Chapter14 Multiple Regression and Correlation Analysis

Chapter 14 Multiple Regression and Correlation Analysis True/False

1. Multiple regression analysis analysis is used when two or more independent variables are used to predict a value of a single dependent variable. Difficulty: Difficult y: Easy Goal: 1 AA!": A! Answer: True

#. Multiple regression analysis analysis is used when one independent variable is used to predict values values of two or more dependent variables. Difficulty: Difficulty: Easy Goal: 1 Answer: $alse

%. The values of b1& b# and b% in a multiple regression e'uation are called the net regression coefficients.

Answer: True

Difficulty: Difficult y: Easy

Goal: 1

(. A net regression coefficient& coefficient& b%& indicates the change in the predicted value for a unit change in X 3 when all other X i variables are held constant.

Answer: True


Goal: 1

). Multiple regression analysis analysis e*amines the relationship of several dependent dependent variables on the independent variable. Difficulty: Difficulty: Medium Goal: 1 Answer: $alse

+. A multiple regression e'uation e'uation defines the relationship between between a dependent variable and a set of independent variables in the form of an e'uation. Difficulty: Difficult y: Easy Goal: 1 Answer: True AACSB: AS

,. -n multiple regression analysis& analysis& a and b1 are sample statistics that estimate the population parameters&

 and / i . Answer: True


Goal: 1

0. The coefficient of multiple multiple determination reports the strength strength of the association between a dependent variable and a set of independent variables. Difficulty: Difficult y: Easy Goal: % Answer: True

Test Test Bank, Chapter#%0 14

. -n a multiple regression analysis analysis with two independent variables& the multiple multiple standard error of estimate measures the variation of the dependent variable about a regression plane. Difficulty: Difficult y: Easy Goal: % Answer: True

12. A coefficient of multiple determination determination could be e'ual to 32.,+. Difficulty: Difficulty: Easy Goal: % Answer: $alse

11. A coefficient of multiple determination e'ualing e'ualing 32. shows that the dependent variable is inversely related to a set of independent variables. variables. Difficulty: Difficulty: Easy Goal: % Answer: $alse

1#. Multiple R # measures the proportion proportion of e*plained variation variation relative to total total variation. Difficulty: Difficult y: Easy Goal: % AA!": A! Answer: True

1%. The multiple multiple coefficient of of determination& determination& R # & reports the proportion of the variation in Y that that is not e*plained by the variation in the set of independent variables. variables. Difficulty: Difficulty: Medium Goal: % Answer: $alse

1(. A correlation matri* shows individual correlation correlation coefficients for all pairs of variables. Difficulty: Difficult y: Easy Goal: , Answer: True

1). A correlation matri* can be used to assess multicollinearity between independent variables. Difficulty: Difficult y: Easy Goal: , AA!": A! Answer: True

1+. A correlation matri* can be used to assess homoscedasticity between independent variables. Difficulty: Difficulty: Easy Goal: , Answer: $alse

1,. To test the global hypothesis hypothesis in multiple regression analysis& analysis& a t4statistic is used. Difficulty: Difficulty: Easy Goal: # Answer: $alse

10. To test the global hypothesis hypothesis in multiple regression analysis& analysis& an $4statistic is used. Difficulty: Difficult y: Easy Goal: # Answer: True AACSB: AS

1. A dummy variable is added to the regression e'uation to control control for error. Difficulty: Difficulty: Easy Goal: 0 Answer: $alse

#%

Test Test Bank, Chapter 14

#2. -f a dummy variable for gender is included in a multiple regression analysis& analysis& 5male5 would be coded as 1 and 5female5 would be coded as #. #. Difficulty: Difficulty: Easy Goal: 0 Answer: $alse

#1. Autocorrelation Autocorrelation often happens when data has been collected over over periods of time. Difficulty: Difficult y: Easy Goal: , Answer: True

9  is different for different values ##. 6omoscedasticity occurs occurs when the variance of the residuals 7 8 3 Y 9. of Y Difficulty: Easy Goal: + AA!": A! Answer: $alse

#%. -n multiple regression analysis& analysis& a residual is the difference between the value of an independent variable and its corresponding dependent variable value. Difficulty: Difficulty: Easy Goal: + Answer: $alse

#(. -n multiple regression analysis& analysis& a residual is the difference between the value of a dependent variable& 9. 8& and its predicted value& Y Difficulty: Difficult y: Easy Goal: + Answer: True

