CFA 2018 Quantitative Analysis Question Bank 03 Multiple Regression and Issues in Regression Analysis 2

Test ID: 7440356

Multiple Regression and Issues in Regression Analysis 2

Question #1 of 106

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Consider the following analysis of variance (ANOVA) table:

Source Sum ofsquares Degreesoffreedom Meansquare

Regression 20 1 20

Error 80 40 2

Total 100 41

The F-statistic for the test of the fit of the model is closest to:

0.10.

10.00.

0.25.

Explanation

The F-statistic isequaltotheratioofthemeansquaredregressiontothemeansquarederror.

F = MSR/MSE = 20 / 2 = 10.

Ananalyst is interestedinforecasting the rate of employment growth andinstabilityfor254metropolitanareas around the

UnitedStates.The analyst's mainpurpose for these forecasts is to estimate the demandfor commercial real estate in each metro area.The independent variables inthe analysis representthe percentage of employmentin each industrygroup.

RegressionofEmployment GrowthRatesandEmploymentInstability

onIndustryMixVariablesfor254U.S.MetroAreas

Model1 Model2

Dependent Variable EmploymentGrowth RateRelative EmploymentInstability

Independent Variables

Coefficient

Estimate t-value

Coefficient

Estimate t-value

Intercept -2.3913 -0.713 3.4626 0.623 % Construction Employment 0.2219 4.491 0.1715 2.096

% Manufacturing Employment 0.0136 0.393 0.0037 0.064

Question #2 of 106

QuestionID:485606 Wholesale Trade Employment," and "% Retail Trade" only.

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Question #7 of 106

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0.0111 to 0.3319. 0.0897to0.2533. -0.0740to0.4170.

Explanation

With a sample size of254, and254 − 6 − 1 = 247degrees offreedom, the critical value fora two-tail 95% t-statistic is very

close to the two-tail 95% statistic of1.96. Using this critical value, the formulafor the 95% confidence interval for the jth coefficientestimateis:

95% confidenceinterval = .Butfirst weneedtofigureoutthe coefficientstandarderror:

Hence, the confidenceintervalis0.1715 ± 1.96(0.08182).

With 95% probability, the coefficient willrangefrom0.0111to0.3319, 95% CI = {0.0111 < b1 < 0.3319}. (StudySession3, LOS 9.f)

Onepossibleproblemthat could jeopardizethe validityoftheemploymentgrowth ratemodelismulticollinearity. Which ofthe

following would mostlikelysuggesttheexistenceofmulticollinearity? The Durbin-Watson statistic differs sufficiently from 2.

The F-statistic suggests that the overall regressionis significant, however the regression coefficients are not individually significant.

The varianceoftheobservations hasincreasedovertime.

Explanation

Onesymptomofmulticollinearityisthattheregression coefficientsmaynot beindividuallystatisticallysignificanteven when according to the F-statistic the overall regressionis significant.The problem ofmulticollinearityinvolves the existence of high correlation between two ormore independent variables.Clearly, as service employment rises, construction employment must

risetofacilitatethegrowth inthesesectors.Alternatively, asmanufacturingemploymentrises, theservicesectormustgrow to servethe broadermanufacturingsector.

The varianceofobservationssuggeststhepossibleexistenceof heteroskedasticity.

IftheDurbin-Watsonstatistic differssufficientlyfrom2, thisisasignthattheregressionerrors havesignificantserial correlation.

(StudySession3, LOS10.l)

MarySteen estimated that if she purchased shares of companies who announcedrestructuringplans at the announcement

and heldthemforfivedays, she wouldearnreturnsinexcessofthoseexpectedfromthemarketmodelof0.9%.These

returnsarestatisticallysignificantlydifferentfrom zero.Themodel wasestimated withouttransactions costs, andinreality

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statistical significance,but not economic significance. statistical and economic significance.

amarketinefficiency.

Explanation

Theabnormalreturnsarenotsufficientto covertransactions costs, sothereisnoeconomic significancetothistrading strategy.This is not an example ofmarket inefficiency because excess returns are not available after covering transactions costs.

Seventy-twomonthlystock returnsforafund between1997and2002areregressedagainstthemarketreturn, measured by

the Wilshire 5000, and two dummy variables.The fund changedmanagers on January2, 2000.Dummy variable one is equal to 1if the returnis fromamonth between2000and2002.Dummy variable number two is equal to 1if the returnis from the second halfoftheyear.Thereare36observations whendummy variableoneequals0, halfof which are whendummy

variabletwoalsoequals zero.Thefollowingaretheestimated coefficient valuesandstandarderrorsofthe coefficients.

