simple and multiple regression analysis

8/20/2019 Simple and Multiple Regression Analysis

1/48

Regression Analysis

ε ++++++= k k xb xb xb xba y ...ˆ 332211

X 1

X 2

X 3

ŷ


2/48

COMMON TYPES OF ANALYSIS?COMMON TYPES OF ANALYSIS?

1.Compare Groupsa. Compare Proportions (e.g. C!i S"uare Test#

2$ %&' P1 P) P* + P,

-. Compare Means (e.g. Ana/sis o0 arian2e$ %&' 31 3) 3* + 3,

).E4amine Strengt! an5 6ire2tion o0 7eations!ips

a. 8i9ariate (e.g. Pearson Correation#r$

8et:een one 9aria-e an5 anot!er' Y a ; -1 41

-. Muti9ariate (e.g. Mutipe 7egression Ana/sis$ 8et:een one 5ep. 9ar. an5 ea2! o0 se9era in5ep. 9aria-es

:!ie !o5ing a ot!er in5ep. 9aria-es 2onstant'

Y a ; -1 41 ; -) 4) ; -* 4* ; + ; -, 4,

STATITICAL 6ATA ANALYSISSTATITICAL 6ATA ANALYSIS


3/48

Simple and Multiple Regression Analysis

Examines whether changes/differences in values of one variable(dependent variable Y are lin!ed to changes/differences in valuesof one or more other variables (independent variables "1# "2# etc.#while controlling for the changes in values of all other "s.

E.g.# $elationship between salar% and gender for people who have the samelevels of education# wor! experience# position level# seniorit%# etc.

&he ' (Y must be metric.

&he )s ("s must be either metric or dumm% var.

*entral +uestion ,ddressed-

)s Y a function of "1# "2# etc. ow )s there a relationship between Y and "1# "2 # etc.# (in each case#after controlling for the effects of all other "s )n what wa%

0hat is the relative impact of each " on Y# holding all other "sconstant (that is# all other "s being eual

0hat does regression anal%sis do


4/48

Simple and Multiple Regression Analysis ore specificall%#

'o values of Y tend to increase/decrease asvalues of "1# "2# etc. increase/decrease

)f so#% how much

,nd

ow strong is the connection/relationship between "s and Y

4 what 5 of differences/variationsin Y values (e.g.# income amongstud% sub6ects can be explained b%(or attributed to differences in" values (e.g. %ears of education#%ears of experience# etc.

X

1

X 2

X 3

ŷ


5/48

Simple and Multiple Regression Analysis 78&E- 8nce we can determine how values of Y change as afunction of values of "

1# "

2# etc.# we will also be able to

predict/estimate the value of Y from specific values of "1# "2#etc.

Y a ; -1 41 ; -) 4) ; -* 4* ; + ; -, 4,;<

&herefore# regression anal%sis# in a sense# is aboutE9&),&)7: values of Y# using information aboutvalues of "s-

Estimation# b% definition# involves

&he ob6ective

&o minimi;e error in estimation.

8r# to compute estimates that are

as close to the true/actual values as possible.


6/48

Simple and Multiple Regression Analysis +


7/48


Estimating Number of Credit Cards*

i

?amil% 7umber

%i

Actual @ of *redit*ards

1 A

2 B3 B

A C

D >

B CC >

> 1

DB=∑ iY

Estimate

+

DBˆ === y y

= ŷ

F &his example was adopted from air# lac!# abin# ,nderson# G &atham# (2B. Multivariate Data Analysis# Bth ed.# Hrentice all.


8/48


Estimating Number of Credit Cardsi

?amil% 7umber

Actual @ of*redit *ards

Estimate for @of *redit

*ards

Error inEstimation

1 A C ?2 B C ?

3 B C ?

A C C ?

D > C ?

B C C ?

C > C ?

> 1 C ?

