hierarchical multiple regression]

8/19/2019 Hierarchical Multiple Regression]

1/90

SW388R7

Data Analysis &

Computers II

Slide 1

Hierarchical Multiple Reression

Di!!erences "et#een hierarchical

and standard multiple reression

Sample pro"lem

Steps in hierarchical multiple reression


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Slide 2

Di!!erences "et#een standard and hierarchicalmultiple reression

Standard multiple reression is used to e$aluate the relationship"et#een a set o! independent $aria"les and a dependent $aria"le%

Hierarchical reression is used to e$aluate the relationship "et#een a

set o! independent $aria"les and the dependent $aria"le controllin

!or or ta'in into account the impact o! a di!!erent set o! independent$aria"les on the dependent $aria"le%

(or e)ample a research hypothesis miht state that there are

di!!erences "et#een the a$erae salary !or male employees and !emale

employees e$en a!ter #e ta'e into account di!!erences "et#een

education le$els and prior #or' e)perience%

In hierarchical reression the independent $aria"les are entered into

the analysis in a se*uence o! "loc's or roups that may contain one or

more $aria"les% In the e)ample a"o$e education and #or' e)perience

#ould "e entered in the !irst "loc' and se) #ould "e entered in thesecond "loc'%


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Slide 3Di!!erences in statistical results

S+SS sho#s the statistical results ,Model Summary A-./ACoe!!icients etc%0 as each "loc' o! $aria"les is entered into the

analysis%

In addition ,i! re*uested0 S+SS prints and tests the 'ey statistic

used in e$aluatin the hierarchical hypothesis chane in R2 !oreach additional "loc' o! $aria"les%

he null hypothesis !or the addition o! each "loc' o! $aria"les

to the analysis is that the chane in R2 ,contri"ution to the

e)planation o! the $ariance in the dependent $aria"le0 is 4ero%

I! the null hypothesis is re5ected then our interpretation

indicates that the $aria"les in "loc' 6 had a relationship to the

dependent $aria"le a!ter controllin !or the relationship o! the

"loc' 1 $aria"les to the dependent $aria"le%


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Slide 4/ariations in hierarchical reression 1

A hierarchical reression can ha$e as many "loc's as there are

independent $aria"les i%e% the analyst can speci!y a hypothesis

that speci!ies an e)act order o! entry !or $aria"les%

A more common hierarchical reression speci!ies t#o "loc's o!$aria"les a set o! control $aria"les entered in the !irst "loc'

and a set o! predictor $aria"les entered in the second "loc'%

Control $aria"les are o!ten demoraphics #hich are thouht to

ma'e a di!!erence in scores on the dependent $aria"le%+redictors are the $aria"les in #hose e!!ect our research

*uestion is really interested "ut #hose e!!ect #e #ant to

separate out !rom the control $aria"les%


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Slide 5/ariations in hierarchical reression 6

Support !or a hierarchical hypothesis #ould "e e)pected to

re*uire statistical sini!icance !or the addition o! each "loc' o!

$aria"les%

Ho#e$er many times #e #ant to e)clude the e!!ect o! "loc'so! $aria"les pre$iously entered into the analysis #hether or not

a pre$ious "loc' #as statistically sini!icant% he analysis is

interested in o"tainin the "est indicator o! the e!!ect o! the

predictor $aria"les% he statistical sini!icance o! pre$iously

entered $aria"les is not interpreted%

he latter stratey is the one that #e #ill employ in our

pro"lems%


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Slide 6

Di!!erences in sol$in hierarchical reressionpro"lems

R2 chane i%e% the increase #hen the predictors $aria"les are

added to the analysis is interpreted rather than the o$erall R2

!or the model #ith all $aria"les entered%

In the interpretation o! indi$idual relationships therelationship "et#een the predictors and the dependent $aria"le

is presented%

Similarly in the $alidation analysis #e are only concerned #ith

$eri!yin the sini!icance o! the predictor $aria"les%Di!!erences in control $aria"les are inored%


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Slide 7A hierarchical reression pro"lem

The problem asks us to examine the feasibilityof doing multiple regression to evaluate therelationships among these variables. Theinclusion of the “controlling for” phrase

indicates that this is a hierarchical multipleregression problem.

Multiple regression is feasible if the dependentvariable is metric and the independentvariables (both predictors and controls) aremetric or dichotomous, and the available datais sufficient to satisfy the sample siere!uirements.


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Slide 8e$el o! measurement ans#er

"#pouse$s highest academic degree" %spdeg& is ordinal, satisfying themetric level of measurement re!uirement for the dependent variable, if'e follo' the convention of treating ordinal level variables as metric.#ince some data analysts do not agree 'ith this convention, a note ofcaution should be included in our interpretation.

"ge" %age& is interval, satisfying the metric or dichotomous level ofmeasurement re!uirement for independent variables.

