Multiple Regression Tugas Data Terpisah

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ASSIGNMENT OF QUANTITATIVE RESEARCH METHODOLOGY

MULTIPLE REGRESSION

Name : Jajat Imanudn

Nm : !""#"$$"$%

Su&je't : Quanttat(e Re)ea*'+ Met+,d,-,./

Le'tu*e* : E-n D*ana0 P1+d

RESEARCH QUESTIONS:

1. Do vocabulary and grammar jointly explain writing ability?

2. Does vocabulary explain writing ability controlling for (in presence of/taking into account

grammar?

!. Does grammar explain writing ability controlling for vocabulary?

DATA

NO1 VOCA2ULARY GRAMMAR 3RITING

1 "# 1$ $2

2 %1 11 "&

! "" ' $1

$ "% 1& && "1 1! $#

" && 1# &2

' $" 1# $#

% "% 1" &'

&& 21 $%

1# &# 12 $'

11 "2 1$ &&

12 "$ 1' "#

1! "' 1" &$

1$ '1 12 &%

1& &" 1# $

1" "' 11 &'

1' &% 1! $2

1% $% 12 $&

1 && 1" &2

2# "# $&

HYPOTHESIS

1. )# * +ointly vocabulary and grammar do not significantly explain writing ability ,1-,2-#



)1* +ointly vocabulary and grammar significantly explain writing ability. (at least one of te

population parameters is not eual to 0ero one ,1#

2. )# * ,1-#)1* ,1#

!. )# * ,2-#)1* 2#

CORRELATION TA2LE

C,**e-at,n)

3456578

9:;<=><4

@ 84<AA<4

Bearson

;orrelation

3456578 1.### ."" .2'2

9:;<=><4@ ."" 1.### .#$!

84<AA<4 .2'2 .#$! 1.###

Cig. (1tailed 3456578 . 1""! 1!45

9:;<=><4@ .##1 . .$2%

84<AA<4 .12! .$2% .

7 3456578 2# 2# 2#

9:;<=><4@ 2# 2# 2#

84<AA<4 2# 2# 2#

!1 3*tn. and V,'a&u-a*/

B 9alue * #.##1 E F #.#&

4eject )#

5nterpretation

6ere is significant positive relationsip between writing ability and vocabulary.

41 3*tn. and G*amma*

B 9alue * #.12! G F #.#&

Do not 4eject )#

5nterpretation

6ere is no significant positive relationsip between writing ability and grammar.

TEST OF OVERALL SIGNIFICANCE 6ANOVA7



ANOVA&

Aodel

Cum of

Cuares df Aean Cuare H Cig.

1 4egression &%2.$!! 4 48!14!% #1%5# .##2a

4esidual &"".&"' !% 55154%

6otal 11$.### 1

a. Bredictors* (;onstantI 84<AA<4I 9:;<=><4@

b. Dependent 9ariable* 3456578

0 H * k β β β === ...21 - # (no linear relationsip

1 H * at least one 0≠iβ (at least one independent variable affects Y

De.*ee ,9 9*eed,m

df 1 - k - 2

df 2 - n J k J 1 - 2# J 2 J 1 - 1'

df t - n J 1 - 2# J 1 - 1

Te)t )tat)t':

P- ValueCig - #.##2 E F #.#&4eject )o

Critical value approach

F

pvalue

HF-!.& H-%.'!%

H-%.'!%GHF-!.&

Decision * 4eject )o

5nterpretation* jointly vocabulary and grammar significantly explain writing ability

TEST OF INDIVIDUAL SIGNIFICANCE 6COEFFICIENT TA2LE7

291.2172

582.433

Re

ReRe ===

gression DF

gressionSS gression MS

33.32717

566.567

Re

ReRe ===

sidual DF esidual SS sidual MS

8.73833.327

291.217

Re

Re===

sidual MS

gression MS F



C,e99'ent)a

Aodel

>nstandardi0ed

;oefficients

Ctandardi0ed

;oefficients

t Cig.