DB=∑ i y C>DB

ˆ === y y

y y =ˆi y


9/48



?amil% 7umber



*ards

Error inEstimation

1 A C I32 B C I1

3 B C I1

A C C

D > C J1

B C C

C > C J1

> 1 C J3

DB=∑ i y

y yi −

C>

DBˆ === y y

y y =ˆi y

Kets now see all

this graphicall%


10/48

Simple and Multiple Regression Analysis1

L

>

C

B

D

A

3

2

1

?1?1

?2# ?3?2# ?3?A?A

?D?D

?B?B?C?C

?>?>

Y Y =M

, c t u a l @

o f c r e d i t c a r d

s

, c t u a l @


s

EstimateEstimate

KetNs spread the dots awa% from each

other to see things more clearl%O


11/48

Simple and Multiple Regression Analysis1

L

>

C

B

D

A

3

2

1

?1?1

?2?2

?3?3?A?A

?D?D

?B?B

?C?C

?>?>

Estimation ErrorEstimation Error

Y Y =M

, c t u a l @


s

, c t u a l @


s :raphic $epresentation

EstimateEstimate

A2tuaA2tua

*an we determine the

total estimation error

for all > families

EstimateEstimate


12/48


i

?amil% 7umber



*ards

Error inEstimation

1 A C I3

2 B C I1

3 B C I1

A C C

D > C J1

B C C

C > C J1

> 1 C J3DB=∑ i y ∑ − ( y yiC

>

DBˆ === y y

0hat would be the

total estimationtotal estimation

error error for all >

families combined

= 0

Solution?

y y =ˆi y y yi −


13/48



?amil% 7umber



*ards

Error inEstimation

Errors 9uared

1 A C I3 L2 B C I1 1

3 B C I1 1

A C C

D > C J1 1

B C C

C > C J1 1

> 1 C J3 L

2

( y yi −

∑ =− 222( y yi

SST = Sum of Squares Total

i y y y =ˆ y yi −

DB=∑ i y C>

DBˆ === y y E( =−∑ y yi


14/48


22 = 99& = )ndex for total (combined amount of estimation error for all families (observations in the sample when using the mean as the estimate.

99& is also the sum of suared deviations from the mean.

o $emember the formula for computing Variance

4 8b6ective in Estimation

inimi;e error# maximi;e precision.

4 *an we cut down the amount of estimation error (99& ow*an we cut down the amount of estimation error (99& ow

Yes# we can# b% using information about other variables b% using information about other variables suspectedto be strong predictors (strongl% related to @ of credit cards

possessed b% families (e.g.# famil% si;efamil% si;e## famil% incomefamil% income# etc...


15/48


i

?amil% 7umber


Family Sie

1 A 2

2 B 2

3 B A

A C A

D > D

B C D

C > B

> 1 B

y x

0e now can attempt to

estimate @ of credit cards

from the information onfamil% si;e# rather than

from its own mean.

KetNs first see this graphicall%O


16/48


1

L

>

C

B

D

A

3

2

1

?1?1

?2?2

?3?3

?A?A?D?D

?B?B

?C?C

?>?>

! " f # r e d i t # a r d s

! " f # r e d i t # a r d s

$$

1 2 3 A D B C

Origina (8aseine$Origina (8aseine$

EstimateEstimate

%%

Family SieFamily Sie

y y =ˆ

QUESTION:QUESTION: Does the mean appear to represent the

closest estimate of the actual c.c. numbers for oursample families ?

That is, is the green line the best line to represent the

location of estimates of of !! for these families?

( yA#2 == y x

Hlot actual numbers of **s

against famil% 9i;e.


