CFA 2018 Quantitative Analysis Question Bank 01 Correlation and Regression

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Test ID: 7440246

Correlation and Regression

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WandaBrunner, CFA, is workingonaregressionanalysis basedon publicly available macroeconomic time-seriesdata. The

mostimportantlimitationofregressionanalysisinthisinstanceis:

the error term of one observation is not correlated with that of another observation.

limitedusefulnessinidentifying profitableinvestmentstrategies. low confidenceintervals.

Explanation

Regressionanalysis basedon publicly availabledataisoflimitedusefulnessifother market participantsarealsoawareofand

makeuseofthisevidence.

Thestandarderrorofestimateis closest tothe: standard deviation of the residuals.

standard deviation of the independent variable.

standard deviation of the dependent variable.

Explanation

Thestandard error of theestimate measuresthe uncertainty in the relationship between the actual and predicted valuesof the

dependent variable. The differences between these values are called the residuals, and thestandard error of theestimate

helps gaugethe fitof the regression line (thesmaller thestandard error of theestimate, the better the fit).

A simplelinear regression equation had a coefficientof determination (R ) of 0.8. What isthe correlation coefficient between

the dependent and independent variables and what isthe covariance between thetwo variables if the varianceof the

independent variable is 4 and the varianceof the dependent variable is 9? Correlation coefficient Covariance

0.89 5.34

0.91 4.80

0.89 4.80

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The correlation coefficientisthesquarerootoftheR, r = 0.89.

To calculatethe covariance multiply the correlation coefficient by the productofthestandarddeviationsofthetwo variables:

COV = 0.89 × √4 × √9 = 5.34

Astudy ofasampleofincomes (inthousandsofdollars)of35 individualsshowsthatincomeisrelatedtoageand yearsofeducation. Thefollowingtableshowstheregressionresults:

Coefficient

S

tandard

Error t-statistic

P

-value

In

te

r

cept

5.

6

5

1 .

27

4 .

44

0 .

01 Ag

e

0 .5

3 ?

1 .

33

0 .

21 Ye

ar

s o

f

E

du

c

a

t

i

o

n

2 .

32

0 .

41 ?

0 .

01 Anova

df

SS

MS

F

Regressio

n

?

215.10 ?

?

Error

?

115.10 ?

Tot

a

l

?

The standard error for the coefficient ofage andt-statistic for years of educationare:

0.32; 1.65.

0.53; 2.96. 0.40; 5.66.

Explanation

standard error for the coefficient ofage = coefficient / t-value = 0.53 / 1.33 = 0.40 t-statistic for the coefficient of education = coefficient / standard error = 2.32 / 0.41 = 5.66

The mean square regression (MSR) is:

6.72.

102.10. 107.55.

Explanation

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dffor Regression = k = 2

MSR = RSS / df = 215.10 / 2 = 107.55

The mean square error (MSE) is:

3.58.

7.11. 3.60.

Explanation

dffor Error = n - k - 1 = 35 - 2 - 1 = 32 MSE = SSE / df = 115.10 / 32 = 3.60

What is the R for the regression?

65%.

76%. 62%.

Explanation SST = RSS + SSE = 215.10 + 115.10

= 330.20

R= RSS / SST = 215.10 / 330.20 = 0.65

What is the predicted income ofa 40-year-old person with 16 years of education?

$62,120.

$63,970. $74,890.

Explanation

income = 5.65 + 0.53 (age) + 2.32 (education) = 5.65 + 0.53 (40) + 2.32 (16)

= 63.97 or $63,970 2

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What is the F-value?

29.88.

1.88. 14.36.

Explanation

F = MSR / MSE = 107.55 / 3.60 = 29.88

Assume ananalyst performs two simple regressions. The first regressionanalysis has an R-squaredof 0.90 anda slope coefficient of 0.10. The second regressionanalysis has an R-squaredof 0.70 anda slope coefficient of 0.25. Which one of the following statements is mostaccurate?

The first regression has more explanatory power than the second regression.

The influence on the dependent variable ofaone unit increase in the independent variable is 0.9 in the first analysis and 0.7 in the secondanalysis.

Results of the secondanalysis are more reliable than the first analysis.

Explanation

The coefficient ofdetermination (R-squared) is the percentage of variation in the dependent variable explained by the variation in the independent variable. The larger R-squared (0.90) of the first regression means that 90% of the variability in the dependent variable is explained by variability in the independent variable, while 70% of that is explained in the second regression. This means that the first regression has more explanatory power than the second regression. Note that the Beta is the slope of the regression line anddoesn't measure explanatory power.

Paul Frank is ananalyst for the retail industry. He is examining the role of television viewing by teenagers on the sales ofaccessory stores. He gathereddataand estimated the following regressionof sales (in millions ofdollars) on the number of hours watched by teenagers (TV, in hours per week):

S

a

les

= 1.05 + 1.6 TV

The predicted sales if television watching is 5 hours per week is:

$9.05 million.

$8.00 million. $2.65 million.

Explanation

The predicted sales are: Sales = $1.05 + [$1.6 (5)] = $1.05 + $8.00 = $9.05 million.

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Question #12 of 120

QuestionID:461433 cannot test the significance of the correlation with this information.

conclude that there is no significant correlation between X and Y. Either the covariance or one of the standard deviations must be negative.

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The covariance cannever be negative. The covariance must be negative.

Explanation

Inorder for the correlation between two variables to be negative, the covariance must be negative. (Standarddeviations are always positive.)

Assume you perform two simple regressions. The first regressionanalysis has an R-squaredof 0.80 anda beta coefficient of 0.10. The second regressionanalysis has an R-squaredof 0.80 anda beta coefficient of 0.25. Which one of the following statements is most

accurate?

The influence on the dependent variable of a one-unit increase in the independent variable is the same in both analyses.

Results from the first analysis are more reliable than the secondanalysis. Explained variability from both analyses is equal.

Explanation

The coefficient ofdetermination (R-squared) is the percentage of variation in the dependent variable explained by the variation in the independent variable. The R-squared (0.80) being identical between the first and second regressions means that 80% of the variability in the dependent variable is explained by variability in the independent variable for both regressions. This means that the first regression has the same explaining power as the second regression.

A sample covariance for the common stock of the Earth Company and the S&P 500 is −9.50. Which of the following statements regarding the estimated covariance of the two variables is mostaccurate?

The two variables will have a slight tendency to move together.

The relationship between the two variables is not easily predicted by the calculated covariance.

The two variables will have a strong tendency to move inopposite directions.