"ighest academic degree" %degree& is ordinal, satisfying the metric or

dichotomous level of measurement re!uirement for independentvariables, if 'e follo' the convention of treating ordinal level variablesas metric. #ince some data analysts do not agree 'ith this convention, anote of caution should be included in our interpretation.

"#ex" %sex& is dichotomous, satisfying the metric or dichotomous level ofmeasurement re!uirement for independent variables.

True 'ith caution

is the correctans'er.

ierarchical multiple regressionre!uires that the dependentvariable be metric and theindependent variables be metricor dichotomous.


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Slide 9Sample si4e *uestion

The second !uestion asks about thesample sie re!uirements for multipleregression.

To ans'er this !uestion, 'e 'ill run theinitial or baseline multiple regression toobtain some basic data about theproblem and solution.


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Slide

!he "aseline reression 1

fter 'e check for violations ofassumptions and outliers, 'e 'illmake a decision 'hether 'e shouldinterpret the model that includes thetransformed variables and omitsoutliers (the revised model), or'hether 'e 'ill interpret the model

that uses the untransformedvariables and includes all casesincluding the outliers (the baselinemodel).

*n order to make this decision, 'erun the baseline regression before'e examine assumptions andoutliers, and record the + for the

baseline model. *f usingtransformations and outlierssubstantially improves the analysis(a - increase in +), 'e interpretthe revised model. *f the increase issmaller, 'e interpret the baselinemodel.

To run the baselinemodel, select Regression| Linear… from the

Analyze model.


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Slide

he "aseline reression 6

First, move thedependent variable spdeg to the Dependent textbox.

Second, move theindependent variables tocontrol for age and sex to the Independent(s) list box.

Third, select the method forentering the variables into theanalysis from the drop do'nMethod menu. *n this example,'e accept the default of Enter fordirect entry of all variables in thefirst block 'hich 'ill force thecontrols into the regression.

Fourth, click on the Next button to tell #/## to addanother block of variablesto the regression analysis.


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Slide

2he "aseline reression 3

First, move thepredictor independentvariable degree to theIndependent(s) list boxfor block -.

Second, click on theStatistics0 button tospecify the statistics

options that 'e 'ant.

#/## identifies that 'e'ill no' be addingvariables to a secondblock.


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Slide

3he "aseline reression 9

Second, mark the checkboxes for ModelFit Descripti!es, and R s"#ared c$ange.

The R s"#ared c$ange statistic 'ill tellus 'hether or not the variables addedafter the controls have a relationship tothe dependent variable.

Fifth, click onthe %ontin#e button to close

the dialog box.

First, mark thecheckboxes forEsti&ates on the Regression%oe''icients panel.

Third, mark theD#rin*atson statistic on theResid#als panel.

Fourth, mark the%ollinearity diagnostics to get tolerance valuesfor testingmulticollinearity.


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Slide

4he "aseline reression :

1lick on the +,

button tore!uest theregressionoutput.


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Slide

5R2 !or the "aseline model

/rior to any transformations of variablesto satisfy the assumptions of multipleregression or the removal of outliers,the proportion of variance in thedependent variable explained by theindependent variables (+) 'as -2.3.

The relationship is statisticallysignificant, though 'e 'ould not stop ifit 'ere not significant because the lackof significance may be a conse!uence ofviolation of assumptions or the inclusionof outliers.

The + of 4.-23 is the benchmarkthat 'e 'ill use to evaluate theutility of transformations and theelimination of outliers.


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Slide

6

Descriptive Statistics

1.78 1.281 136

45.80 14.534 136

1.60 .491 136

1.65 1.220 136

SPOUSES HIGHEST

DEGREE

AGE OF RESPONDENT

RESPONDENTS SEX

RS HIGHEST DEGREE

Mean S!. De"#a#$n N

Sample si4e ; e$idence and ans#er

ierarchical multiple regression re!uires that theminimum ratio of valid cases to independentvariables be at least 5 to 3. The ratio of validcases (367) to number of independent variables(6) 'as 85.6 to 3, 'hich 'as e!ual to or greater

than the minimum ratio. The re!uirement for aminimum ratio of cases to independent variables'as satisfied.

*n addition, the ratio of 85.6 to 3 satisfied thepreferred ratio of 35 cases per independentvariable.

The ans'er to the !uestion is true.


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Slide

7

Assumption o! normality !or the dependent$aria"le *uestion

aving satisfied the level of measurementand sample sie re!uirements, 'e turn ourattention to conformity 'ith three of theassumptions of multiple regression9

normality, linearity, and homoscedasticity.

:irst, 'e 'ill evaluate the assumption ofnormality for the dependent variable.


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Slide

8Run the script to test normality

First, move the variables to thelist boxes based on the role thatthe variable plays in the analysisand its level of measurement.

Third, mark the checkboxesfor the transformations that'e 'ant to test in evaluating

the assumption.

Second, click on the Nor&ality optionbutton to re!uest that #/## producethe output needed to evaluate theassumption of normality.

Fourth, click onthe ;< button toproduce the output.


