .(

)$,)f 4(0 1-6

&.1.%&.%)15

(*.5%,0& %- .$,

'1.1:

W(%-. YTM"@PZ 1//,10& .(


22/35

VV


T >,.,0+%-, .$,

)(-4%',-),

1-' /0,'%).%(-

%-.,0215&:

S H,2%,3

1-156&%&

&$,,.& .(

+1f, &*0, 155

%-4(0+1.%(- %&

/0,&,-.,'

/0(/,056 Y,:8:

&%8-%4%)1-.

4%8*0,& 1-'

*-%.&Z:

H,2%,3 /5(.&

1-' 801/$& .(

%-&*0, .$,6

10, /0(/,056

51


23/35

VO

B91+/5,& (4 .$, 0,80,&&%(- (*./*. 40(+ F?W 1-' ?DLD#EC &.1.%&.%)15 1-156&%& /0(801+& 10, /0,&,-.,' %-

A%8*0, S 1-' A%8*0, Q:

)CYNJA a (O>KL@A HF JAYJABBCHG @CGA >@HGY SCEW BE>ECBECD>@ HNELNE FJHK b#: SCEWHNE HNE@CAJB5


24/35

VP

Regression Analysis: Torque, N-m (Y) versus RPM (X)

The regression equation is

Torque, N-m (Y) = 5.43 - 0.00434 RPM (X)

Predictor Coef SE Coef T P

Constant 5.4326 0.4816 11.28 0.000

RPM (X) -0.0043420 0.0009540 -4.55 0.004

S = 0.617555 R-Sq = 77.5% R-Sq(adj) = 73.8%

Analysis of Variance

Source DF SS MS F P

Regression 1 7.8994 7.8994 20.71 0.004

Residual Error 6 2.2882 0.3814

Total 7 10.1877

Unusual Observations

Torque,

Obs RPM (X) N-m (Y) Fit SE Fit Residual St Resid

6 601 4.120 2.823 0.262 1.297 2.32R

R denotes an observation with a large standardized residual.


25/35

VU

Regression Analysis: Torque, N-m (Y) versus RPM (X) without Outlier

The regression equation is

Torque, N-m (Y) = 5.49 - 0.00491 RPM (X)

Predictor Coef SE Coef T P

Constant 5.4914 0.1706 32.19 0.000

RPM (X) -0.0049115 0.0003485 -14.09 0.000

S = 0.218446 R-Sq = 97.5% R-Sq(adj) = 97.1%

Analysis of Variance

Source DF SS MS F P

Regression 1 9.4791 9.4791 198.65 0.000

Residual Error 5 0.2386 0.0477

Total 6 9.7177

)CYNJA c (O>KL@A HF JAYJABBCHG >G>@QBCB HNELNE FJHK #3*3.$/ SCEW >GI SCEWHNE HNE@CAJB5


26/35

VT

)CYNJA d (O>KL@A HF JAYJABBCHG @CGA >@HGY SCEW BE>ECBECD>@ HNELNE FJHK !E>E:@NB SCEWHNE HNE@CAJB5


27/35

VS

HAR P&3$+2 #$52$,,&(3 S,&35 4+/+ B2+3,)(2@+/&(3

?1-6 .%+,& .$, 0,51.%(-&$%/


28/35

VQ

(O>KL@A 65 D- .$%& ,91+/5,@ 2(5.18, '0(/ +,1&*0,+,-.& 10, .1f,- 1)0(&& 1 '%&)$108%-8 )1/1)%.(0 1& 1

4*-).%(- (4 .%+,: >1.1 .01-&4(0+1.%(- %& 0,j*%0,' .( *.%5%7, 5%-,10 0,80,&&%(- 1-' .$,- .01-&4(0+,' 1.1 )(55,).,' Time, s Voltage, V

0 4.98

0.1 1.84

0.2 0.680.3 0.25

0.4 0.09

0.5 0.03


29/35

Va

W5(. '1.1 (- 0,8*510

19,&

](5.18, %& (


30/35

OM

#$, 4%-15 &.,/ %& .(

.01-&4(0+ .$,

%-4(0+1.%(- (


31/35

O"

HAT D78/&?8$ +3;


32/35

OV

W(56-(+%15 0,80,&&%(- 1-156&%& %& /,04(0+,'


33/35

OO

[0,1., 1''%.%(-15 )(5*+-& 4(0 #V@

#O@ 1-' #P: #$,&, -(3


34/35

OP

HATA0 D78/&?8$ #$52$,,&(3

?*5.%/5, 0,80,&&%(- ,91+%-,& .$, 0,51.%(-&$%/


35/35

[0,1.,' 1''%.%(-15

)(5*+-& 4(0 HW?V@ 1-'

HW?t# 1-' .$,-

/,04(0+ .$, 0,80,&&%(-

1-156&%&:

G%.$ .$, )(,44%)%,-.&

-(3 (

Statistics and Regression

Documents

Transcript of Statistics and Regression