&.#K ;onfidence 5nterval

for =

= Ctd. Lrror =eta ower =ound >pper =ound

1 (;onstant '.&%" 1#.$$& .'2" .$'% 1$.$&# 2."22

9:;<=><4

@

1# 1!! ."&% 51#$5 .##1 .2"" .#&

84<AA<4 1#" 1;"$ .2$$ !1;5" .1'1 .2'" 1.$!"

a. Dependent 9ariable* 3456578

0 H * 0=iβ (no linear relationsip

1 H * 0≠iβ (linear relationsip does exist between Mi and @

6est Ctatistic*

ib

i

S

bt

0−= (df - n J k J 1

!1 V,'a&u-a*/

ib

i

S

bt

0−=

863.3151.0

585.0==t

P-value approach

Bvalue - #.##1E F #.#&

4eject )o


F/2 F/2

t#.#2& t- !.%"!

- 2.11#

t-!.%"!Gt#.#2& - 2.11#

4eject )o

5nterpretation* vocabulary significantly explain writing ability controlling for grammar.

41 G*amma*



ib

i

S

bt

0−=

430.1406.0

580.0==t

P-value approachBvalue - #.1'1G F #.#&

Do not reject )o


F/2 F/2

t- 1.$!# t#.#2&

- 2.11#

t-1.$!#Et#.#2& - 2.11#

Decision* Do not reject )o

5nterpretation

8rammar does not significantly explain writing ability controlling for vocabulary.

ESTIMATED REGRESSION EQUATION

C,e99'ent)a

Aodel

>nstandardi0ed

;oefficients

Ctandardi0ed

;oefficients

t Cig.

&.#K ;onfidence 5nterval

for =

= Ctd. Lrror =eta ower =ound >pper =ound

1 (;onstant %1#$ 1#.$$& .'2" .$'% 1$.$&# 2."22

9:;<=><4@ 1# .1&1 ."&% !.%"! .##1 .2"" .#&

84<AA<4 1#" .$#" .2$$ 1.$!# .1'1 .2'" 1.$!"

a. Dependent 9ariable* 3456578

k k X b X b X bbY ++++=

∧

...22110

21 580.0585.0586.7 X X Y ++=

∧

Lstimated writing ability - '.&%" N #.&%& (9ocabulary N #.&%# (8rammar

5nterpretation*1. 9ocabulary

5f vocabulary increases by 1 pointI writing ability will increase by #.&%&

2. 8rammar5f grammar increases by 1 pointI writing ability will increase by #.&%#

9ocabulary - &#8rammar - 1#

)10(580.0)50(585.0586.7 ++=

∧

WA



- '.&%" N 2.2& N &.% - $2."!"

8< CONFIDENCE INTERVAL

0 H * 0=iβ

1 H * 0≠iβ

1−−±

k ni t b

!1 V,'a&u-a*/- #.&%& O 2.11# (#.1&1- #.&%& O #.!1- #.&%& J #.!1I #.&%& N #.!1- #.2""I #.#$3e are &K confident tat te true population parameter ( β1 is between #.2"" and #.#$.4eject )#

P# #.2"" #.#$

41 G*amma*- #.&%# O 2.11# (#.$#"- #.&%# O #.%&'- #.&%# J #.%&'I #.&%# N #.%&'- #.2''I 1.$!'3e are &K confident tat te true population parameter ( β1 is between #.2'' and 1.$!'.4eject )#

P #.2'' # 1.$!'

R4= COEFFICIENT OF DETERMINATION

ANOVA&

AodelCum of Cuares df Aean Cuare H Cig.

1 4egression #41;55 2 21.21' %.'!% .##2a

4esidual &"".&"' 1' !!.!2'

6otal !!;81""" 1


b. Dependent 9ariable* 3456578



M,de- Summa*/

Aodel 4 4 Cuare

<djusted 4

Cuare

Ctd. Lrror of

te Lstimate

;ange Ctatistics

4 Cuare

;ange H ;ange df1 df2

Cig. H

;ange

1 .'12a 1"% .$$ &.''! .&#' %.'!% 2 1' .##2


5nterpretation*

• 9ocabulary and grammar account for &#.'K of variability in writing ability.

•&#.'K of variability in writing ability can be explained by its relationsip wit vocabulary

and grammar.

%7.50507.01149.000

582.433

SST

SSR 2====r

Multiple Regression Tugas Data Terpisah

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