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Slide

9

Descriptives

1.78 .110

1.56

2.00

1.75

1.00

1.640

1.281

0

4

4

2.00

.573 .208

%1.051 .413

Mean

&$'e( )$*n!

U++e( )$*n!

95, -$n#!en/e

Ine("a $( Mean

5, T(#e! Mean

Me!#an

a(#an/e

S!. De"#a#$n

M#n#*

Ma#*

Rane

Ine(*a(#e Rane

Se'ne

*($#

SPOUSES

HIGHEST DEGREE

Sa# #/ S!. E(($(

-ormality o! the dependent $aria"lespouse


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Slide

2!

-ormality o! the trans!ormed dependent $aria"lespouse


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Slide

2-ormality o! the control $aria"le ae

Fext, 'e 'ill evaluate theassumption of normality forthe control variable, age.


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Slide

22

Descriptives

45.99 1.023

43.98

48.00

45.31

43.50282.465

16.807

19

89

70

24.00

.595 .148

%.351 .295

Mean

&$'e( )$*n!

U++e( )$*n!

95, -$n#!en/e

Ine("a $( Mean

5, T(#e! Mean

Me!#ana(#an/e

S!. De"#a#$n

M#n#*

Ma#*

Rane

Ine(*a(#e Rane

Se'ne

*($#

AGE OF RESPONDENT

Sa##/ S!. E(($(

-ormality o! the control $aria"le ae

The independent variable "age" %age&satisfied the criteria for a normal distribution.The ske'ness of the distribution (4.5E5) 'asbet'een >3.4 and ?3.4 and the kurtosis ofthe distribution (>4.653) 'as bet'een >3.4and ?3.4.


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Slide

23

-ormality o! the predictor $aria"lehihest academic deree

Fext, 'e 'ill evaluate theassumption of normality forthe predictor variable,highest academic degree.


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Slide

24

Descriptives

1.41 .071

1.27

1.55

1.35

1.001.341

1.158

0

4

4

1.00

.948 .149

%.051 .297

Mean

&$'e( )$*n!

U++e( )$*n!

95, -$n#!en/e

Ine("a $( Mean

5, T(#e! Mean

Me!#ana(#an/e

S!. De"#a#$n

M#n#*

Ma#*

Rane

Ine(*a(#e Rane

Se'ne

*($#

RS HIGHEST DEGREE

Sa##/ S!. E(($(

-ormality o! the predictor $aria"lerespondent


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Slide

25

Assumption o! linearity !or spouse


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26Run the script to test linearity

First, click on the Linearity option button to re!uestthat #/## produce theoutput needed to evaluatethe assumption of linearity.

Third, click on the+, button to

produce the output.

Ghen the linearity option isselected, a default set oftransformations to test is marked.

Second , since 'e have decided to

use the log transformation of thedependent variable, 'e mark thecheck box for the @ogarithmictransformation and clear the checkbox for the Hntransformed versionof the dependent variable.


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Slide

27

inearity test spouse


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28

inearity test spouse


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29Assumption o! homoeneity o! $ariance *uestion

#ex is the only dichotomous

independent variable in the analysis.Ge 'ill test if for homogeneity ofvariance using the logarithmictransformation of the dependentvariable 'hich 'e have alreadydecided to use.


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Slide

3!

Run the script to testhomoeneity o! $ariance

First, click on the-o&ogeneity o' !ariance option button to re!uestthat #/## produce theoutput needed to evaluatethe assumption of linearity.

Third, click on the+, button to

produce the output.

Ghen the homogeneity of varianceoption is selected, a default set oftransformations to test is marked.

Second , since 'e have decided touse the log transformation of thedependent variable, 'e mark thecheck box for the @ogarithmictransformation and clear the checkbox for the Hntransformed versionof the dependent variable.


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Slide

3

Assumption o! homoeneity o! $ariance ; e$idence andans#er

Kased on the @evene Test, thevariance in "log of spouse$s highestacademic degree%@A#/BCAD@A34(3?#/BCA)&" 'ashomogeneous for the categories of"sex" %sex&. The probabilityassociated 'ith the @evene statistic(4.72=) 'as pD4.84E, greater thanthe level of significance for testingassumptions (4.43). The nullhypothesis that the group variances'ere e!ual 'as not reLected.

The homogeneity of varianceassumption 'as satisfied. Theans'er to the !uestion is true.


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32Includin the trans!ormed $aria"le in the data set 1

*n the evaluation for normality, 'e resolved a problem 'ithnormality for spouses highest academic degree 'ith alogarithmic transformation. Ge need to add this transformedvariable to the data set, so that 'e can incorporate it in ourdetection of outliers.

Ge can use the script to compute transformed variables and addthem to the data set.

Ge select an assumption to test (Formality is the easiest), markthe check box for the transformation 'e 'ant to retain, andclear the check box "Belete variables created in this analysis."

NOTE: this will leave the transformedvariable in the data set. To remove it,you can delete the column or close the

data set without saving.