Explanation

The actual value of the covariance for two variables is not very meaningful because its measurement is extremely sensitive to the scale of the two variables, ranging from negative to positive infinity. Covariance can, however be converted into the correlation coefficient, which is more straightforward to interpret.

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experience, annual income and type of college degrees, ifany. A regressionofannual dollar revenue on the number of courses offered each year yields the results shown below.

C

o

e

ff

icie

n

t

Esti

ma

tes

Pre

d

ictor

Coe

ff

icie

n

t St

anda

r

d

Error o

f

the Coe

ff

icie

n

t

I

n

tercept

0.10

0.50 Slope (Number o

f

Courses)

2.20

0.60

Which statement about the slope coefficient is mostcorrect, assuming a 5% level of significance and 50 observations?

t-Statistic: 0.20. Slope: Not significantly different from zero.

t-Statistic: 3.67. Slope: Significantly different from zero. t-Statistic: 3.67. Slope: Not significantly different from zero.

Explanation

t = 2.20/0.60 = 3.67. Since the t-statistic is larger thananassumed critical value ofabout 2.0, the slope coefficient is statistically significant.

A simple linear regression is run to quantify the relationship between the returnon the common stocks of medium sized companies (Mid Caps) and the returnon the S&P 500 Index, using the monthly returnon Mid Cap stocks as the dependent variable and the monthly return

on the S&P 500 as the independent variable. The results of the regressionare shown below:

CoefficientStandard Error of Coefficient t-Value

Intercept 1.71 2.950 0.58

S&P 500 1.52 0.130 11.69

R = 0.599

Use the regression statistics presentedabove andassume this historical relationship still holds in the future period. If the expected return

on the S&P 500 over the next period were 11%, the expected returnon Mid Cap stocks over the next period would be:

18.4%.

20.3%. 33.8%.

Explanation

Y = intercept + slope(X)

Mid Cap Stock returns = 1.71 + 1.52(11) =18.4%

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measures the strength of association between the two variables more exactly. indicates the percentage of variation explained by a regression model.

indicates whether the slope of the regression line is positive or negative.

Explanation

Ina simple linear regression the coefficient ofdetermination (R ) is the squared correlation coefficient, so it is positive even when the correlation is negative.

Consider the regression results from the regressionof Y against X for 50 observations:

Y = 0.78 - 1.5 X

The st

anda

r

d

error o

f

the estim

a

te is 0.40

and

the st

anda

r

d

error o

f

the coe

ff

icie

n

t is 0.45.

Which of the following reports the correct value of the t-statistic for the slope and correctly evaluates H: b ≥ 0 versus H: b < 0 with 95% confidence?

t= 3.750; slope is significantly different fromzero.

t = -3.333;slopeissignificantly negative.

t = -3.750;slopeissignificantly different from zero.

Explanation

The test statistic ist = (-1.5 - 0) / 0.45 = -3.333. The critical 5%, one-tailt-valuefor48 degreesoffreedom is +/- 1.667. However, in the Schweser Notes youshoulduse the closest degreesoffreedom numberof40df. which is +/-1.684. Therefore, theslopeisless than zero. Wereject thenullinfavorof thealternative.

BeaCarroll, CFA, has performedaregressionanalysisof therelationship between6-month LIBORand the U.S. ConsumerPriceIndex (CPI). Heranalysisindicatesastandarderrorofestimate (SEE) that is high relative to total variability. Which of thefollowing conclusions regarding therelationship between6-month LIBORandCPI canCarroll mostaccurately draw from herSEE analysis? Therelationship between the two variablesis:

veryweak. very strong. positively correlated.

Explanation

TheSEE is thestandarddeviationof theerror termsin theregression, andisanindicatorof thestrength of therelationship between the dependent andindependent variables. TheSEE will below if therelationship isstrongand conversely will be high if therelationship is weak.

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Question #23 of 120

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Thestandarderrorof theestimate measures the variability of the:

actual dependent variable values about the estimated regression line. predicted y-valuesaround the meanof theobserved y-values.

valuesof thesampleregression coefficient.

Explanation

Thestandarderrorof theestimate (SEE) measures theuncertainty in therelationship between theindependent anddependent variables and helpsgauge thefit of theregressionline (thesmaller thestandarderrorof theestimate, the better thefit).

Remember that theSEE isdifferent from thesum ofsquarederrors (SSE). SSE = thesum of (actual value - predicted value). SEE is the thesquareroot of theSSE "standardized" by thedegreesoffreedom, orSEE = [SSE / (n - 2)]

TheR ofasimpleregressionof twofactors, AandB, measures the:

impact on B of a one-unit change in A.

statisticalsignificanceof the coefficient in theregressionequation.

percent of variability ofonefactorexplained by the variability of thesecondfactor.

Explanation

The coefficient ofdetermination measures the percentageof variationin thedependent variableexplained by the variationin the independent variable.

Consider theregressionresultsfrom theregressionof Y against X for 50observations:

Y = 0.78 + 1.2 X

The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45.

Which of thefollowingreports the correct valueof thet-statistic for theslopeand correctly evaluatesitsstatisticalsignificance with 95% confidence?

t= 1.789; slope is not significantly different fromzero.

t = 3.000;slopeissignificantly different from zero. t = 2.667;slopeissignificantly different from zero.

Explanation

Perform a t-test todetermine whether theslope coefficient ifdifferent from zero. The test statistic ist = (1.2 - 0) / 0.45 = 2.667. The criticalt-valuesfor48 degreesoffreedom are ± 2.011. Therefore, theslopeisdifferent from zero.

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Which of thefollowingstatementsabout thestandarderrorof theestimate (SEE)isleastaccurate?

The SEEwill be high if the relationshipbetween the independent and dependent variables is weak.

TheSEE may be calculatedfrom thesum of thesquarederrorsand thenumberof observations.

Thelarger theSEE thelarger theR.

Explanation

TheR, or coefficient ofdetermination, is the percentageof variationin thedependent variableexplained by the variationin the independent variable. A higherR meansa betterfit. TheSEE issmaller when thefit is better.

Ananalyst performs twosimpleregressions. Thefirst regressionanalysis hasanR-squaredof0.40anda beta coefficient of1.2. The secondregressionanalysis hasanR-squaredof0.77anda beta coefficient of1.75. Which oneof thefollowingstatementsis most

accurate?

The R-squared of the first regression indicates that there is a 0.40 correlation between the independent and the dependent variables.

Thefirst regressionequation has moreexplaining power than thesecondregressionequation. Thesecondregressionequation has moreexplaining power than thefirst regressionequation.