17/48


1

L

>

C

B

D

A

3

2

1

?1

?2

?3

?A ?D

?B

?C

?>

! " f # r e d i t # a r d s

! " f # r e d i t # a r d s

$$

1 2 3 A D B C

Origina (8aseine$Origina (8aseine$

EstimateEstimate

%%


&eneric Equation for any

straight line' $= a ( )*

xba y 11ˆ +=

xba y 22ˆ +=

xba y 33ˆ +=

+egression ,ine

y y =ˆ

y xa y =+= Eˆ

$egression Kine

(Kine of est ?itII

new improved

location for **estimates (see next

slide


18/48


1

L

>

C

B

D

A

3

2

1

?1?1

?2?2

?3?3

?A?A?D?D

?B?B

?C?C

?>?>

! " f # r e d i t # a r d s

! " f # r e d i t # a r d s

$$

1 2 3 A D B C

OriginaOrigina(8aseine$(8aseine$EstimateEstimate

%%


$eg. Kine (Kine ofest ?itIInew

improved location

for ** estimates

y

Estimation E$$8$ ˆ( y y −

$egression Kine will

inimi;e = total estimation error.2ˆ( y y∑ −

bxa y +=ˆ

ut# how do we !now the valuesthe values aa andand b b in (the reg. linebxa y +=ˆ


19/48

∑ −

∑ −−

= 2(

((

x x

y y x x

b

xb ya −=

Actual # of credit cards

bxa y +=ˆ

KetNs use above formulas to compute the values of Pa Q

and Pb Q for the regression line in our example.

0e will need- and

EQUATION FOR REGRESSION LINE (LINE OF BESTFIT)--

alues of a and b for the regression line-

# y

# x #(( y y x x −−∑ ∑ −

2

( x x


20/48


i

?amil% 7umber

Actual ! of *redit

*ards

FamilySie

1 A 2 ? ? ? ?

2 B 2 ? ? ? ?

3 B A ? ? ? ?

A C A ? ? ? ?

D > D ? ? ? ?

B C D ? ? ? ?

C > B ? ? ? ?

> 1 B ? ? ? ?

C>

DB==Y 2D.A

>

3A== x

x x −

(( =−−∑ y y x x

y y − (( y y x x −−

2( =−∑ x x

2

( x x −

-e need' #(( y y x x −−∑ ∑ −2

( x xand# y # x

y x


21/48


i

?amil% 7umber

Actual ! of *redit

*ards

FamilySie

1 A 2 I2.2D I3 B.CD D.B2D

2 B 2 I2.2D I1 2.2D D.B2D

3 B A I.2D I1 .2D .B2D

A C A I.2D .B2D

D > D .CD 1 .CD .DB2D

B C D .CD .DB2D

C > B 1.CD 1 1.CD 3.B2D

> 1 B 1.CD 3 D.2D 3.B2D

C

>

DB==Y 2D.A

>

3A== x

x x −

1C(( =−−∑ y y x x

y y − (( y y x x −−

D.1C

2

( =−∑ x x

2

( x x −

-e need' #(( y y x x −−∑ ∑ −2

( x xand# y # x

y x


22/48

REGRESSION LINE (LINE OF BEST FIT):

a =2.87 b = .97

LC1.D.1C

1C

2(

((==

∑ −

∑ −−=

x x

y y x xb

>C.22D.A(LC1.C =−=−= xb ya

x y LC.>C.2ˆ +=

bxa y +=ˆ

YI)ntercept

$egression *oefficient



23/48


1

L

>

C

B

D

A

3

2

1

?1?1

?2?2

?3?3

?A?A

?D?D

?B?B

?C?C

?>?>

! " f # r e d i t # a r d s

! " f # r e d i t # a r d s

$$

1 2 3 A D B C

OriginaOrigina(8aseine$(8aseine$

EstimateEstimate

%%


x y LC.>C.2ˆ +=

y

*an we tell how much estimation error how much estimation error we havecommitted b% using the new regression line

Ne:Ne:Impro9e5Impro9e5EstimatesEstimates

"es, e#amine differences bet$een our househol%&s

actual of !!s an% their ne$'regression estimates.


24/48


i?amil%

7umber

Actual ! of *redit

*ards

FamilySie

$egressionEstimate

Error

($esidual

Errors9uared

1 A 2 ? ? ?

2 B 2 ? ? ?

3 B A ? ? ?

A C A ? ? ?

