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8/20/2019 Simple and Multiple Regression Analysis
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Regression Analysis
ε ++++++= k k xb xb xb xba y ...ˆ 332211
X 1
X 2
X 3
ŷ
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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
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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
8/20/2019 Simple and Multiple Regression Analysis
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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
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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.
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Simple and Multiple Regression Analysis +
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Simple and Multiple Regression Analysis
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.
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Simple and Multiple Regression Analysis
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
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Simple and Multiple Regression Analysis
Estimating Number of Credit Cardsi
?amil% 7umber
Actual @ of*redit *ards
Estimate for @of *redit
*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%
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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 @
o f c r e d i t c a r d
s
EstimateEstimate
KetNs spread the dots awa% from each
other to see things more clearl%O
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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 @
o f c r e d i t c a r d
s
, c t u a l @
o f c r e d i t c a r d
s :raphic $epresentation
EstimateEstimate
A2tuaA2tua
*an we determine the
total estimation error
for all > families
EstimateEstimate
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Simple and Multiple Regression Analysis
i
?amil% 7umber
Actual @ of*redit *ards
Estimate for @of *redit
*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 −
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Simple and Multiple Regression Analysis
Estimating Number of Credit Cardsi
?amil% 7umber
Actual @ of*redit *ards
Estimate for @of *redit
*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
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Simple and Multiple Regression Analysis
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...
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Simple and Multiple Regression Analysis
i
?amil% 7umber
Actual @ of*redit *ards
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
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Simple and Multiple Regression Analysis
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
$$
1 2 3 A D B C
Origina (8aseine$Origina (8aseine$
EstimateEstimate
%%
Family SieFamily Sie
y y =ˆ
QUESTION:QUESTION: Does the mean appear to represent the
closest estimate of the actual c.c. numbers for oursample families ?
That is, is the green line the best line to represent the
location of estimates of of !! for these families?
( yA#2 == y x
Hlot actual numbers of **s
against famil% 9i;e.
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Simple and Multiple Regression Analysis
1
L
>
C
B
D
A
3
2
1
?1
?2
?3
?A ?D
?B
?C
?>
! " f # r e d i t # a r d s
! " f # r e d i t # a r d s
$$
1 2 3 A D B C
Origina (8aseine$Origina (8aseine$
EstimateEstimate
%%
Family SieFamily Sie
&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
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Simple and Multiple Regression Analysis
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
$$
1 2 3 A D B C
OriginaOrigina(8aseine$(8aseine$EstimateEstimate
%%
Family SieFamily Sie
$eg. Kine (Kine ofest ?itIInew
improved location
for ** estimates
y
Estimation E$$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
8/20/2019 Simple and Multiple Regression Analysis
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∑ −
∑ −−
= 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
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Simple and Multiple Regression Analysis
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
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Simple and Multiple Regression Analysis
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
8/20/2019 Simple and Multiple Regression Analysis
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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
Simple and Multiple Regression Analysis
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Simple and Multiple Regression Analysis
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
%%
Family SieFamily Sie
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.
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Simple and Multiple Regression Analysis
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
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Simple and Multiple Regression Analysis
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
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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 =
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Simple and Multiple Regression Analysis
$ $ 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*)
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y y ˆ−??
Simple and Multiple Regression Analysis
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
%%
Family SieFamily Sie
x y LC.>C.2ˆ +=
8riginal
aseline
E$$8$
for F<
y y −ˆ y
y y −
7ew E$$8$
(
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Simple and Multiple Regression Analysis
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.
.
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Simple and Multiple Regression Analysisi
?amil% 7umber
%i
Actual @ of*redit *ards
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
8/20/2019 Simple and Multiple Regression Analysis
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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 ++=
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Simple and Multiple Regression Analysis
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
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Simple and Multiple Regression Analysis
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
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$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:
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SST 3 22 SSE 3 4*56
7#at is o,r ne" R
2
8
Simple and Multiple Regression Analysis
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.
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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 =
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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% =
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Simple and Multiple Regression Analysis
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$emember-
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Eer&ise %: Re0o t#e &re0it &ar0analsis "it# SPSS*
First/ Correlations an0 Si+.le Re'ression
Net/ 1,lti.le Re'ression (also as; or .art
an0 .artial &orrelations*)
SPSS CREIT CAR FILE
http://smb//datastore01/website/mqm497/MQM%20497%20SPSS%20Data%20Files/MQM497%20Credit%20Card%20Regression%20Model.savhttp://smb//datastore01/website/mqm497/MQM%20497%20SPSS%20Data%20Files/MQM497%20Credit%20Card%20Regression%20Model.sav
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Simple and Multiple Regression Analysis
E"E$*)9E 2-
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No%* Is oerall F si'ni
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Simple and Multiple Regression Analysis $egression ,nal%sis
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Simple and Multiple Regression Analysis
E",HKE 1- )ncome = 2A J 1A gender .
*oded- ?emale = # ale = 1
)ncome = 12 J 1 Education Years J > :ender
*oded- ?emale = # ale = 1
eaningeaning
,verage income of females
with no education is S12.
,mong people of the same gender# ever%additional %ear of education results in an
average additional income of S1#.
ales ma!e# on average# S> more in
comparison with females who have the
same number of %ears of education.
,verage income of females is S2A#.
ales on average ma!e S1A more than females
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Eer&ise : S,..ose "e are intereste0 in;no"in' "#at role/ i an/ 0e+o'ra.#i&ara&teristi&s (i*e*/ age, sex_Dummy,educ, sibs, agewed, incomdol)/ as "ell as
?o satisa&tion (satjob-2)/ an0 +arria'esatisa&tion (hapmar-2) .la in 0eter+inin'one>s oerall #a..iness in lie (#a..-2)*
Use t#e 'ss*2 0ata
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Eer&ise 4: S,..ose "e are intereste0in ;no"in' "#at role/ i an/ t#e ollo"in'0e+o'ra.#i& ara&teristi&s .la in0eter+inin' one>s in&o+e (rin&+0ol):
Age,ex_Dummy !"#male, 1#$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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Simple and Multiple Regression Analysis
+./00*
0.4