Explanation

The coefficient ofdetermination (R-squared)is the percentageof variationin thedependent variableexplained by the variationin the independent variable. ThelargerR-squared (0.77)of thesecondregression means that 77%of the variability in thedependent variableis explained by variability in theindependent variable, whileonly 40%of that isexplainedin thefirst regression. This means that thesecond regression has moreexplaining power than thefirst regression. Note that theBetais theslopeof theregressionlineanddoesn't measure explaining power.

JasonBrock, CFA, is performingaregressionanalysis toidentify andevaluateany relationship between the commonstock ofABTCorp and theS&P100index. Heutilizes monthly datafrom the past five years, andassumes that thesum of thesquarederrorsis .0039. The calculatedstandarderrorof theestimate (SEE)isclosest to:

0.0082. 0.0360. 0.0080.

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Explanation

Thestandarderrorofestimateofaregressionequation measures thedegreeof variability between theactualandestimated Y-values. TheSEE may also bereferred toas thestandarderrorof theresidualor thestandarderrorof theregression. TheSEE isequal to the squareroot of the meansquarederror. Expressedinaformula,

SEE = √(SSE / (n-2)) = √(.0039 / (60-2)) = .0082

Determineandinterpret the correlation coefficient for the two variables X and Y. Thestandarddeviationof X is0.05, thestandard deviationof Y is0.08, and their covarianceis −0.003.

−0.75 and the two variables are negatively associated. −1.33and the two variablesarenegatively associated. +0.75 and the two variablesare positively associated.

Explanation

The correlation coefficient is the covariancedivided by the product of the twostandarddeviations, i.e. −0.003 / (0.08 × 0.05).

EricaBasenj, CFA, has beengivenanassignment by her boss. She has beenrequested toreview thefollowingregressionoutput to answer questionsabout therelationship between the monthly returnsof theToffeeInvestment Management (TIM) High YieldBond Fund and thereturnsof theindex (independent variable).

RegressionStatistics

R ??

Standard Error ?? Observations 20 ANOVA

df SS MS F SignificanceF

Regression 1 23,516 23,516 ? ?

Residual 18 ? 7

Total 19 23,644

RegressionEquation

Coefficients Std.Error t-statistic P-value

Intercept 5.2900 1.6150 ? ?

Slope 0.8700 0.0152 ? ?

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Whatisthe valueofthe F-statistic?

3,359.

0.9945.

0.0003.

Explanation

F = meansquareregression / meansquareerror = 23,516 / 7 = 3,359. (Study Session3, LOS 9.k)

Heteroskedasticity can bedefinedas:

nonconstant variance of the error terms. errortermsthataredependent.

independent variablesthatare correlated with each other.

Explanation

Heteroskedasticity occurs whenthe varianceoftheresidualsisnotthesameacrossallobservationsinthesample. Autocorrelationrefers todependenterrorterms. (Study Session3, LOS10.m)

Considerthefollowinganalysisof variance (ANOVA)table:

Source Sum ofsquares Degrees offreedom Meansquare

Regression 500 1 500

Error 750 50 15

Total 1,250 51

TheR andthe F-statistic are, respectively:

R = 0.40 and F= 33.333. R = 0.40and F = 0.971. R = 0.67and F = 0.971.

Explanation

R = 500 / 1,250 = 0.40. The F-statistic is 500 / 15 = 33.33.

Considerthe case whenthe Y variableisin U.S. dollarsandthe X variableisin U.S. dollars. The 'units' ofthe covariance between Y and

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Question #42 of 120

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correlationandoutliers.

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ey

Ja

rs

G

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ey

42 .

2

20 .8

Ja

rs

20 .8

36 .5

Standish wantstolearn moreaboutthe performanceofthefund. He performsalinearregressionofthefund's monthly returnsoverthe pasttwo yearsonalarge capitalizationindex. Theresultsare below:

AN

O

VA

d

f

SS

MS

F

R

eg

r

e

ss

i

o

n

1

9

2 .5

300

9

2 .5

300

9

2

8.

0

9

117 R

e

s

i

du

a

l

22

72 .

4662

5

3 .

2

9

3

9

21 Tot

a

l

23

164 .99

63 C

o

efficien

ts

S

t

an

d

a

r

d

E

rr

o

r t

-

st

a

t

i

st

ic

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-va

l

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t

e

r

cep

t

0 .

14

89

23

0 .

3

9

166

9

0 .

3

8

022

5

0 .

707424

La

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ge

C

ap

I

n

d

ex

1 .

20

5

602

0 .

227467

5. 30011

2 .5

6 E-

0

5

Standish forecaststhefund'sreturn, baseduponthe predictionthatthereturntothelarge capitalizationindex usedintheregression will be10%. Healso wantsto quantify thedegreeofthe predictionerror, as wellasthe minimum and maximum sensitivity thatthefund actually has with respecttotheindex.

He planstosummarize hisresultsinareport. Inthereport, he willalsoinclude caveats concerningthelimitationsofregressionanalysis. Helistsfourlimitationsofregressionanalysisthat hefeelsareimportant:relationships between variables can changeovertime, multicollinearity leadstoinconsistentestimatesofregression coefficients, iftheerrortermsare heteroskedastic thestandarderrorsfor theregression coefficient may not bereliable, andiftheerrortermsare correlated with each otherovertimetheteststatistics may not be reliable.

Giventhe variance/covariance matrix for Grey and Jars, inaone-sided hypothesistestthatthereturnsare positively correlated H: ρ ≤ 0 vs. H: ρ > 0, Standish would:

reject the null at the 5% but not the 1% level of significance. rejectthenullatthe1%levelofsignificance.

needtogather moreinformation before beingabletoreach a conclusion concerning significance.

Explanation

First, we must computethe correlation coefficient, which is0.53 = 20.8 / (42.2 × 36.5) .

Thet-statistic is:2.93 = 0.53 × [(24 - 2) / (1 − 0.53 × 0.53)] , andfordf = 22 = 24 − 2, thet-statisticsforthe 5%and1%levelare1.717 and2.508 respectively. (Study Session3, LOS 9.g)

0

1

0.5

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Question #47 of 120

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Ofthefour caveatsofregressionanalysislisted by Standish, theleastaccurateis:

the relationships of variables change over time.

multicollinearity leadstoinconsistentestimatesoftheregression coefficients.

iftheerrortermsare heteroskedastic thestandarderrorsfortheregression coefficients may not bereliable.