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Second, click on theNor&ality option button tore!uest that #/## do the testfor normality, including thetransformation 'e 'ill mark.

First, move the variable#/BCA to the list box forthe dependent variable.

Fifth, click on

the +, button.

Third, mark the transformation'e 'ant to retain (@ogarithmic)and clear the checkboxes forthe other transformations.

Fourth, clear the checkbox for the option"Belete variablescreated in this analysis".


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Slide


*f 'e scroll to the rightmostcolumn in the data editor, 'esee than the log of #/BCA inincluded in the data set.


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35

Includin the trans!ormed $aria"le in the list o!$aria"les in the script 1

*f 'e scroll to the bottom ofthe list of variables, 'e seethat the log of #/BCA is notincluded in the list of availablevariables.

To tell the script to add thelog of #/BCA to the list ofvariables in the script, clickon the Reset button. This'ill start the script overagain, 'ith a ne' list ofvariables from the data set.


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Slide

36

Includin the trans!ormed $aria"le in the list o!$aria"les in the script 6

*f 'e scroll to the bottom ofthe list of variables no', 'esee that the log of #/BCA isincluded in the list of availablevariables.


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37Detection o! outliers *uestion

*n multiple regression, an outlier in the solutioncan be defined as a case that has a large residualbecause the e!uation did a poor Lob of predictingits value.

Ge 'ill run the regression again incorporating anytransformations 'e have decided to test, and have#/## compute the standardied residual for eachcase. 1ases 'ith a standardied residual largerthan ?N> 6.4 'ill be treated as outliers.


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Slide

38he re$ised reression usin trans!ormations

To run the regression to

detect outliers, select theLinear Regression commandfrom the menu that dropsdo'n 'hen you click on theDialog Recall button.


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Slide

39

he re$ised reressionsu"stitutin trans!ormed $aria"les

+emove the variable #/BCAfrom the list of independentvariables. *nclude the log of

the variable, @A#/BCA.

1lick on the Statistics0button to select statistics'e 'ill need for the

analysis.


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Slide

4!he re$ised reression selectin statistics

Second, mark the checkboxes for ModelFit Descripti!es, and R s"#ared c$ange.

The R s"#ared c$ange statistic 'ill tellus 'hether or not the variables addedafter the controls have a relationship tothe dependent variable.

Sixth, click onthe %ontin#e button to closethe dialog box.

First, mark thecheckboxes forEsti&ates on the Regression%oe''icients panel.

Third, mark theD#rin*atson statistic on theResid#als panel.

Fifth, mark the%ollinearity diagnostics to get tolerance valuesfor testingmulticollinearity.

Fourth, mark thecheckbox for the%ase.ise diagnostics,'hich 'ill be used to

identify outliers.


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Slide

4he re$ised reression sa$in standardi4ed residuals

Mark the checkbox for

Standardized Resid#als sothat #/## saves a ne'variable in the data editor.Ge 'ill use this variable toomit outliers in the revisedregression model.

1lick on the%ontin#e button to closethe dialog box.


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Slide

42he re$ised reression o"tainin output

1lick on the +, button to obtainthe output for therevised model.


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Slide

43.utliers in the analysis

*f cases have a standardied residual larger than ?N> 6.4,#/## creates a table titled %ase.ise Diagnostics, in 'hich itlists the cases and values that results in their being an outlier.

*f there are no outliers, #/## does not print the %ase.iseDiagnostics table. There 'as no table for this problem. Theans'er to the !uestion is true.

Ge can verify that all standardied residuals'ere less than ?N> 6.4 by looking theminimum and maximum standardiedresiduals in the table of +esidual #tatistics.Koth the minimum and maximum fell in theacceptable range.

#ince there 'ere no outliers,'e can use the regression Lustcompleted to make our decision

about 'hich model to interpret.


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44Selectin the model to interpret *uestion

#ince there 'ere no outliers, 'e canuse the regression Lust completed to

make our decision about 'hichmodel to interpret.

*f the + for the revised model ishigher by - or more, 'e 'ill baseout interpretation on the revisedmodelJ other'ise, 'e 'ill interpretthe baseline model.


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Slide

45

Selectin the model to interpret ; e$idence andans#er

/rior to any transformations of variables tosatisfy the assumptions of multiple regressionand the removal of outliers, the proportion ofvariance in the dependent variable explained bythe independent variables (+) 'as -2.3.fter substituting transformed variables, theproportion of variance in the dependent variableexplained by the independent variables (+)'as -=.3.

#ince the revised regression model did notexplain at least t'o percent more variance thanexplained by the baseline regression analysis,the baseline regression model 'ith all cases andthe original form of all variables should be usedfor the interpretation.

The transformations used to satisfy theassumptions 'ill not be used, so cautionsshould be added for the assumptions violated.

:alse is the correct ans'er to the !uestion.