D > D ? ? ?

B C D ? ? ?C > B ? ? ?

> 1 B ? ? ?

y y ˆ− ŷ 2ˆ( y y −

x y LC.>C.2ˆ +=

∑ −2ˆ( y y

x y

ŷ


25/48


i?amil%

7umber

Actual ! of *redit

*ards

?amil%9i;e

$egression$egressionEstimateEstimate

Error

($esidual

Errors9uared

1 A 2 A.>1 I.>1 .BB

2 B 2 A.>1 1.1L 1.A2

3 B A B.CB I.CB .D>

A C A B.CB .2A .B

D > D C.C3 .2C .C

B C D C.C3 I.C3 .D3C > B >.C I.C .AL

> 1 B >.C 1.3 1.BL

y y ˆ− ŷ2

ˆ( y y −

x y LC.>C.2ˆ += >1.A2(LC.>C.2ˆ =+= y

∑ −= 2ˆ( y y5.486

SSE = Sum of Squares Error .SS +esidual

x y


26/48

Simple and Multiple Regression Analysis &otal aseline Error using the mean (SS Total 10

7ew or $emaining Error (SS Error or SS +esidual 21345 6 212

78EST9":' ow much of the original estimation error have we explained awa% (eliminated b% using the regression model (instead of the mean

1B.D1A / 22 = .CD1 or CD5CD5 0hat is this called

5 of differences in @ of **s among households that isexplained b% differences in their famil% si;e.

0hat does the remaining 2D5 represent

22 R D.A>B = 1B.D1A1B.D1A (99 $egression99 $egression or 99 Explained

78EST9":' -hat ; of estimation error have we explained (eliminated b%using the regression model

Hercent of variation (differences in number of credit cards owned b% families

that can be accounted for b%- (a all other potential predictors not included in the

model# be%ond famil% si;e# and (b unexplainable random/chance variations.

"1

&otal ar.

in Y = 22

1B.D

D.D

Y

$ $ 22 =


27/48


$ $ 22 is a measure of our success regarding accurac% of our estimation effort.

$ 2 = 5 of estimation error that we have been able to explain awa% b% using the regression model# instead of using the mean.

$ 2 indicates how much better we can predict Y from information about

"s# rather than from using its own mean. $ 2 = 5 of differences (variations in Y values that is explained b%

(attributable to differences in " values.

7ote- 0hen dealing with onl% two variables (a single " and Y-

KetNs now examine all this graphicall%O

>BB.CD.22

D1A.1B2==== Rr

$ 2 = 99 $egression / 99 &otal = 1B.D/22 = CD5

Pearson Correlationo ! "it# $%(NOT &ontrollin' oran ot#er ar*)


28/48

y y ˆ−??


1

L

>

C

B

D

A

3

2

1

?1?1

?2?2

?3?3

?A?A?D?D

?B?B

?C?C

?>?>

! " f # r e d i t # a r d s

! " f #

r e d i t # a r d s

$$

1 2 3 A D B C

OriginaOrigina(8aseine$(8aseine$EstimateEstimate

%%


x y LC.>C.2ˆ +=

8riginal

aseline

E$$8$

for F<

y y −ˆ y

y y −

7ew E$$8$

(


29/48


D.D = 99E = &he amount of estimation error for the > sample familieswhen using simple regression (i.e.# a regression model that includesonl% information about famil% si;e.

*an we reduce the amount of estimationerror (99E to an even lower level and#thus# improving the estimation process ow

Yes# b% adding information on a second variables suspected to bestrongl% related to @ of credit cards (e.g.# famil% incomeII"2.

.