Explanation

Inthe presenceof multicollinearlity, theregression coefficients wouldstill be consistent butunreliable. Theother possibleshortfallslisted are valid. (Study Session3, LOS 9.k)

Weareexaminingtherelationship betweenthenumberof cold callsa broker makesandthenumberofaccountsthefirm asa whole opens. We havedeterminedthatthe correlation coefficientisequalto0.70, basedonasampleof16observations. Istherelationship statistically significantata10%levelofsignificance, why or why not? Therelationship is:

not significant; the critical value exceeds the t-statisticby 1.91. significant;thet-statistic exceedsthe critical value by 3.67. significant;thet-statistic exceedsthe critical value by 1.91.

Explanation

The calculatedteststatistic ist-distributed with n - 2degreesoffreedom:

t = r√(n - 2) / √(1 - r) = 2.6192 / 0.7141 = 3.6678

From atable, the critical value = 1.76

Which ofthefollowingstatementsaboutthestandarderrorofestimateisleastaccurate? Thestandarderrorofestimate:

measures the Yvariable's variability that is not explained by the regression equation. isthesquareofthe coefficientofdetermination.

isthesquarerootofthesum ofthesquareddeviationsfrom theregressionlinedivided by (n − 2).

Explanation

Note:The coefficientofdetermination (R )isthesquare ofthecorrelationcoefficientinsimplelinearregression. 2

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Considertheregressionresultsfrom theregressionof Y against X for 50observations: Y = 5.0 + 1.5 X

Thestandarderrorofthe coefficientis0.50andthestandarderroroftheforecastis0.52. The 95% confidenceintervalforthe predicted valueof Y if X is10is:

{18.980 < Y < 21.019}.

{18.954< Y <21.046}.

{19.480< Y <20.052}.

Explanation

The predicted valueof Y is: Y = 5.0 + [1.5 (10)] = 5.0 + 15 = 20. The confidenceintervalis20 ± 2.011 (0.52)or{18.954< Y <21.046}.

Which ofthefollowingstatementsaboutlinearregressionanalysisismostaccurate?

An assumption of linear regression is that the residuals are independently distributed.

The coefficientofdeterminationisdefinedasthestrength ofthelinearrelationship between two variables.

Whenthereisastrongrelationship betweentwo variables we can concludethata changein one will causea changeintheother.

Explanation

Even whenthereisastrongrelationship betweentwo variables, we cannot concludethata causalrelationship exists. The coefficientof determinationisdefinedasthe percentageoftotal variationinthedependent variableexplained by theindependent variable.

Asample covarianceoftworandom variablesis most commonly utilizedto:

calculate the correlation coefficient,which is a measure of the strength of their linear relationship.

identify and measurestrongnonlinearrelationships betweenthetwo variables.

estimatethe "pure" measureofthetendency oftwo variablesto movetogetherovera period oftime.

Explanation

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Regressionanalysis hasanumberofassumptions. Violationsoftheseassumptionsinclude which ofthefollowing? Independent variables that are not normally distributed.

A zero meanoftheresiduals.

Residualsthatarenotnormally distributed.

Explanation

Theassumptionsincludeanormally distributedresidual with a constant varianceanda meanof zero.

Forthe caseofsimplelinearregression with oneindependent variable, which ofthefollowingstatementsaboutthe correlation coefficient isleastaccurate?

If the correlation coefficient is negative, it indicates that the regression line has a negative slope coefficient.

The correlation coefficient can vary between −1and +1.

Iftheregressionlineisflatandtheobservationsaredisperseduniformly abouttheline, the correlation coefficient will be +1.

Explanation

Correlationanalysisisastatisticaltechniqueusedto measurethestrength oftherelationship betweentwo variables. Themeasure ofthis relationshipiscalled thecoefficient ofcorrelation.

Iftheregressionlineisflatand the observationsare dispersed uniformlyabouttheline,thereis no linear relationship betweenthetwo variablesandthecorrelation coefficient will be zero.

Both oftheother choicesareCORRECT.

Intheestimatedregressionequation Y = 0.78 - 1.5 X, which ofthefollowingisleastaccurate wheninterpretingtheslope coefficient?

If the value of X is zero, the value of Ywill be -1.5.

Thedependent variabledeclines by -1.5 unitsif X increases by 1unit.

Thedependent variableincreases by 1.5 unitsif X decreases by 1unit.

Explanation

Thesloperepresentsthe changeinthedependent variableforaone-unit changeintheindependent variable. Ifthe valueof X is zero, the valueof Y will beequaltotheintercept, inthis case, 0.78.

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Question #58 of 120

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residuals are mean reverting; that is, they tend towards zero over time.

residualsareindependently distributed.

expected valueoftheresidualsis zero.

Explanation

Theassumptionsregardingtheresidualsarethattheresiduals havea constant variance, havea meanof zero, andareindependently

distributed.

Inthescatter plot below, the correlation betweenthereturnonstock Aandthe marketindex is:

positive.

notdiscernableusingthescatter plot.

negative.

Explanation

Inthescatter plot, higher valuesofthereturnonstock Aareassociated with higher valuesofthereturnonthe market, i.e. a positive

correlation betweenthetwo variables.

Ananalystisexaminingtherelationship betweentworandom variables, RCRANTZ and GSTERN. He performsalinearregressionthat

producesanestimateoftherelationship:

RCRANTZ = 61.4 − 5.9GSTERN

Which interpretationofthisregressionequationisleastaccurate?

The intercept term implies that if GSTERN is zero, RCRANTZ is 61.4.

The covarianceofRCRANTZ and GSTERN isnegative.

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Question #59 of 120

QuestionID:461421

Question #60 of 120

QuestionID:461467

Question #61 of 120

QuestionID:461483

ᅞ A) ᅚ B) ᅞ C) Explanation

Theslope coefficientinthisregressionis -5.9. This meansaoneunitincreaseof GSTERN suggestsa decreaseof 5.9 unitsof RCRANTZ. Theslope coefficientisthe covariancedivided by the varianceoftheindependent variable. Since variance (asquaredterm) must be positive, anegativeslopeterm impliesthatthe covarianceisnegative.

Ron James, CFA, computedthe correlation coefficientfor historicaloil pricesandtheoccurrenceofaleap yearand hasidentifieda statistically significantrelationship. Specifically, the priceofoildeclinedevery fourth calendar year, allotherfactors held constant. James hasmostlikely identified which ofthefollowing conditionsin correlationanalysis?

Positive correlation.

Spurious correlation.

Outliers.

Explanation

Spurious correlationoccurs whentheanalysiserroneously indicatesalinearrelationship betweentwo variables whennoneexists. There isnoeconomic explanationforthisrelationship;thereforethis would be classifiedasspurious correlation.