C

oefficient

Value

S

tandard

error

Mar

k

e

t

1.4

3000

0

.

3

1

9

000

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00

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6

2

0

.

00067

5

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u

mm

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2

−

0

.

00

1

3

2

0

.

000733

Whatisthep-valueforatestofthe hypothesisthatthe betaofthefundisgreaterthan1?

Between 0.05 and 0.10. Lowerthan 0.01.

Between 0.01and 0.05.

Explanation

The betaismeasured bythe coefficientofthemarket variable.Thetestis whetherthe betaisgreaterthan1, not zero, sothe t-statistic isequalto (1.43 − 1) / 0.319 = 1.348, which isin betweenthet-values (with 72 − 3 − 1 = 68 degreesoffreedom)of 1.29 forap-valueof0.10and1.67forap-valueof0.05.

Autumn VoikuisattemptingtoforecastsalesforBrookfield Farms basedonamultipleregressionmodel. Voiku has constructedthefollowingmodel:

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Voikuusesmonthlydatafromtheprevious180monthsofsalesdataandfortheindependent variables.Themodelestimates (with coefficient standard errors inparentheses)are:

sales =10.2 + (4.6 × CPI) + (5.2 × IP) + (11.7 × GDP) (5.4) (3.5) (5.9) (6.8)

Thesumofsquarederrorsis140.3andthetotalsumofsquaresis368.7.

Voiku calculatestheunadjustedR, theadjustedR, andthestandarderrorofestimateto be0.592, 0.597, and0.910,

respectively.

Voikuis concernedthatoneormoreoftheassumptionsunderlyingmultipleregression has been violatedin heranalysis.Ina

conversation with DaveGrimbles, CFA, a colleague whois considered bymanyinthefirmto beaquantspecialist, Voikusays, "It is myunderstanding that there are five assumptions ofamultiple regressionmodel:"

Assumption1: Thereisalinearrelationship betweenthedependentandindependent variables.

Assumption2: The independent variables are not random, and there is zero correlation

betweenanytwooftheindependent variables.

Assumption3: Theresidualtermisnormallydistributed with anexpected valueof zero. Assumption4: Theresidualsareserially correlated.

Assumption5: The variance of the residuals is constant.

Grimblesagrees with Miller'sassessmentoftheassumptionsofmultipleregression.

Voiku tests andfails to reject each of the followingfournull hypotheses at the 99% confidence interval: Hypothesis 1: The coefficient onGDP is negative.

Hypothesis2: Theintercepttermisequalto-4.

Hypothesis3: A2.6% increaseintheCPI willresultinanincreaseinsalesofmorethan 12.0%.

Hypothesis 4: A1% increase inindustrial production will result ina1% decrease in sales.

Figure1:Partialtableofthe Student'st-distribution(One-tailedprobabilities)

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Question #15 of 106

QuestionID:461569

Partial

Results

fro

m

Regression

ARAR

on

S

ize

and

Extent

of

Indexing

Question #23 of 106

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Question #24 of 106

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independent variablesarenotrandomandnoexactlinearrelationshipexists betweenthetwoormoreindependent variables, errortermisnormallydistributed with anexpected valueof zeroand constant variance, andtheerrortermisserially

uncorrelated. (StudySession3, LOS10.f)

Considerthefollowingregressionequation: Sales= 20.5 + 1.5R&D + 2.5ADV -3.0COMP

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Which of the followingis NOTa correct interpretation of this regressioninformation?

If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million.

IfR&Dandadvertising expenditures are $1million each and there are 5 competitors,

expectedsalesare $9.5million.

One more competitor will mean $3million less in sales (holding everything else constant).

Explanation

Ifa company spends $1 millionmore onR&D (holding everything else constant), sales are expected to increase by $1.5

million.Always beawareoftheunitsofmeasureforthedifferent variables.

When constructingaregressionmodel to predict portfolio returns, ananalyst runs aregressionfor the past five yearperiod. After examining the results, she determines that anincrease ininterest rates two years ago hada significant impact on portfolioresultsforthetimeoftheincreaseuntilthepresent.Byperformingaregressionovertwoseparatetimeperiods, the

analyst would beattemptingtoprevent which typeofmisspecification?

Using a lagged dependent variable as an independent variable. Forecasting the past.

Incorrectlypoolingdata.