Multiple Choice

#). -n multiple regression analysis& analysis& residual analysis is used to test the re'uirement that 9 A the variation in the the residuals is the same same for all fitted values of Y " the independent variables variables are the direct cause of of the dependent variable  the number of independent independent variables included in the analysis is correct correct D prediction error is minimi;ed Difficulty: Difficulty: Medium Goal: + Answer: A AACSB: AS

#+. A valid multiple regression analysis analysis assumes or re'uires that A the dependent variable variable is measured using an ordinal& ordinal& interval& or ratio scale scale " the residuals follow follow an $4distribution $4distribution  the independent variables and the dependent dependent variable have a linear relationship D the observations observations are autocorrelated autocorrelated Difficulty: Difficulty: Medium Goal: 1 Answer: 

Statistical Techniques in Business & Economics, in!"#archal"$athen, in!"#archal"$athen, 13"e

#(2

#,. 6ow is the degree of association between a set of independent independent variables and a dependent variable measured< A onfidence intervals. " Autocorrelation  oefficient of of multiple determination D !tandard error error of estimate estimate Difficulty: Difficulty: Medium Goal: % AA!": A! Answer: 

#0. -n a multiple multiple regression regre ssion A=>?A A=>?A table& e*plained e*plaine d variation is represented by A the regression regression sum of s'uares " the total sum of s'uares s'uares  the regression regression coefficients coefficients D the correlation correlation matri* Difficulty: Medium Goal: # AA!": A! Answer: A

#. -f the coefficient of multiple determination determination is 2.01& what percent of variation is not e*plained< e*plained< A 1@ " 2@  ++@ D 01@ Goal: % Answer: A

%2. -n multiple regression analysis& analysis& testing the global null hypothesis hypothesis that the multiple regression coefficients are all ;ero is based on A a % statistic statistic " a t statistic  a  statistic D binomial distribution Difficulty: Difficulty: Easy Goal: # Answer: 

%1. hat is the the range of values for multiple R< A 3122@ to 3122@ inclusive " 3122@ to 2@ inclusive inclusive  2@ to B122@ inclusive inclusive D Cnlimited range Difficulty: Difficulty: Easy Goal: % Answer: 

%#. hen does multicollinearity multicollinearity occur in a multiple regression analysis< analysis< A The dependent variables are highly highly correlated " The independent independent variables are are minimally correlated correlated  The independent independent variables are are highly correlated correlated D The independent independent variables have have no correlation correlation Difficulty: Difficulty: Medium Goal: , Answer: 

#(1


%%. -n multiple regression analysis& analysis& when the independent variables are highly correlated& correlated& this situation is called . . A Autocorrelation " Multicollinearity  6omoscedasticity D curvilinearity Difficulty: 6ard Goal: , AA!": A! Answer: "

%(. -n the general multiple regression e'uation e'uation which of the following variables represents represents the Y intercept< A b1 " *1

9  Y D a

Answer: D

Difficulty: Difficulty: Easy

Goal: 1

%). -f there are four independent variables in a multiple regression regression e'uation& there are also four A Y 4intercepts. 4intercepts. " regression coefficients.  dependent variables. D constant terms. Difficulty: Difficulty: Easy Goal: 1 Answer: "

%+. hat does the multiple multiple standard error of estimate estimate measure< 9 for a change in X 1 A hange in Y " The 5error5 or variability variability in predicting 8  The regression mean s'uare s'uar e error in the A=>?A A=>?A table D Amount of e*plained variation variation Difficulty: Difficulty: Medium Goal: % Answer: "

%,. -f a multiple regression analysis is based on ten independent independent variables collected from a sample of 1#) observations& what will be the value of the denominator in the calculation of the multiple standard error of estimate< A 1#) " 12  11( D 11) Difficulty: Difficulty: Medium Goal: % Answer: 


#(#

%0. -f the correlation between the two independent independent variables of a regression analysis is 2.11 and each independent variable is highly correlated to the dependent variable& what does this indicate< A Multicollinearity Multicollinearity between these two independent independent variables " A negative relationship is not not possible  >nly one of the two independent variables will will e*plain a high percent of the variation D An effective effective regression e'uation Difficulty: Difficulty: Easy Goal: , Answer: D

%. -f the correlation between the two independent independent variables of a regression analysis is 2.11 and and each independent variable is highly correlated to the dependent variable& what does this indicate< A >nly one of the independent variables should should be used in the regression e'uation. " The independent independent variables are are strongly related. related.  Two Two separate regression e'uations e'uations are re'uired. D "oth independent variables variables should be used to predict the dependent variable. variable. Difficulty: Difficulty: Easy Goal: , Answer: D