Themostappropriate measureofthedegreeof variability oftheactualY-valuesrelativetotheestimatedY-valuesfrom aregression equationisthe:

sum of squared errors (SSE). standarderroroftheestimate (SEE).

coefficientofdetermination (R).

Explanation

TheSEE isthestandarddeviationoftheerrortermsintheregression, andisanindicatorofthestrength oftherelationship betweenthe dependentandindependent variables. TheSEE will below iftherelationship isstrong, and conversely will be high iftherelationship is weak.

A variable Y isregressedagainstasingle variable X across24observations. The valueoftheslopeis1.14, andthe constantis1.3. The mean valueof X is1.10, andthe mean valueof Y is2.67. Thestandarddeviationofthe X variableis1.10, andthestandarddeviationof

the Y variableis2.46. Thesum ofsquarederrorsis 89.7. Foran X valueof1.0, whatisthe 95% confidenceintervalforthe Y value?

−1.68 to 6.56.

−1.83to6.72.

0.59 to4.30.

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Question #62 of 120

QuestionID:461426

Question #63 of 120

QuestionID:461505

ᅞ A) ᅚ B) ᅞ C) Explanation

Firstthestandarderroroftheestimate must be calculated-itisequaltothesquarerootofthe meansquarederror, which isequaltothe

sum ofsquarederrorsdivided by thenumberofobservations minus2 = (89.7 / 22) = 2.02. The varianceofthe predictionisequalto:

= 2.06

The prediction valueis1.3 + (1.0 × 1.14) = 2.44. Thet-valuefor22degreesoffreedom is2.074. Theendpointsoftheintervalare2.44 ± 2.074 × 2.06 = −1.83and6.72.

Supposethe covariance between Y and X is10, the varianceof Y is25, andthe varianceof X is64. Thesamplesizeis30. Usinga 5% levelofsignificance, which ofthefollowingstatementsismostaccurate? Thenull hypothesisof:

no correlation is rejected.

no correlation cannot berejected.

significant correlationisrejected.

Explanation

The correlation coefficientisr = 10 / (5 × 8) = 0.25. Theteststatistic ist = (0.25 × √28) / √(1 − 0.0625) = 1.3663. The criticalt-valuesare ± 2.048. Therefore, we cannotrejectthenull hypothesisofno correlation.

Considerthefollowinganalysisof variance (ANOVA)table:

Source Sum ofsquares Degrees offreedom Meansquare

Regression 556 1 556

Error 679 50 13.5

Total 1,235 51

TheR forthisregressionis:

0.55.

0.45.

0.82.

Explanation

R = RSS/SST = 556/1,235 = 0.45.

1/2

2

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Question #64 of 120

QuestionID:461406

Question #65 of 120

QuestionID:461401

Question #66 of 120

QuestionID:461463

ᅞ A) ᅚ B)

Rafael Garza, CFA, is consideringthe purchaseofABCstock fora client's portfolio. Hisanalysisincludes calculatingthe covariance betweenthereturnsofABCstock andtheequity marketindex. Which ofthefollowingstatementsregarding Garza'sanalysisismost

accurate?

A covariance of +1 indicates a perfect positive covariance between the two variables.

The covariance measuresthestrength ofthelinearrelationship betweentwo variables.

Theactual valueofthe covarianceisnot very meaningful becausethe measurementis very sensitivetothescaleofthetwo variables.

Explanation

Covarianceisastatistical measureofthelinearrelationship oftworandom variables, buttheactual valueisnot meaningful becausethe measureisextremely sensitivetothescaleofthetwo variables. Covariance canrangefrom negativeto positiveinfinity.

Which ofthefollowingstatementsregardingscatter plotsismostaccurate? Scatter plots:

are used to examine the third moment of a distribution (skewness).

illustratethescatteringsofasingle variable.

illustratetherelationship betweentwo variables.

Explanation

Ascatter plotisa collectionof pointsonagraph whereeach pointrepresentsthe valuesoftwo variables. They areusedtoexaminethe relationship betweentwo variables.

Aregression betweenthereturnsonastock anditsindustry index returnsgivesthefollowingresults:

C

o

efficien

t

S

t

an

d

a

r

d

Err

o

r t

-va

l

u

e

Inter

c

e

p

t

2 .

1

2 .

01

1 .

04 Industr

y

Inde

x

1 .9

0 .

31

6 .

13

Thet-statistic critical valueatthe0.01levelofsignificanceis2.58 Standarderrorofestimate = 15.1

Correlation coefficient = 0.849

Theregressionstatistics presentedindicatethatthedispersionofstock returnsabouttheregressionlineis:

72.10.

(25)

ᅞ C)

Question #67 of 120

QuestionID:461409

Question #68 of 120

QuestionID:461476

Question #69 of 120

QuestionID:461438

63.20.

Explanation

Thestandarddeviationofthedifferences betweentheactualobservationsandthe projectionofthoseobservations (theregressionline)is calledthestandarderroroftheestimate. Thestandarderroroftheestimateistheunsystematic risk.

Which ofthefollowingstatementsabout covarianceand correlationisleastaccurate?

A zero covariance implies a zero correlation.

Thereisnorelation betweenthesignofthe covarianceandthe correlation.

The covarianceand correlationarealwaysthesamesign, positiveornegative.

Explanation

Theothertwo choicesareaccuratestatements. The correlationistheratioofthe covariancetothe productofthestandarddeviationsof thetwo variables. Therefore, the covarianceandthe correlation havethesamesign, anda zero covarianceimpliesa zero correlation.

Themostappropriateteststatistic toteststatisticalsignificanceofaregressionslope coefficient with 45 observationsand2independent variablesisa:

one-tail t-statisticwith 42 degrees of freedom.

two-tailt-statistic with 42degreesoffreedom.

one-tailt-statistic with 43degreesoffreedom.

Explanation

df = n − k − 1 = 45 − 2 − 1

Which ofthefollowingisleastlikelyanassumptionoflinearregression?

The residuals are normally distributed.

Theindependent variableis correlated with theresiduals.

The varianceoftheresidualsis constant.

Explanation

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Question #70 of 120

QuestionID:461450

Question #71 of 120

QuestionID:461419

Question #72 of 120

QuestionID:461494

ᅞ A)

If X and Y are perfectly correlated, regressing Y onto X willresultin which ofthefollowing:

the regression line will be sloped upward.

thealpha coefficient will be zero.

thestandarderrorofestimate will be zero.