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Slide

46Rerunnin the "aseline reression 1

aving decided to use the baselinemodel for the interpretation of thisanalysis, the #/## regressionoutput 'as re>created.

To run the baseline regressionagain, select the LinearRegression command fromthe menu that drops do'n'hen you click on the DialogRecall button.


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Slide


+emove the transformedvariable lgspdeg from the

dependent variable textboxand add the variable spdeg.

1lick on the Sa!e button to remove

the re!uest tosave standardiedresiduals to thedata editor.


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48

Re$ised reression usin trans!ormationsand omittin outliers 3

1lear the checkbox for

Standardized Resid#als so that #/## does notsave a ne' set of themin the data editor 'hen itruns the ne' regression.

1lick on the%ontin#e button to closethe dialog box.


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Slide


1lick on the +,

button tore!uest theregressionoutput.


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5!Assumption o! independence o! errors *uestion

Ge can no' check theassumption of independenceof errors for the analysis 'e'ill interpret.


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5

Model Summaryc

.014a .000 %.015 1.290 .000 .013 2 133 .987

.531 .281 .265 1.098 .281 51.670 1 132 .000 1.754

M$!e

1

2

R R S*a(e

A!:*e!

R S*a(e

S!. E(($( $

;e E#ae

R S*a(e

-;ane F -;ane !1 !2 S#. F -;ane

-;ane Sa##/

D*(#n%<

a$n

P(e!#/$(= >-$nan?@ RESPONDENTS SEX@ AGE OF RESPONDENTa.

P(e!#/$(= >-$nan?@ RESPONDENTS SEX@ AGE OF RESPONDENT@ RS HIGHEST DEGREE.

De+en!en a(#ae= SPOUSES HIGHEST DEGREE/.

Assumption o! independence o! errorse$idence and ans#er

aving selected a regression model forinterpretation, 'e can no' examine thefinal assumptions of independence oferrors.

The Burbin>Gatson statistic is used to

test for the presence of serial correlationamong the residuals, i.e., theassumption of independence of errors,'hich re!uires that the residuals orerrors in prediction do not follo' apattern from case to case.

The value of the Burbin>Gatson statisticranges from 4 to 8. s a general rule ofthumb, the residuals are not correlatedif the Burbin>Gatson statistic isapproximately -, and an acceptablerange is 3.54 > -.54.

The Burbin>Gatsonstatistic for this problem is3.=58 'hich falls 'ithinthe acceptable range.

*f the Burbin>Gatson

statistic 'as not in theacceptable range, 'e'ould add a caution to thefindings for a violation ofregression assumptions.The ans'er to the!uestion is true.


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52Multicollinearity *uestion

The final condition that can havean impact on our interpretationis multicollinearity.


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53Multicollinearity ; e$idence and ans#er

The tolerance values for all of the independent variablesare larger than 4.349 "highest academic degree" %degree&

(.EE4), "age" %age& (.E58) and "sex" %sex& (.E8=).

Multicollinearity is not a problem in this regression analysis.

True is the correct ans'er to the !uestion.


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54

.$erall relationship "et#een dependent $aria"leand independent $aria"les *uestion

The first finding 'e 'ant toconfirm concerns therelationship bet'een the

dependent variable and the setof predictors after including thecontrol variables in the analysis.


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55

.$erall relationship "et#een dependent $aria"leand independent $aria"les ; e$idence and ans#er

ierarchical multiple regression 'as performed to test thehypothesis that there 'as a relationship bet'een the dependentvariable "spouse$s highest academic degree" %spdeg& and thepredictor independent variables "highest academic degree"%degree& after controlling for the effect of the control independentvariables "age" %age& and "sex" %sex&. *n hierarchical regression,the interpretation for overall relationship focuses on the change in+. *f change in + is statistically significant, the overallrelationship for all independent variables 'ill be significant as 'ell.


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56


Kased on model - in the Model #ummary table 'here the predictors'ere added , (:(3, 36-) D 53.7=4, pI4.443), the predictorvariable, highest academic degree, did contribute to the overallrelationship 'ith the dependent variable, spouse$s highest academicdegree. #ince the probability of the : statistic (pI4.443) 'as less

than or e!ual to the level of significance (4.45), the null hypothesisthat change in + 'as e!ual to 4 'as reLected. The researchhypothesis that highest academic degree reduced the error inpredicting spouse$s highest academic degree 'as supported.


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57


The increase in + by including the predictor variables("highest academic degree") in the analysis 'as 4.-23,not 4.-83.

Hsing a proportional reduction in error interpretation for+, information provided by the predictor variables

reduced our error in predicting "spouse$s highestacademic degree" %spdeg& by -2.3, not -8.3.

The ans'er to the!uestion is false becausethe problem stated anincorrect statistical value.


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58

Relationship o! the predictor $aria"le and thedependent $aria"le *uestion

*n these hierarchical regressionproblems, 'e 'ill focus theinterpretation of individual relationships

on the predictor variables and ignore thecontribution of the control variables.