Explanation

Therelationship betweenreturnsandthedependent variables can changeovertime, soitis criticalthatthedata bepooled

correctly.Runningtheregressionformultiplesub-periods (inthis casetwo)ratherthanonetimeperiod canproducemore

accurate results.

Questions #27-32 of 106

RegressionofOperatingProfitonPopulation,OperatingHours,and

Question #31 of 106

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(LOS10.c)

The standarddeviation ofregressionresiduals is closest to:

15.47

0.42

239.42

Explanation

SSE = SST-RSS = 10,898 -6,349 = 4,549

MSE = SSE/(n-k-1) = 4,549/19 = 239.42

SEE = (MSE) = 15.47

t= beta- beta /S = 6.767-5 /2.56 = 0.69. Wefailtorejectthenull hypothesis.

(LOS10.i)

The operatingprofit model as specifiedis mostlikelya:

Time series regression Cross-sectional regression Autoregressivemodel

Explanation

Cross-sectionaldatainvolvemanyobservationsforthesametimeperiod.Time-seriesdatausesmanyobservationsfrom

different time periods for the same entity.

(LOS10.a)

DaveTurnerisasecurityanalyst whoisusingregressionanalysistodetermine how welltwofactorsexplainreturnsfor

commonstocks.Theindependent variablesarethenaturallogarithmofthenumberofanalystsfollowingthe companies, Ln(no.ofanalysts), andthenaturallogarithmofthemarket valueofthe companies, Ln(market value).Theregressionoutput generatedfroma statistical programis givenin the following tables. Each p-value corresponds to a two-tail test.

Turnerplanstousetheresultintheanalysisoftwoinvestments. WLK Corp. hastwelveanalystsfollowingitandamarket capitalization of $2.33 billion. NGRCorp. has two analysts followingit andamarket capitalization of $47million.

Table 1: Regression Output

Variable CoefficientStandardErroroftheCoefficient t-statistic p-value

Intercept 0.043 0.01159 3.71 < 0.001

Ln(No. ofAnalysts) −0.027 0.00466 −5.80 < 0.001 0.5

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Multicollinearityoccurs whenthereisa high correlationamongindependent variablesandmayexistifthereisasignificant F

-statistic forthefitoftheregressionmodel, butatleastoneinsignificantindependent variable when weexpectallofthemto be significant.In this case the coefficient onln(market value) wasnot significant at the1% level, but the F-statistic wassignificant. It wouldmakesense that thesizeof thefirm, i.e., themarket value, and thenumberofanalysts would bepositively correlated.

(StudySession3, LOS10.l)

Which of thefollowingis NOTamodel that hasaqualitativedependent variable?

Discriminant analysis. Logit.

Eventstudy.

Explanation

Aneventstudyistheestimationoftheabnormalreturns--generallyassociated with aninformationalevent-thattakeon quantitative values.

Which ofthefollowingstatementsregarding heteroskedasticityisleastaccurate?

Multicollinearity is a potential problem only in multiple regressions, not simple regressions.

Heteroskedasticityonlyoccursin cross-sectionalregressions.

Thepresenceof heteroskedastic errortermsresultsina varianceoftheresidualsthat

istoolarge.

Explanation

Ifthereareshiftingregimesinatime-series (e.g., changeinregulation, economic environment), itispossibleto have

heteroskedasticityina time-series.

JohnRains, CFA, isaprofessoroffinanceatalargeuniversitylocatedinthe Eastern UnitedStates. Heisactivelyinvolved

with hislocal chapteroftheSocietyof FinancialAnalysts.Recently, he wasaskedtoteach onesessionofaSociety-sponsored

CFAreview course, specifically teaching the classaddressing the topic ofquantitativeanalysis.Basedupon hisfamiliarity with theCFAexam, hedecides that thefirst part of thesessionshould beareview of the basic elementsofquantitativeanalysis,

such as hypothesistesting, regressionandmultipleregressionanalysis. He wouldliketodevotethesecond halfofthereview

sessiontothepracticalapplicationofthetopics he coveredinthefirst half.

Rainsdecidesto constructasampleregressionanalysis casestudyfor hisstudentsinordertodemonstratea"real-life"

applicationofthe concepts. He begins by compilingfinancialinformationonafictitious company calledBigRig, Inc.According

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Question #50 of 106

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0.20

5.00

Explanation

The F-statistic isequal to theratioof themeansquaredregression to themeansquarederror.

F = MSR / MSE = 20 / 4 = 5.