Explanation

If X and Y are perfectly correlated, allofthe points will plotontheregressionline, sothestandarderroroftheestimate will be zero. Note thatthesignofthe correlation coefficient willindicate which way theregressionlineis pointing (there can be perfectnegative correlation slopingdownwardas wellas perfect positive correlationslopingupward). Alphaistheinterceptandisnotdirectly relatedtothe

correlation.

Thetable below showsasampleofreturnsontwosecurities:

Period 1 2 3 4 Mean

Security P 0.2% 0.5% 1.1% −0.6% 0.3%

Security Q −0.3% 0.9% 1.5% −0.5% 0.4%

Thesample covariance betweenthetwosecurities' returnsis closestto:

0.78.

0.62.

0.47.

Explanation

Period ₁ ₂ ₃ ₄ _S um

−0.1 0.2 0.8 −0.9

−0.7 0.5 1.1 −0.9

0.07 0.10 0.88 0.81 1.86

Adependent variableisregressedagainstasingleindependent variableacross100observations. The meansquarederroris2.807, and the meanregressionsum ofsquaresis117.9. Whatisthe correlation coefficient betweenthetwo variables?

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(28)

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ᅞ A)

ᅚ B)

ᅞ C)

Question #78 of 120

QuestionID:461415

Question #79 of 120

QuestionID:461410

ᅞ A) ᅞ B)

ᅚ C)

Question #80 of 120

QuestionID:461484

explainthereturnonequity, includingfinancialleverageand capitalexpenditures. In his model:

return on equity is the independent variable, and financial leverage and capital expenditures are dependent variables

returnonequity isthedependent variable, andfinancialleverageand capitalexpendituresare independent variables.

returnonequity, financialleverage, and capitalexpendituresareallindependent variables.

Explanation

Thedependent variableisreturnonequity. Thisis what he wantstoexplain. The variables heusestodotheexplaining (i.e., the independent variables)arefinancialleverageand capitalexpenditures.

The Y variableisregressedagainstthe X variableresultinginaregressionlinethatis horizontal with the plotofthe pairedobservations widely dispersedabouttheregressionline. Basedonthisinformation, which statementismostlikelyaccurate?

X is perfectlypositivelycorrelated to Y.

The correlation between X and Y is closeto zero.

TheR ofthisregressionis closeto100%.

Explanation

Perfect correlation meansthatalltheobservationsfallontheregressionline. AnR of100% means perfect correlation. Whenthereisno correlation, theregressionlineis horizontal.

Which ofthefollowingstatementsregardingthe coefficientofdeterminationisleastaccurate? The coefficientofdetermination:

cannot decrease as independent variables are added to the model.

isthe percentageofthetotal variationinthedependent variablethatisexplained by the independent variable.

may rangefrom −1to +1.

Explanation

Inasimpleregression, the coefficientofdeterminationis calculatedasthe correlation coefficientsquaredandrangesfrom 0to +1.

Given: Y = 2.83 + 1.5X

Whatisthe predicted valueofthedependent variable whenthe valueofanindependent variableequals2?

2

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Question #81 of 120

QuestionID:461434

Question #82 of 120

QuestionID:461413

ᅚ A) ᅞ B)

5.83

-0.55

2.83

Explanation

Y = 2.83 + (1.5)(2)

= 2.83 + 3

= 5.83

Paul Frank isananalystfortheretailindustry. Heisexaminingtheroleoftelevision viewing by teenagersonthesalesofaccessory stores. Hegathereddataandestimatedthefollowingregressionofsales (in millionsofdollars)onthenumberof hours watched by teenagers (in hours per week):

Sales = 1.05 + 1.6TV

Which ofthefollowingisthemostaccurateinterpretationoftheestimatedresults? IfTV watching:

goes upby one hour per week, sales of accessories increase by $1.6 million.

changes, no changeinsalesisexpected.

goesup by one hour per week, salesofaccessoriesincrease by $1.60.

Explanation

Theinterpretationoftheslope coefficientisthe changeinthedependent variable (salesin millionsofdollars)foragivenone-unit change intheindependent variable (TV hours per week). Theinterceptof1.05 meansthat1.05 milliondollars worth ofaccessoriesisexpectedto besoldevenifTV watchingis zero.

Asampleof paired pointsAandBisshown below. Whatisthe covariance betweenthe valuesofAandB?

S

a

mpl

e

A

B

1 1 2

2

4

5

3

9

7

4 11 10

5 14 12

20.55.

29.76.

(31)

ᅞ C)

Questions #83-88 of 120

7.80.

Explanation

S

a

mpl

e

A

-

m

ean

(

A

)

B

-

m

ean

(B)

P

r

od

u

c

t

1

1 −

6 .8

2 −5.

2

3

5.

36

2

4 −

3 .8

5 −

2 .

2

8.

36

3

9

1 .

2

7 −

0 .

2 −

0 .

24

4

11

3 .

2

10

2 .8

8.9

6

5

14

6 .

2

12

4 .8

2

9.

76 m

ean

7 .8

7 .

2 Su

m

8

2 .

2

Cov = 82.20 / (5 - 1) = 20.55

Cynthia JonesisDirectorofMarketingat VancouverIndustries, alarge producerofathletic apparelandaccessories. Approximately three yearsago, Vancouverexperiencedincreased competitioninthe marketplace, and consequently salesforthat yeardeclinednearly 20%.

Atthattime, Jones proposedanew marketing campaignforthe company, aimedat positioning Vancouver's productlinestowarda youngertargetaudience. Although thenew marketingeffort wassignificantly more costly than previous marketing campaigns, Jones

assured hersuperiorsthattheresultingincreaseinsales would morethan justify theadditionalexpense. Jones wasgivenapprovalto proceed with theimplementationof her plan.

Three yearslater, in preparationforanupcomingshareholders meeting, theCEO of Vancouver hasasked Jonesforanevaluationofthe marketing campaign. Sales haveincreasedsincetheinceptionofthenew marketing campaignnearly three yearsago, buttheCEO is questioning whethertheincreaseisduetothe marketingexpendituresor can beattributedtootherfactors. Jonesisexaminingthe

followingdataonthefirm'saggregaterevenueand marketingexpenditureoverthelast10 quarters. Jones planstodemonstratethe effectivenessof marketingin boostingsalesrevenue. She choosestoutilizeasimplelinearregression model. Theoutputisasfollows:

A

gg

r

ega

t

e

R

even

u

e

(Y)

Ad

ve

rt

i

s

ing

E

x

p

en

d

i

tur

e

(

X

)

Y

X

Y

X

300

7 .5

9

0 ,

000

2 ,

2

5

0

5

6 .