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59

Coefficientsa

1.781 .577 3.085 .002

.001 .008 .009 .100 .920 .956 1.046

%.023 .231 %.009 %.100 .920 .956 1.046

.525 .521 1.007 .316

.003 .007 .037 .495 .622 .954 1.049

.114 .198 .044 .575 .566 .947 1.056

.559 .078 .533 7.188 .000 .990 1.010

>-$nan?

AGE OF RESPONDENT

RESPONDENTS SEX

>-$nan?

AGE OF RESPONDENT

RESPONDENTS SEX

RS HIGHEST DEGREE

M$!e

1

2

) S!. E(($(

Unan!a(!#e!

-$e#/#en

)ea

San!a(!#e!

-$e#/#en

S#. T$e(an/e IF

-$#nea(#B Sa##/

De+en!en a(#ae= SPOUSES HIGHEST DEGREEa.

Relationship o! the predictor $aria"le and thedependent $aria"le ; e$idence and ans#er

Kased on the statistical test of the b coefficient

(t D =.322, pI4.443) for the independentvariable "highest academic degree" %degree&,the null hypothesis that the slope or bcoefficient 'as e!ual to 4 (ero) 'as reLected.The research hypothesis that there 'as arelationship bet'een "highest academicdegree" and "spouse$s highest academicdegree" 'as supported.


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6!

Coefficientsa

1.781 .577 3.085 .002

.001 .008 .009 .100 .920 .956 1.046

%.023 .231 %.009 %.100 .920 .956 1.046

.525 .521 1.007 .316

.003 .007 .037 .495 .622 .954 1.049

.114 .198 .044 .575 .566 .947 1.056

.559 .078 .533 7.188 .000 .990 1.010

>-$nan?

AGE OF RESPONDENT

RESPONDENTS SEX

>-$nan?

AGE OF RESPONDENT

RESPONDENTS SEX

RS HIGHEST DEGREE

M$!e

1

2

) S!. E(($(

Unan!a(!#e!

-$e#/#en

)ea

San!a(!#e!

-$e#/#en

S#. T$e(an/e IF

-$#nea(#B Sa##/

De+en!en a(#ae= SPOUSES HIGHEST DEGREEa.

Relationship o! the predictor $aria"le and thedependent $aria"le ; e$idence and ans#er

The b coefficient for the relationshipbet'een the dependent variable "spouse$shighest academic degree" %spdeg& and theindependent variable "highest academicdegree" %degree&. 'as .55E, 'hich impliesa direct relationship because the sign ofthe coefficient is positive. igher numericvalues for the independent variable"highest academic degree" %degree& areassociated 'ith higher numeric values forthe dependent variable "spouse$s highestacademic degree" %spdeg&.

The statement in the problem that "surveyrespondents 'ho had higher academicdegrees had spouses 'ith higher academic

degrees" is correct. The ans'er to the!uestion is true 'ith caution. 1aution ininterpreting the relationship should beexercised because of an ordinal variabletreated as metricJ and violation of theassumption of normality.


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Slide

6/alidation analysis *uestion

The problem states therandom number seed to usein the validation analysis.

/ lid i l i


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Slide

62

/alidation analysisset the random num"er seed

To set the random numberseed, select the Rando&

N#&er Seed… commandfrom the /rans'or& menu.

Oalidate the results ofyour regression analysisby conducting a =5N-5cross>validation, usingEE2=E8 as the randomnumber seed.


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Slide

63Set the random num"er seed

First, click on theSet seed to optionbutton to activatethe text box.

Second, type in therandom seed stated inthe problem.

Third, click on the ;<button to complete thedialog box.

Fote that #/## does notprovide you 'ith anyfeedback about the change.

/ lid ti l i


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64

/alidation analysiscompute the split $aria"le

To enter the formula for thevariable that 'ill split the

sample in t'o parts, clickon the %o&p#te… command.

Slid


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Slide

65he !ormula !or the split $aria"le

First, type the name for thene' variable, split, into the/arget 0ariale text box.

Second, the formula for thevalue of split is sho'n in thetext box.

The uniform(3) functiongenerates a random decimalnumber bet'een 4 and 3.The random number iscompared to the value 4.=5.

*f the random number is lessthan or e!ual to 4.=5, thevalue of the formula 'ill be 3,

the #/## numeric e!uivalentto true. *f the randomnumber is larger than 4.=5,the formula 'ill return a 4,the #/## numeric e!uivalentto false.

Third, click on the;< button tocomplete the dialogbox.

Slid


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Slide

66he split $aria"le in the data editor

*n the data editor, thesplit variable sho's arandom pattern of erosand ones.

To select the cases for thetraining sample, 'e select

the cases 'here split D 3.

Slid


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67Repeat the reression !or the $alidation

To run the regression for thevalidation training sample,select the Linear Regression command from the menu thatdrops do'n 'hen you click onthe Dialog Recall button.