30/48

Simple and Multiple Regression Analysisi

?amil% 7umber

%i


Family Sie Family9ncome

1 A 2 1A

2 B 2 1B

3 B A 1AA C A 1C

D > D 1>

B C D 21

C > B 1C

> 1 B 2D

Generic Equation for aGeneric Equation for a linear planelinear plane:: 2211ˆ xb xba y ++=

1 x 2 x

KetNs examine the regression plane for our example graphicall%.

0e now can attempt

to estimate @ of **s

from our information

on famil% si;e andfamil% incomeO

8ur regression model

will now be a linear

plane# rather than astraight lineO

Y # f C dit C d


31/48

21 21B.B3.A>2.ˆ x x y ++=

KetNs now see

how much error

in estimation we

are committing

b% using this

multiple

regression

model.

Y = # of Credit Cards

X1 = Family Size

Family Income

E 1 2

3 A D B

C >

12

11

19

8

7

!"

$

2

1

For+,las are aailale or&o+.,tin' al,es o a/ % an0 2

1ULTIPLE REGRESSION1OEL FOR OUR E$A1PLE:

,ctual

$egression Estimate

2211ˆ xb xba y ++=


32/48


i?amil%

7umber

Actual ! of *redit

*ards

FamilySie

Family9ncome

(S

$egression EstimateEstimate

Error

($esidual

Errors9uared

1 A 2 1A ? ? ?

2 B 2 1B ? ? ?

3 B A 1A ? ? ?

A C A 1C ? ? ?

D > D 1> ? ? ?

B C D 21 ? ? ?C > B 1C ? ? ?

> 1 B 2D ? ? ?

y y ˆ−Y ̂2

ˆ( y y −

∑ −2ˆ( y y

21 21B.B3.A>2.ˆ x x y ++= ŷ

y 1 x 2 x


33/48


i?amil%

7umber

Actual ! of *redit

*ards

FamilySie

Family9ncome

(S

$egressionEstimate

Error

($esidual

Errors9uared

1 A 2 1A A.CC I.CC .DL

2 B 2 1B D.2 .> .BA

3 B A 1A B.3 I.3 .

A C A 1C B.B> .32 .1

D > D 1> C.D3 .AC .22

B C D 21 >.1> I1.1> 1.3LC > B 1C C.LD .D .

> 1 B 2D L.BC .33 .11

y y ˆ−Y ̂2

ˆ( y y −

∑ −=2

ˆ( y y3.05SSE = Sum of Squares Error .+esidual

21 21B.B3.A>2.ˆ x x y ++= CC.A1A(21B.2(B3.A>2.ˆ =++= y

y 1 x 2 x

8nique .additional contri)ution of %% .family income.family income )eyond %102 = 132


34/48

$9ntercept$9ntercept# PaQ

(:"TE' 8nl% when all "s

can meaningfull% ta!e onvalue of ;ero# the intercept

will have a meaningful/direct/

practical interpretation.

8therwise# it is simpl% an aid

in increasing accurac% of

estimation.

bb and bb!! = +egression #oefficients= +egression #oefficients

015>- ,mong families of the same income# an increase in

famil% si;e b% one person would# on average# result in .B3

more credit cards.

012.ˆ x x y ++=

T#e 1ULTIPLE REGRESSION 1OEL FOR OUR E$A1PLE:


35/48

SST 3 22 SSE 3 4*56

7#at is o,r ne" R

2

8


21 21B.B3.A>2.ˆ x x y ++=

99 $egression = 22 R 3.D = 1>.LD

$ $ 22= 1>.LD / 22 = .>B1 or >B5

T#e 1ULTIPLE REGRESSION 1OEL FOR OUR E$A1PLE:

Hercent of differences in householdsN

number of **s that is explained b%

differences in famil% si;e and famil%

income.

&he $emaining 1A5

(3.D / 22 = .1A

Hercent of variation in number of credit

cards that can be accounted for b% (a all

other relevant factors not included in the

model# be%ond famil% si;e and income# and

(b unexplainable random/chance

variations.