2

5

320

9.

0

102 ,

400

2 ,88

0

8

1 .

00

310

8.5

9

6 ,

100

2 ,

63

5

72 .

2

5

33

5

8.

2

112 ,

22

5

2 ,

747 67

.

24

3

5

0

9.

0

122 ,5

00

3 ,

1

5

0

8

1 .

00

400

8.5

160 ,

000

3 ,

400 72

.

2

5

430

10 .

0

1

8

4 ,9

00

4 ,

300 100

.

00

3

9

0

10 .5

1

5

2 ,

100

4 ,

0

95

110 .

2

5

3

8

0

9.

0

144 ,

400

3 ,

420

8

1 .

00

430

11 .

0

1

8

4 ,9

00

4 ,

730 121

.

00 T

O

TA

L

3 ,

64

5

9

1 .

2

1 ,

34 9,5

2

5

33 ,

607

8

42 .

24

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Question #

8 3 of 120

Question ID: 461444

Question #

8 4 of 120

Question ID: 461445

Question #

85 of 120

Question ID: 461446

Slope coefficient = 34.74 Standard error of slope coefficient = 9.9166

2 9313 Standard error of intercept =

9

2 .

2 8401

2

8 ANOVA

D

f

SS

MS

Regression 1 1

2 ,665.1

2 5760 1

2 ,665.1

2

576 Residual

8 8,

2

57.374

2

38 1,03

2 .17178

Total

9

2 0,9

22 .5

Jonesdiscusses herfindings with her marketresearch specialist, Mira Nair. Nairtells Jonesthatsheshould check her modelfor

heteroskedasticity. Sheexplainsthatinthe presenceof conditional heteroskedasticity, the model coefficientsandt-statistics will be

biased.

Forthe questions below, assumeat-valueof2.306.

Which ofthefollowingisclosestto theupperlimitofthe 95% confidenceintervalfortheslope coefficient?

57.61.

111.72.

62.84.

Explanation

Upper Limit= coefficient + (2.306 x standarderrorofthe coefficient)

= 34.74 + (2.306 x 9.917) = 57.61 (Study Session3, LOS11.f)

Which ofthefollowingisclosestto thelowerlimitofthe 95% confidenceintervalfortheslope coefficient?

11.87.

72.84.

12.24.

Explanation

Lower Limit = Coefficient - (2.306 x Standard Errorofthe coefficient)

= 34.74 - (2.306 x 9.917)

= 34.74 - 22.87 = 11.87

(Study Session3, LOS11.f)

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Question #

89 of 120

Question ID: 461440

Question #

9 0 of 120

Question ID: 461424

Question #

9 1 of 120

Question ID: 461402

The computed valueofthe F-Statistic = MSR/MSE = 12,665.12576 / 1,032.17178 = 12.27, whereMSRandMSE arefrom theANOVA table. (Study Session3, LOS11.j)

Linearregressionis basedonanumberofassumptions. Which ofthefollowingisleastlikely anassumptionoflinearregression?

Values of the independent variable are not correlated with the error term.

Thereisatleastsome correlation betweentheerrortermsfrom oneobservationtothenext.

The varianceoftheerrortermseach periodremainsthesame.

Explanation

When correlation (betweentheerrortermsfrom oneobservationtothenext)exists, autocorrelationis present. Asaresult, residualterms

arenotnormally distributed. Thisisinconsistent with linearregression.

Supposethe covariance between Y and X is0.03andthatthe varianceof Y is0.04andthe varianceof X is0.12. Thesamplesizeis30. Usinga 5%levelofsignificance, which ofthefollowingismostaccurate? Thenull hypothesisof:

no correlation is not rejected.

significant correlationisrejected.

no correlationisrejected.

Explanation

The correlation coefficientisr = 0.03 / (√0.04 * √0.12) = 0.03 / (0.2000 * 0.3464) = 0.4330.

Theteststatistic ist = (0.4330 × √28) / √(1 − 0.1875) = 2.2912 / 0.9014 = 2.54.

We canfindthe criticalt-valuesfrom at-table, usingdf = 28 andtwo-tailed 95%significance (recallthatforat-testthedegreesof

freedom = n − 2).

The criticalt-valuesare ± 2.048. Therefore, werejectthenull hypothesisofno correlation.

Ifthe correlation betweentwo variablesis −1.0, thescatter plot wouldappearalonga:

a curved line running from southwest to northeast.

straightlinerunningfrom southwesttonortheast.

straightlinerunningfrom northwesttosoutheast.

Explanation

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Questions #

9

2 -9

7 of 120

astraightlinerunningfrom northwesttosoutheast.

RebeccaAnderson, CFA, hasrecently accepteda positionasafinancialanalyst with EagleInvestments. She will beresponsiblefor

providinganalyticaldatato Eagle's portfolio managerforseveralindustries. Inaddition, she willfollow each ofthe major public corporations withineach ofthoseindustries. Asoneof herfirstassignments, Anderson has beenaskedto provideadetailedreporton

oneof Eagle's currentinvestments. She wasgiventhefollowingdataonsalesforCompany XYZ, the makeroftoilettissue, as wellas toilettissueindustry sales ($ millions). She has beenaskedtodevelop a modeltoaidinthe predictionoffuturesaleslevelsforCompany XYZ. She proceeds by recallingsomeofthe basic conceptsofregressionanalysisshelearned whileshe was preparingfortheCFA

exam.

Y

ea

r

I

n

d

ustry

S

a

l

e

s

(X

)

C

o

mp

an

y

S

a

l

e

s

(Y

)

(X

-

X

)

1 $3,000

$750

84,100

2 $3,

2

00 $800

8,100

3 $3,400

$850

1

2 ,100

4 $3,350

$8

2

5 3,600

5 $3,500

$900

44,100

Totals

$16,450

$4,1

2

5

15

2 ,000

CoefficientEstimates

Predictor Coefficient Stand.Error of

theCoefficient t-statistic

Intercept -94.88 32.97 ??

Slope (Industry Sales) 0.2796 0.0363 ??