Slid


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68=sin >split> as the selection $aria"le

First, scrolldo'n the list ofvariables andhighlight thevariable split .

Second, click on theright arro' button tomove the split variableto the #electionOariable text box.

Slid


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69Settin the $alue o! split to select cases

Ghen the variable named

split is moved to the#election Oariable textbox, #/## adds "DP" afterthe name to prompt up toenter a specific value forsplit.

1lick on theR#le0 buttonto enter avalue for split .

Slid


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7!Completin the $alue selection

First, type the valuefor the trainingsample, 3, into the0al#e text box.

Second, click on the

%ontin#e button tocomplete the value entry.

Slid


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7Re*uestin output !or the $alidation analysis

Ghen the value entrydialog box is closed, #/##

adds the value 'e enteredafter the e!ual sign. Thisspecification no' tells#/## to include in theanalysis only those casesthat have a value of 3 forthe split variable.

1lick on the +, button to

re!uest theoutput.

Slid


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Slide

72/alidation analysis 1

The validation analysis re!uires that theregression model for the =5 trainingsample replicate the pattern of statisticalsignificance found for the full data set.

*n the analysis of the =5 training sample, therelationship bet'een the set of independentvariables and the dependent variable 'asstatistically significant, :(6, 346) D 33.57E,pI4.443, as 'as the overall relationship in theanalysis of the full data set, :(6, 36-) D 3=.-65,pI4.443

Slide


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Slide


The validation of a hierarchical regressionmodel also re!uires that the change in +demonstrate statistical significance in theanalysis of the =5 training sample.

The + change of 4.-8Esatisfied this re!uirement(: change(3, 346) D68.63E, pI4.443).

Slide


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The pattern of significance for the individualrelationships bet'een the dependent variable andthe predictor variable 'as the same for theanalysis using the full data set and the =5training sample.

The relationship bet'een highest academic degree andspouse$s highest academic degree 'as statistically significantin both the analysis using the full data set (tD=.322,pI4.443) and the analysis using the =5 training sample(tD5.828, pI4.443). The pattern of statistical significance ofthe independent variables for the analysis using the =5training sample matched the pattern identified in theanalysis of the full data set.

Slide


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The total proportion of variance explained in themodel using the training sample 'as -5.-(.54-), compared to 84.7 (.76=) for thevalidation sample. The value of + for thevalidation sample 'as actually larger than the

value of + for the training sample, implying abetter fit than obtained for the training sample.

This supports a conclusion that the regressionmodel 'ould be effective in predicting scores forcases other than those included in the sample.

The validation analysissupported thegeneraliability of thefindings of the analysis tothe populationrepresented by the samplein the data set.

The ans'er to the!uestion is true.

SW388R7

Data Analysis & Steps in complete hierarchical


76/90

Data Analysis &

Computers II

Slide 7?

Steps in complete hierarchicalreression analysis

he !ollo#in !lo# charts depict the process !or sol$in the complete

reression pro"lem and determinin the ans#er to each o! the

*uestions encountered in the complete analysis%

e)t in italics ,e%% True, False, True with caution, Incorrectapplication of a statistic0 represent the ans#ers to each speci!ic

*uestion%

Many o! the steps in hierarchical reression analysis are identical to

the steps in standard reression analysis% Steps that are di!!erent are

identi!ied #ith a maenta "ac'round #ith the speci!ics o! the

di!!erence underlined%

Slide Complete Hierarchical multiple reression analysis


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Slide

77

Complete Hierarchical multiple reression analysisle$el o! measurement

Incorrect

application o'a statistic

Fo*s the dependentvariable metric and the

independent variablesmetric or dichotomousP

Qes

Ruestion9 do variables included in the analysis satisfy the levelof measurement re!uirementsP

;rdinal variables includedin the relationshipP

Fo

Qes

/r#e

/r#e .it$ ca#tion

Cxamine all independentvariables S controls as'ell as predictors



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Slide

78

Complete Hierarchical multiple reression analysissample si4e

1ompute the baselineregression in #/##

Qes

+atio of cases toindependent variables atleast 5 to 3P

Qes

Fo Inappropriateapplication o'a statistic

Ruestion9 Fumber of variables and cases satisfy sample siere!uirementsP

Qes

+atio of cases toindependent variables atpreferred sample sie of atleast 35 to 3P

Fo

/r#e

/r#e .it$ ca#tion

*nclude both controls andpredictors, in the count ofindependent variables



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Slide

79

Ruestion9 each metric variable satisfies the assumption ofnormalityP

Complete Hierarchical multiple reression analysisassumption o! normality

The variable satisfiescriteria for a normaldistributionP

Qes

Hse transformationin revised model,no caution needed

@og, s!uare root, orinversetransformationsatisfies normalityP

*f more than onetransformationsatisfies normality,

use one 'ithsmallest ske'

/r#e

False

Qes

Fo

Fo

Hse untransformedvariable in analysis,add caution tointerpretation forviolation of normality

Test the dependentvariable and bothcontrols and predictorindependent variables



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Slide

8!