Ananalystis buildingaregressionmodel which returnsaqualitativedependant variable basedonaprobabilitydistribution.

Thisisleastlikelya:

discriminant model.

probit model.

logitmodel.

Explanation

Aprobitmodelisaqualitativedependant variable which is basedonanormaldistribution.Alogitmodelisaqualitative

dependant variable which is basedonthelogistic distribution.Adiscriminantmodelreturnsaqualitativedependant variable

basedonalinearrelationship that can beusedforrankingor classificationintodiscretestates.

WandaBrunner, CFA, istryingto calculatea 98% confidenceinterval (df = 40)foraregressionequation basedonthe

followinginformation:

C

oefficient

Standard

E

rror

In

t

er

c

ep

t

-10.60

%

1.357

DR

0.52

0.023

C

S

0.32

0.025

Which ofthefollowingare closesttothelowerandupper boundsfor variableCS?

0.274 to 0.367.

0.267to0.374.

0.260 to0.381.

Explanation

The critical t-valueis2.42at the 98% confidencelevel (two tailed test).Theestimatedslope coefficient is0.32and the

Question #56 of 106

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Explanation

The coefficient ofdeterminationis thestatistic used toidentifyexplanatorypower.This can be calculatedfrom theANOVA

tableas3.896/6.327 x 100 = 61.58%.

Theresidualstandarderrorof0.3indicates that thestandarddeviationof theresidualsis0.3million housingstarts. Without

knowledgeof thedatafor thedependent variableit isnot possible toassess whether thisisasmalloralargeerror.

The F statistic doesnot enableus to concludeon both independent variables.It onlyallowsus thereject the hypothesis that all

regression coefficientsare zeroandaccept the hypothesis that at least oneisn't.

(StudySession3, LOS10.g)

Theestimatedstandarddeviationof housingstarts (inmillions)isclosestto:

0.3

0.22

0.47

Explanation

Housingstartsis thedependent variable.

Varianceofdependent variable = SST/(n-1) = 6.327/29 = 0.22

Standarddeviation = (0.22) = 0.467

(StudySession3, LOS 9.j)

Which of thefollowingis theleast appropriatestatement inrelation toR-squareandadjustedR-square:

Adjusted R-square is a value between 0 and 1 and can be interpreted as a percentage

AdjustedR-squaredecreases when theaddedindependent variableaddslittle value

totheregressionmodel

R-squaretypicallyincreases whennew independent variablesareaddedtothe

regressionregardlessof theirexplanatorypower

Explanation

AdjustedR-square can benegativeforalargenumberofindependent variables that havenoexplanatorypower.Theother

twostatementsare correct.

(StudySession3, LOS10.h)

ᅞ A) regression. However, the analyst uses returns of portfolios of stocks instead of individual stocks in the regression. Which of the following

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Question #61 of 106

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Question #62 of 106

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willincreasethepowerofthetest bygivingtheteststatistic moredegreesoffreedom.

Explanation

Theuseofportfoliosreducesthestandarddeviationofthereturns, which reducesthestandarddeviationoftheresiduals.

DavidBlack wants to test whether theestimated betainamarket modelisequal toone. He collectedasampleof60monthly

returnsonastock andestimatedtheregressionofthestock'sreturnsagainstthoseofthemarket.Theestimated beta was

1.1, andthestandarderrorofthe coefficientisequalto0.4. WhatshouldBlack concluderegardingthe betaif heusesa5%

levelofsignificance? Thenull hypothesis that betais:

equal to one cannot be rejected.

equal tooneisrejected.

notequaltoone cannot berejected.

Explanation

The calculatedt-statistic ist = (1.1 − 1.0) / 0.4 = 0.25.The criticalt-valuefor (60 − 2) = 58 degreesoffreedomisapproximately

2.0.Therefore, thenull hypothesis that betaisequal toone cannot berejected.

Supposetheanalyst wantstoaddadummy variablefor whetheraperson hasanundergraduate collegedegreeanda

graduatedegree. WhatistheCORRECTrepresentationifaperson has both degrees?

UndergraduateDegree

Dummy Variable

GraduateDegree

Dummy Variable

1 1

0 1

0 0

Explanation

Assigninga zeroto both categoriesisappropriateforsomeone with neitherdegree.Assigningonetotheundergraduate

categoryand zero to thegraduate categoryisappropriateforsomeone with onlyanundergraduatedegree.Assigning zero to

theundergraduate categoryandone to thegraduate categoryisappropriateforsomeone with onlyagraduatedegree.