Analysis ofVarianceTable(ANOVA)

Source df

(Degrees ofFreedom)

SS

(Sum of Squares)Mean Square(SS/df)F-statistic

Regression 1 (#ofindependent variables) 11,899.50 (SSR) 11,899.50 (MSR) 59.45

Error 3 (n-2) 600.50 (SSE) 200.17 (MSE)

Total 4 (n-1) 12,500 (SSTotal)

Abbreviated Two-tailed t-table

df 10% 5%

2 2.920 4.303

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Questions #101

-

106 of 120

Question #101 of 120

Question ID: 485550

Question #102 of 120

Question ID: 485551

Milky Way, Inc. isalarge manufacturerof children'stoysandgames basedinthe UnitedStates. Their products have high name brand recognition, and have beensoldinretailoutletsthroughoutthe UnitedStatesfornearly fifty years. Thefounding managementteam was

boughtout by agroup ofinvestorsfive yearsago. Thenew managementteam, led by RussellStepp, decidedthatMilky Way shouldtry

toexpanditssalesintothe Western European market, which hadnever beentapped by theformerowners. UnderStepp'sleadership,

additional personnelare hiredintheResearch andDevelopmentdepartment, andanew marketing planspecific tothe European marketis implemented. Beinganew playerinthe European market, Stepp knowsthatit willtakeseveral yearsforMilky Way toestablish its brand nameinthe marketplace, andis willingto maketheexpendituresnow inexchangeforincreasedfuture profitability.

Now, five yearsafterenteringthe European market, Stepp isreviewingtheresultsof his plan. Salesin Europe haveslowly butsteadily

increasedoversinceMilky Way'sentranceintothe market, but profitability seemsto haveleveledout. Stepp decidesto hirea consultant, Ann Hays, CFA, toreview andevaluatetheir Europeanstrategy. Oneof Hays' firsttasksonthe job isto perform aregressionanalysison Milky Way's Europeansales. Sheisseekingtodetermine whethertheadditionalexpendituresonresearch anddevelopmentand

marketingforthe European marketshould be continuedinthefuture.

Hays begins by establishingarelationship betweenthe EuropeansalesofMilky Way (in millionsofdollars)andthetwoindependent

variables, thenumberofdollars (in millions)spentonresearch anddevelopment (R&D)and marketing (MKTG). Baseduponfive yearsof

monthly data, Hays constructsthefollowingestimatedregressionequation:

Estimated Sales = 54.8

2 + 5.97 (MKTG) + 1.45 (R&D)

Additionally, Hays calculatesthefollowingregressionestimates:

C

o

effi

c

ien

t

S

t

an

d

a

r

d E

rr

o

r

Intercept

54.8

2

3.165 MKTG

5.97

1.8

2

5 R&D

1.45

0.987

Hays beginstheanalysis by determiningif both oftheindependent variablesarestatistically significant. Totest whethera coefficientis

statistically significant meanstotest whetheritisstatistically significantly differentfrom:

zero.

theuppertail critical value.

slope coefficient.

Explanation

The magnitudeofthe coefficientrevealsnothingabouttheimportanceoftheindependent variableinexplainingthedependent variable.

Therefore, it must bedeterminedifeach independent variableisstatistically significant. Thenull hypothesisisthattheslope coefficient foreach independent variableequals zero. (Study Session3, LOS 9.a)

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Question #10

8 of 120

Question ID: 461439

(43)

Question #111 of 120

Question ID: 461412

Question #112 of 120

Question ID: 461493

Question #113 of 120

Question ID: 461431

ᅚ A)

Which term isleastlikelytoapply toaregression model?

Goodness of fit.

Coefficientof variation.

Coefficientofdetermination.

Explanation

Goodnessoffitand coefficientofdeterminationaredifferentnamesforthesame concept. The coefficientof variationisnotdirectly part

ofaregression model.

Dan Gates, CFAisforecasting priceelasticity ofdemandfor GMX Inc's products. Gatesused monthly revenuesforthe pastfour years asthedependent variable ($ millions)and price perunitastheindependent variable. Theresultsareshown below.

Sales = 23.45 − 0.6Price

Standarderror (intercept) = 10.22

Standarderror (slope) = 0.03

Standarderrorofestimate = 8.32

Standarderrorofforecast = 8.93

The 95% confidenceintervalfor predicted valueof monthly salesgiven price was$2.00 perunitisclosestto:

$6 million to $39million.

$4 millionto$40 million.

$12 millionto$33 million.

Explanation

The predicted valueofsales when price = $2.00is23.45 − 0.6(2) = $22.25 million

Thereare4 years × 12 = 48 monthly observations. D.O.F = n−2 = 46

t (95%, 46, 2-tailed) = 2.013

Forthe confidenceintervalof predicted value, makesuretousethestandarderrorofforecast

95% confidenceinterval = 22.25 ± (2.013)(8.93)or$4.27to$40.23 million

The purposeofregressionisto:

explain the variation in the dependent variable.

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ᅞ B) ᅞ C)

Question #114 of 120

Question ID: 461441

Question #11

5 of 120

Question ID: 461416

Question #116 of 120

Question ID: 461506

getthelargestR possible.

explainthe variationintheindependent variable.

Explanation

Thegoalofaregressionistoexplainthe variationinthedependent variable.

SeraSmith, aresearch analyst, hada hunch thatthere wasarelationship betweenthe percentage changeinafirm'snumberof

salespeopleandthe percentage changeinthefirm'ssalesduringthefollowing period. Smith ranaregressionanalysisonasampleof 50 firms, which resultedinaslopeof0.72, aninterceptof +0.01, andanR valueof0.65. Basedonthisanalysis, ifafirm madeno changes inthenumberofsales people, what percentage changeinthefirm'ssalesduringthefollowing perioddoestheregression model predict?

+1.00%.

+0.65%.

+0.72%.

Explanation

Theslopeoftheregressionrepresentsthelinearrelationship betweentheindependent variable (the percent changeinsales people)and thedependent variable, whiletheinterceptrepresentsthe predicted valueofthedependent variableiftheindependent variableisequalto

zero. Inthis case, the percentage changeinsalesisequalto:0.72(0) + 0.01 = +0.01.

ThomasManx isattemptingtodeterminethe correlation betweenthenumberoftimesastock quoteisrequestedon hisfirm's website andthenumberoftrades hisfirm actually processes. He hasexaminedsamplesfrom severaldaystradingand quotesand has determinedthatthe covariance betweenthesetwo variablesis 88.6, thestandarddeviationofthenumberof quotesis18, andthe standarddeviationofthenumberoftrades processedis14. BasedonManx'ssample, whatisthe correlation betweenthenumberof

quotesrequestedandthenumberoftrades processed?

0.18.

0.35.

0.78.

Explanation

Correlation = Cov (X,Y) / (Std. Dev. X)(Std. Dev. Y) Correlation = 88.6 / (18)(14) = 0.35

Which statementismostaccurate? Assumea 5%levelofsignificance. The F-statistic is:

2

(45)