Ruestion9 relationship bet'een dependent variable and metric

independent variable satisfies assumption of linearityP

Complete Hierarchical multiple reression analysisassumption o! linearity

/robability of /earsoncorrelation (r) IDlevel of significanceP

/robability of correlation(r) for relationship 'ithany transformation of *OID level of significanceP

Fo

*ea1relations$ip2No ca#tion

needed

Fo

Hse transformationin revised model

Qes

*f independent variable'as transformed tosatisfy normality, skipcheck for linearity. *f more than one

transformationsatisfieslinearity, use one'ith largest r

*f dependent variable 'astransformed for normality, usetransformed dependentvariable in the test for linearity.

Qes

/r#e

Test both

control andpredictorindependent variables



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Slide

8

Complete Hierarchical multiple reression analysisassumption o! homoeneity o! $ariance

/robability of @evenestatistic ID level ofsignificanceP

Qes

Fo

*f dependent variable 'astransformed for normality,substitute transformeddependent variable in the testfor the assumption ofhomogeneity of variance

Ruestion9 variance in dependent variable is uniform across thecategories of a dichotomous independent variableP

/r#e

Bo not test transformations ofdependent variable, add caution tointerpretation for violation ofhomoscedasticity

False

Test bothcontrol andpredictorindependent variables

Slide Complete Hierarchical multiple reression


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Slide

82

Complete Hierarchical multiple reressionanalysis detectin outliers

Fo

*s the standardied residualfor any case greater than?N>6.44P

Ruestion9 fter incorporating any transformations, no outliers

'ere detected in the regression analysis%

*f any variables 'ere transformedfor normality or linearity, substitutetransformed variables in theregression for the detection ofoutliers.

QesFalse

/r#e

+emove outliers and runrevised regression again.



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Slide

83

Complete Hierarchical multiple reression analysispic'in reression model !or interpretation

+ for revised regression

greater than + forbaseline regression by -or moreP

/ick baseline regression 'ithuntransformed variables and allcases for interpretation

/ick revised regression 'ithtransformations and omittingoutliers for interpretation

Qes Fo

Ruestion9 interpretation based on model that includestransformation of variables and removes outliersP

False/r#e



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Slide

84

Complete Hierarchical multiple reression analysisassumption o! independence o! errors

+esiduals areindependent,

Burbin>Gatson bet'een3.5 and -.5P

Fo

Qes

Ruestion9 serial correlation o! errors is not a pro"lem in this reressionanalysisP

N+/E3 ca#tion'or !iolation o'ass#&ption o'independence o'errors

False

/r#e



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Slide

85

Complete Hierarchical multiple reression analysismulticollinearity

Tolerance for all *Osgreater than 4.34,indicating no

multicollinearityP

Fo

Qes

False

Ruestion9 Multicollinearity is not a pro"lem in this reression analysisP

/r#e

N+/E3 $alt t$eanalysis #ntil prole& isdiagnosed



86/90

Slide

86

Complete Hierarchical multiple reression analysiso$erall relationship

Qes

/robability of : test of +change less thanNe!ual tolevel of significanceP

FoFalse

Qes

#trength of + change forpredictor variablesinterpreted correctlyP

FoFalse

Fo

Qes

/r#e

/r#e .it$ ca#tion

#mall sample, ordinalvariables, or violation ofassumption in therelationshipP

Ruestion9 :inding about overall relationship bet'een

dependent variable and independent variables.



87/90

Slide

87

Co plete e a c cal ult ple e ess o a alys sindi$idual relationships

Qes

/robability of t testbet'een predictors and BOID level of significanceP

Qes

Fo

Qes

Birection of relationshipbet'een predictors and BOinterpreted correctlyP

Qes

FoFalse

False

Ruestion9 :inding about individual relationship bet'een

independent variable and dependent variable.

Fo

Qes

/r#e

/r#e .it$ ca#tion




88/90

Slide

88

p p yindi$idual relationships

Boes the stated variablehave the largest beta

coefficient (ignoring sign)among predictorsP

FoFalse

Ruestion9 :inding about independent variable 'ith largest

impact on dependent variable.


Fo

Qes

/r#e

/r#e .it$ ca#tion

Qes



89/90

S de

89

p p y$alidation analysis 1

Qes

/robability of F;O testfor training sample IDlevel of significanceP

Qes

FoFalse

/robability of : for +change for training sampleID level of significanceP

FoFalse

Qes

#et the random seed and randomlysplit the sample into =5 trainingsample and -5 validationsample.

Ruestion9 he $alidation analysis supports the enerali4a"ility o! the!indins@



90/90

9!

p p y$alidation analysis 6

Qes

Qes

#hrinkage in + (+ fortraining sample > + forvalidation sample) I -P

FoFalse

/r#e

/attern of significance forpredictor variables intraining sample matchespattern for full data setP

FoFalse

hierarchical multiple regression]

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