Assigningaoneto both categoriesis correctsinceitreflectsthepossessionof both degrees.

VikasRathod, anenrolled candidatefor theCFA LevelIIexamination, hasdecided toperforma calendar test toexamine

Question #63 of 106

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Question #64 of 106

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Question #65 of 106

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daysofthe week.Asaproxyfor blue-chips, he hasdecidedtousetheS&P 500index.Theanalysis willinvolvetheuseof

dummy variablesandis basedonthepast780tradingdays. Hereareselectedfindingsof hisstudy:

RSS 0.0039

SSE 0.9534

SST 0.9573

R-squared 0.004

SEE 0.035

Jessica Jones, CFA, afriendofRathod, overhearsthat heisinterestedinregressionanalysisand warns himthat whenever

heteroskedasticityispresentinmultipleregressionthis couldunderminetheregressionresults.Shementionsthatoneeasy

way tospot conditional heteroskedasticityis through ascatterplot, but sheadds that thereisamoreformal test.

Unfortunately, she can't quiterememberitsname. Jessica believes that heteroskedasticity can berectifiedusing Whit

e-correctedstandarderrors. Herson Jonathan who hasalsotakenpartinthediscussion, hearsthis commentandarguesthat

White correction wouldtypicallyreducethenumberofTypeIerrorsinfinancialdata.

How manydummy variablesshouldRathoduse?

Five Four Six

Explanation

Thereare5 tradingdaysina week, but weshoulduse (n − 1)or4dummiesinorder toensureno violationsofregression

analysisoccur.

(StudySession3, LOS10.j)

Whatismostlikelyrepresented bytheinterceptoftheregression?

The intercept is not a driver of returns, only the independent variables

Thereturnonaparticulartradingday

Thedrift ofarandom walk

Explanation

Theomitted variableisrepresented by theintercept.So, if we havefour variables torepresent Monday through Thursday, the

intercept wouldrepresentreturnson Friday.

(StudySession3, LOS10.j)

Questions #71-76 of 106

R = RSS / SST = 100 / 400 = 0.25

The F-statistic isequaltotheratioofthemeansquaredregressiontothemeansquarederror.

F = 100 / 7.5 = 13.333

Damon Washburn, CFA, is currentlyenrolledasapart-timegraduatestudentatState University. Oneof hisrecent

assignmentsfor his courseonQuantitativeAnalysisis toperformaregressionanalysisutilizing the concepts coveredduring

thesemester. Hemust interpret theresultsof theregressionas wellas the test statistics. Washburnis confident in hisability to

calculate thestatistics because the classisallowed tousestatisticalsoftware. However, herealizes that theinterpretationof

thestatistics will bethetruetestof his knowledgeofregressionanalysis. Hisprofessor hasgiventothestudentsalistof

questionsthatmust beanswered bytheresultsoftheanalysis.

Washburn hasestimatedaregressionequationin which 160quarterlyreturnsontheS&P 500areexplained bythree

macroeconomic variables:employmentgrowth (EMP)asmeasured bynonfarmpayrolls, grossdomestic product (GDP)

growth, andprivateinvestment (INV).Theresultsof theregressionanalysisareasfollows:

CoefficientEstimates

Parameter Coefficient StandardError

ofCoefficient

Intercept 9.50 3.40

EMP -4.50 1.25

GDP 4.20 0.76

INV -0.30 0.16

OtherData:

Regressionsumofsquares (RSS) = 126.00

Sumofsquarederrors (SSE) = 267.00

Durbin-Watsonstatistic (DW) = 1.34

Abbre

v

iated

T

able

of

the

S

tudent's

t-distribution

(One-

T

ailed

Probabilities

)

df p=0.10 p=0.05 p=0.025 p=0.01 p=0.005

3 1.638 2.353 3.182 4.541 5.841

10 1.372 1.812 2.228 2.764 3.169

50 1.299 1.676 2.009 2.403 2.678

100 1.290 1.660 1.984 2.364 2.626

120 1.289 1.658 1.980 2.358 2.617

200 1.286 1.653 1.972 2.345 2.601

C

ritical

Values

for

D

urbin-

W

atson

S

tatistic

(

α

=

0

.

0

5

)

K=1 K=2 K=3 K=4 K=5

n d d d d d d d d d d

2

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no significant positive serial correlation in the residuals.