36/48

d cba

car yx

+++

+=

1

d cba

cbr yx

+++

+=

2

"1=?amil% 9i;e

"2 = ?amil%

)ncome

ddaa

b bcc

$= @ of **

Pearson9si+.leCorrelationo ! "it# $%(not&ontrollin' or

$2)

Pearson9si+.le Correlationo ! "it# $2(not

&ontrollin' or$ ?

Total Variation/Error in $ = SS Total = a ( ) ( c ( d =

>2L.22

11.1D

2 ==

yxr

>BC.CD.22

D.1B1 === yxr

23L>.EB3.Eˆ X y +−=

1LC.>C.2ˆ X y += r 2 = $ 2 = (aJc / (aJbJcJd

r 2 = (bJc / (aJbJcJd = 1D.12 / 22 = .B>C

"1=?amil%

si;e

$

SS+ SS+ ==

a ( c a ( c =


37/48

99$ = a J b Jc = 1>.LD

99& = a J b J c J d = 22

$ $ 22 = 99$ / 99&= 99$ / 99& = (a J b J c / (a J b J c J d = 1>.LD / 221>.LD / 22 = >B5

99E =

99E = d = 22 R 1>.LD = 3.D

21 21B.B3.A>2.ˆ x x y ++=

"1=?amil% 9i;e

"2 = ?amil% )ncome

ddaa

b bcc

78&E- c is explained b%

both "1 and "2

$ 2 :raphicall% =


38/48


i?amil%

7umber

,ctual @ of *redit

*ards

?amil%9i;e

?amil%)ncome

(S

$egressionEstimate

Error

($esidual

Errors9uared

1 A 2 1A A.CC I.CC .DL

2 B 2 1B D.2 .> .BA

3 B A 1A B.3 I.3 .

A C A 1C B.B> .32 .1

D > D 1> C.D3 .AC .22

B C D 21 >.1> I1.1> 1.3LC > B 1C C.LD .D .

> 1 B 2D L.BC .33 .11

y y ˆ−Y ̂2

ˆ( y y −

∑ −=2

ˆ( y y3.05SSE = Sum of Squares Error .+esidual

21 21B.B3.A>2.ˆ x x y ++= CC.A1A(21B.2(B3.A>2.ˆ =++= y

y 1 x 2 x

8nique .additional contri)ution of % = 212 >102 = 132$emember-


39/48

Eer&ise %: Re0o t#e &re0it &ar0analsis "it# SPSS*

First/ Correlations an0 Si+.le Re'ression

Net/ 1,lti.le Re'ression (also as; or .art

an0 .artial &orrelations*)

SPSS CREIT CAR FILE

http://smb//datastore01/website/mqm497/MQM%20497%20SPSS%20Data%20Files/MQM497%20Credit%20Card%20Regression%20Model.savhttp://smb//datastore01/website/mqm497/MQM%20497%20SPSS%20Data%20Files/MQM497%20Credit%20Card%20Regression%20Model.sav


40/48


E"E$*)9E 2-


41/48

No%* Is oerall F si'ni


42/48

Simple and Multiple Regression Analysis $egression ,nal%sis


43/48


E",HKE 1- )ncome = 2A J 1A gender .

*oded- ?emale = # ale = 1

)ncome = 12 J 1 Education Years J > :ender

*oded- ?emale = # ale = 1

eaningeaning

,verage income of females

with no education is S12.

,mong people of the same gender# ever%additional %ear of education results in an

average additional income of S1#.

ales ma!e# on average# S> more in

comparison with females who have the

same number of %ears of education.