Question #77 of 106

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Explanation

Thestandarderrorof theestimateisequal to [SSE/(n − k − 1)] = [267.00/156] = approximately1.31. (StudySession3,

LOS 9.j)

An analyst is testing to see whether a dependent variable is related to three independent variables. He finds thattwo of the independent

variables are correlated with each other, butthatthe correlation is spurious. Which of the following is most accurate? There is:

no evidence of multicollinearity and serial correlation.

evidenceofmulticollinearity butnotserial correlation.

evidence of multicollinearity and serial correlation.

Explanation

Just because the correlation is spurious, does not mean the problem of multicollinearity will go away. However, there is no evidence of

serial correlation.

Which of thefollowingisleastlikelyamethodused todetect heteroskedasticity?

Test of the variances.

Breusch-Pagantest.

Durbin-Watsontest.

Explanation

TheDurbin-Watson test isused todetect serial correlation.TheBreusch-Pagan test isused todetect heteroskedasticity.

63monthlystock returnsforafund between1997and2002areregressedagainstthemarketreturn, measured bythe

Wilshire5000, andtwodummy variables.Thefund changedmanagerson January2, 2000.Dummy variableoneisequalto1

if thereturnisfromamonth between2000and2002.Dummy variablenumber twoisequal to1if thereturnisfrom the

second halfof theyear.Thereare36observations whendummy variableoneequals0, halfof which are whendummy

variabletwoalsoequals0.Thefollowingaretheestimated coefficient valuesandstandarderrorsofthe coefficients.

C

oefficient Value

S

tandard

error

Mar

k

e

t

1.43000

0.31

9

000

Du

mm

y

1 0.00162

0.000675

Du

mm

y

2 0.00132

0.000733

ᅞ A)

ᅚ B)

ᅞ C)

Question #

8

0 of 106

QuestionID:461746

ᅞ A)

ᅚ B)

ᅞ C)

Question #

8

1 of 106

QuestionID:461757

ᅞ A)

ᅚ B)

ᅞ C)

Whatisthep-valueforatestofthe hypothesisthatperformanceinthesecond halfoftheyearisdifferentthanperformancein

thefirst halfoftheyear?

Lower than 0.01.

Between0.05and0.10.

Between0.01and0.05.

Explanation

Thedifference betweenperformancein thesecondandfirst halfof theyearismeasured bydummy variable2.Thet-statistic

isequalto0.00132 / 0.000733 = 1.800, which is betweenthet-values (with 63 − 3 − 1 = 59 degreesoffreedom)of1.671fora

p-valueof0.10, and2.00forap-valueof0.05 (notethatthetestisatwo-sidedtest).

When twoormoreof theindependent variablesinamultipleregressionare correlated with each other, the conditionis called:

conditional heteroskedasticity. multicollinearity.

serial correlation.

Explanation

Multicollinearityrefers to the condition when twoormoreof theindependent variables, orlinear combinationsof the

independent variables, inamultipleregressionare highly correlated with each other.This conditiondistorts thestandarderror

ofestimateandthe coefficientstandarderrors, leadingtoproblems when conductingt-testsforstatisticalsignificanceof

parameters.

Ananalyst hasrunseveralregressions hoping topredict stock returns, and wants to translate thisintoaneconomic

interpretationfor his clients.

Return = 0.03 + 0.020Beta-0.0001MarketCap (in billions) + ε

A correctinterpretationoftheregression mostlikelyincludes:

prediction errors are always on the positive side.

a billiondollarincreaseinmarket capitalization willdrivereturnsdown by0.01%. astock with zero betaand zeromarket capitalization willreturnprecisely3.0%.

Explanation

The coefficientofMarketCapis0.01%, indicatingthatlarger companies haveslightlysmallerreturns. Notethata company

Question #

8

2 of 106

QuestionID:461607

ᅚ A)

ᅞ B)

ᅞ C)

Question #

8

3 of 106

QuestionID:461645

ᅚ A)

ᅞ B)

ᅞ C)

Questions #

8

4-

89

of 106

Consider thefollowingestimatedregressionequation, with calculatedt-statisticsof theestimatesasindicated:

A

U

T

O =

10.0

+

1.25

P

I

+

1.0

T

EEN

-

2.0

I

N

S

with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63.

The equation was estimated over 40 companies. The predicted value of AUTO if PI is 4, TEEN is 0.30, and INS = 0.6 is closest to:

14.10.

14.90.

17.50.

Explanation

PredictedAUTO = 10 + 1.25 (4) + 1.0 (0.30)-2.0 (0.6)

= 10 + 5 + 0.3-1.2

= 14.10

An analyst runs a regression of monthly value-stock returns on five independent variables over 48 months. The total sum of squares is 430, and the sum of squared errors is 170. Testthe null hypothesis atthe 2.5% and 5% significance level that all five of the independent

variablesareequalto zero.

Rejected at 2.5% significance and 5% significance.

Rejected at 5% significance only.

Not rejected at 2.5% or 5.0% significance.

Explanation

The F-statistic is equal to the ratio of the mean squared regression (MSR) to the mean squared error (MSE).

RSS = SST - SSE = 430 - 170 = 260

MSR = 260 / 5 = 52

MSE = 170 / (48 - 5 - 1) = 4.05

F = 52 / 4.05 = 12.84

The critical F-valuefor5and42degreesoffreedomata5% significancelevelisapproximately2.44.The critical F-valuefor5and42

degrees of freedom at a 2.5% significance level is approximately 2.89. Therefore, we can rejectthe null hypothesis at either level of

significance and conclude that at least one of the five independent variables explains a significant portion of the variation of the dependent

variable.

Question #

8

4 of 106

QuestionID:485641 be responsible for providing research on the airline industry. Pinnacle Airlines, a leader in the industry, represents a large holding in Smith Brothers' portfolio. Looking back overpastresearch on Pinnacle, Carterrecognizesthatthe company historically has beenastrong

performer in what is considered to be a very competitive industry. The stock price over the last 52-week period has outperformed that of

other industry leaders, although Pinnacle's net income has remained flat. Carter wonders if the stock price of Pinnacle has become

overvalued relative to its peer group in the market, and wants to determine if the timing is right for Smith Brothers to decrease its position in Pinnacle.

Carter decides to run a regression analysis, using the monthly returns of Pinnacle stock as the dependent variable and monthly returns of

the airlines industry as the independent variable.

Analysis

of

Variance

T

able

(A

N

OVA

)

Which of the following is least likely to be an assumption regarding linear regression?

The variance of the residuals is constant.

A linear relationship exists between the dependent and independent variables.

Theindependent variableis correlated with theresiduals.

Explanation

Although the linear regression model is fairly insensitive to minor deviations from any of these assumptions, the independent variable is

Question #

8

6 of 106

QuestionID:485643

Based upon her analysis, Carter has derived the following regression equation: Ŷ = 1.75 + 3.25X. The predicted value of the Y variable equals50.50, ifthe:

coefficient of the determination equals 15.

predicted value of the dependent variable equals 15.

predicted value of the independent variable equals 15.

Question #

89

of 106

QuestionID:485646

Point 1: Data derived from regression analysis may be homoskedastic.

Point 2: Data from regression relationships tends to exhibit parameter instability. Point 3: Results of regression analysis may exhibit autocorrelation.

Question #

9

1 of 106

QuestionID:461678

ᅞ A)

ᅞ B)

ᅚ C)

Mul

t

iple

R

0.

8

170

88

R

0.667632

Ad

j

us

t

ed

R

0.617777

S

t

andard

E

rror 1.655

89

1

Ob

ser

v

a

t

ions

24

A

N

OVA

df

SS

M

S

Regression 3 110.156

8

36.71

89

5

Residual

20 54.

8

3

9

5 2.741

9

75

To

t

al

23 164.

99

63

C

oefficients

S

tandard

E

rror

t-

S

tatistic

In

t

er

c

ep

t

-0.23

8

21

0.3

88

717

-0.612

8

2

J

anuary

2.560552

1.232634

2.077301

S

m

all

Cap

Inde

x

0.23134

9

0.123007

1.

88

077

8

L

arge

Cap

Inde

x

0.

9

51515

0.25452

8

3.73

8

35

9

Gloucester willperformanF-testfortheequation. Healsoplanstotestforserial correlationand conditionalandunconditional

heteroskedasticity.

JasonBrown, CFA, isinterestedinGloucester'sresults. Hespeculatesthattheyareeconomicallysignificantinthatexcessreturns could be earned by shorting the large capitalization and the small capitalization indexes in the month of January and using the proceeds to buy

the fund.

The percent of the variation in the fund's return that is explained by the regression is:

61.78%.

81.71%.

66.76%.

Explanation

The R tells us how much of the change in the dependent variable is explained by the changes in the independent variables in the

regression: 0.667632.