,verage income of females is S2A#.

ales on average ma!e S1A more than females


44/48

Eer&ise : S,..ose "e are intereste0 in;no"in' "#at role/ i an/ 0e+o'ra.#i&ara&teristi&s (i*e*/ age, sex_Dummy,educ, sibs, agewed, incomdol)/ as "ell as

?o satisa&tion (satjob-2)/ an0 +arria'esatisa&tion (hapmar-2) .la in 0eter+inin'one>s oerall #a..iness in lie (#a..-2)*

Use t#e 'ss*2 0ata


45/48

Eer&ise 4: S,..ose "e are intereste0in ;no"in' "#at role/ i an/ t#e ollo"in'0e+o'ra.#i& ara&teristi&s .la in0eter+inin' one>s in&o+e (rin&+0ol):

Age,ex_Dummy !"#male, 1#$emale%,

age &rst married ! agewed %,

'ears o$ education completed ! educ %, and

(olitical party a)liation--republic!"#Democrat, 1#*epublican% *

Use t#e 'ss*2 0ata


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Assignment 5

'ata file 9alar%.sav contains information about ACA emplo%ees hired b% a idwestern ban!

between 1LBL and 1LC1 (78&E- 'ue to 9H99 site license restrictions# this h%perlin! will

not wor! if %ou are off campus. 8f the ACA emplo%ees# 2D> were men# 21B women# 3Cwhite# and 1A nonIwhite. &he ban! was subseuentl% involved in EE8* litigationU the

ban! was accused of gender and race discrimination in its hiring and compensation

practices. &he two issues that were of particular interest in the litigation were alleged

gender and racial ineualities not onl% in the ban!Ns beginning salaries (variable salbeg#

but also in its later salaries (variable salnow.

1. Hrint# examine# and interpret correlation coefficients between beginning salar%(salbeg and age in years (age# education in years (edlevel# employment category or 6ob

classification levelIIrated from 1=lowest to >=highest (6obcat# and work experience in

months (wor!.

2. *onduct the appropriate anal%sis to see- (a 0hat role each of the variables age#

education (edlevel# employment category (6obcat# and work experience (wor! pla%ed#

holding all other variables constant# in determining the ban!Ns beginning salaries ?orexample# what was the differential pa% for one additional %ear of education among new

hires who otherwise had the same age# emplo%ment categor%# and wor! experience (b

0hich of the above demographic characteristics had the strongest influence on beginning

pa% ow can %ou tell (c 0hat percent of the differences in emplo%eesN beginning

salaries can be explained b%/attributed to difference in all of the above characteristics

A i t 5

http://www.cob.ilstu.edu/udrive/MQM/MQM%20497/Hemmasi/MQM497_Data_Files/SALARY.savhttp://www.cob.ilstu.edu/udrive/MQM/MQM%20497/Hemmasi/MQM497_Data_Files/SALARY.sav


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Assignment 5

3. 7ow conduct the appropriate anal%sis to indicate# holding all other variables

constant# what roles gender (sex# male=! female=" pla%ed in determining beginning

salaries at the ban!. &hat is# what was the differential beginning pa% between male andfemale emplo%ees who otherwise had the same age# education# emplo%ment categor%# and

wor! experience 'oes this evidence support the charges of gender discrimination in the

ban!Ns practices regarding initial compensation

A. 'uring litigation# it was charged that the ban!Ns unfair compensation practices had

continued be%ond its initial salar% decisions. &hat is# the prosecution claimed that with

time# not onl% the beginning salar% disparities between men and women did not shrin!# butfurther widened. *onduct the appropriate anal%sis to indicate (a ever%thing else being

eual# what roles gender pla%ed in determining emplo%eesN later salaries at the ban!

(salnow. &hat is# what was the average differential pa% between male and female

emplo%ees who otherwise had the same age# education# employment category# work

experience# and #ob seniority $variable time represents seniority in terms of number of

months employed at the bank% (b *ompare the later pa% disparities %ou have 6ustidentified with the beginning pa% disparities %ou had found in uestion 3 above to explain

if the evidence supports the prosecutionNs charges of continued gender discrimination

be%ond initial salar% decisions# resulting in widening disparities in later pa%.

78&E- ?or each uestion# provide thorough explanations on corresponding pages and

parts of %our printout.


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+./00*

0.4

simple and multiple regression analysis

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