2

2

Question #

9

2 of 106

QuestionID:461679

of the CFA curriculum, and unconditional heteroskedasticity is generally considered less serious than conditional heteroskedasticity.

Question #

9

6 of 106

QuestionID:461683

The index fund regression should provide a higher R than the active manager regression. R is the sum of squares regression divided by

the total sum of squares.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly

Question #

99

of 106

QuestionID:461644

ᅞ A)

ᅚ B)

ᅞ C)

Question #100 of 106

QuestionID:461675

The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% level of significance are ± 2.03.

The calculated t-values are:

tforR&D = 1.25 / 0.45 = 2.777

tforADV = 1.0/ 2.2 = 0.455

t for COMP = -2.0 / 0.63 = -3.175

t for CAP = 8.0 / 2.5 = 3.2

Therefore, R&D, COMP, and CAP are statistically significant.

A dependent variable is regressed againstthree independent variables across 25 observations. The regression sum of squares is 119.25,

and the total sum of squares is 294.45. The following are the estimated coefficient values and standard errors of the coefficients.

Coefficient ValueStandard error

1 2.43 1.4200

2 3.21 1.5500

3 0.18 0.0818

What is the p-value for the test of the hypothesis that all three of the coefficients are equal to zero?

Between 0.05 and 0.10.

lower than 0.025.

Between 0.025 and 0.05.

Explanation

This test requires an F-statistic, which is equal to the ratio of the mean regression sum of squares to the mean squared error.

The mean regression sum of squares is the regression sum of squares divided by the number of independent variables, which is 119.25 /

3 = 39.75.

The residual sum of squares is the difference between the total sum of squares and the regression sum of squares, which is 294.45 −

119.25 = 175.20. The denominator degrees of freedom is the number of observations minus the number of independent variables, minus 1, which is 25 − 3 − 1 = 21. The mean squared error is the residual sum of squares divided by the denominator degrees of freedom, which is 175.20 / 21 = 8.34.

The F-statistic is 39.75 / 8.34 = 4.76, which is higher than the F-value (with 3 numerator degrees of freedom and 21 denominator degrees offreedom)of3.07atthe5% levelofsignificanceand higherthanthe F-valueof3.82atthe2.5% levelofsignificance.The conclusionis

thatthep-valuemust belowerthan0.025.

Rememberthep-valueistheprobabilitythatliesabovethe computedteststatistic foruppertailtestsor below the computedteststatistic

ᅚ A) possible. We should have used only two dummy variables. Multicollinearity is a problem in this case. Specifically, a linear combination of independent variablesisperfectly correlated. X1 + X2 + X3 = 1.

There are too many dummy variables specified, so the equation will suffer from multicollinearity.

The management of a large restaurant chain believes that revenue growth is dependent upon the month of the year. Using a standard 12

Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market

Question #103 of 106

QuestionID:461540

Jacob Warner, CFA, is evaluating a regression analysis recently published in a trade journal that hypothesizes thatthe annual performance of the S&P 500 stock index can be explained by movements in the Federal Funds rate and the U.S. Producer Price Index (PPI). Which ofthefollowingstatementsregarding hisanalysisis mostaccurate?

The p-value is the smallest level of significance for which the null hypothesis can be rejected. Therefore, for any given variable, if the p-value of a variable is less than the significance level, the null hypothesis can be rejected and the variable is considered to be statistically significant.

An analyst is estimating a regression equation with three independent variables, and calculates the R, the adjusted R, and the

F-statistic. The analystthen decides to add a fourth variable to the equation. Which of the following is most accurate?

The R and F-statistic will be higher, but the adjusted R could be higher or lower.

TheadjustedR will be higher, buttheR and F-statistic could be higherorlower.

The R will be higher, butthe adjusted R and F-statistic could be higher or lower.

Explanation

ᅞ C)

Question #106 of 106

QuestionID:461742

ᅞ A)

ᅚ B)

ᅞ C)

Take first differences of the dependent variable.

Explanation

Thefirstdifferencingisnotaremedyforthe collinearity, noristheinclusionofdummy variables.The bestpotentialremedyistoattempt

to eliminate highly correlated variables.

A variable is regressed againstthree other variables, x, y, and z. Which of the following would NOT be an indication of multicollinearity? X is closelyrelatedto:

3.

y .

3y + 2z.

Explanation

If x is related to y, the relationship between x and y is not linear, so multicollinearity does not exist. If x is equal to a constant (3), it will be correlated with theinterceptterm.

2