(2. hat does the correlation matri* for a multiple regression regression analysis contain< A Multiple correlation coefficients " !imple correlation correlation coefficients coefficients  Multiple coefficients coefficients of of determination determination D Multiple standard standard errors of estimate Difficulty: Difficulty: Easy Goal: , Answer: "

(1. hat can we conclude if the global test of regression does not reect the null null hypothesis< A A strong relationship e*ists among the variables " =o relationship e*ists between between the dependent variable and any of the independent variables variables  The independent independent variables are are good predictors predictors D Good forecasts forecasts are possible Difficulty: Difficulty: Easy Goal: ( Answer: "

(#. hat can we conclude if the global test of regression reects the null hypothesis< hypothesis< A !trong correlations correlations e*ist among among the variables " =o relationship e*ists between between the dependent variable and any of the independent variables variables  At least one of the net regression coefficients coefficients is not e'ual to ;ero. D Good predictions predictions are not possible possible Difficulty: Difficulty: Easy Goal: ( Answer: 

(%. hat are the degrees of freedom freedom associated with the regression sum of s'uares< s'uares< A =umber of independent variables " 1  $4ratio D 7n 3 # Difficulty: Medium Goal: # AA!": A! Answer: A

#(%


((. hich of the following following is a characteristic characteristic of the  4distribution< 4distribution< A =ormally distributed " Fositively sewed  =egatively sewed D E'ual to the t4distribution t4distribution Difficulty: Difficulty: Medium Goal: ( Answer: " AACSB: CA

(). -n a regression analysis& three independent independent variables are used in the e'uation based on a sample of forty observations. observations. hat are the degrees of of freedom associated with with the  4statistic< 4statistic< A % and % " ( and (2  % and %+ D # and % Difficulty: Difficulty: Medium Goal: ( Answer: 

(+. 6ypotheses concerning concerning individual regression coefficients coefficients are tested using which statistic< statistic< A t'statistic " %'statistic #  χ 7chi4s'uare statistic D  Difficulty: Easy Goal: ) Answer: A

(,. The coefficient coefficient of determination measures measures the proportion of A e*plained variation variation relative to to total variation. variation. " variation due to to the relationship relationship among variables. variables.  error variation relative relative to total total variation. D variation due to regression. Difficulty: Difficulty: Medium Goal: % Answer: A

(0. hat happens as the scatter of data values about the regression regression plane increases< A !tandard error of estimate increases increases # " R decreases  71 3 R #  increases D Error sum of s'uares increases E All of the above are correct Difficulty: Difficult y: Medium Goal: % AA!": A! Answer: E Scrambling: Locked


#((

(. $or a unit change in the first independent variable with other other things being held constant& constant& what change

9 = ).# + +.% X − ,.1 X < can be e*pected in the dependent variable in the multiple regression e'uation Y 1 # A 3 ,.1 " B +.%  B ).# D B (.( Difficulty: Difficulty: Easy Goal: 1 Answer: "

)2. The best e*ample of a null hypothesis for a global test of a multiple regression regression model is: A 6 > : / 1 = / # = / % = / ( " 6 > : H 1 = H # = H % = H (  6 2 : /1 = 2 D -f $ is greater than than #2.22 then reect Difficulty: Easy Goal: ( Answer: A

)1. The best e*ample of an alternate hypothesis for a global test of a multiple regression regression model is: A 6 1 : / 1 = / # = / % = / ( " 6 1 : /1 ≠ / # ≠ / % ≠ / (  6 1 : =ot all the /I s are 2 D -f $ is less than #2.22 then then fail to reect reect Difficulty: Difficulty: Easy Goal: ( Answer: 

)#. The best e*ample of a null hypothesis for testing an individual individual regression coefficient coefficient is: A 6 > : / 1 = / # = / % = / ( " 6 > : H 1 = H # = H % = H (  6 2 : /1 = 2 D -f $ is greater than than #2.22 then reect Difficulty: Easy Goal: ) Answer: 

AA!": A!

9  are used to: )%. -n multiple regression regression analysis& residuals residuals 7 8 3 Y A Frovide a global test of a multiple regression model. model. " Evaluate multicollinearity multicollinearity  Evaluate homoscedasticity homoscedasticity D ompare two regression coefficients Difficulty: Difficulty: Easy Goal: + Answer: 

#()


)(. -n multiple regression& a dummy variable can be included in a multiple multiple regression model as A An additional additional 'uantitative 'uantitative variable " A nominal variable with with three or more values  A nominal variable with with only two values D A new regression coefficient Difficulty: Difficulty: Easy Goal: 0 Answer: 

)). Multiple regression analysis analysis is applied when analy;ing the relationship relationship between A An independent independent variable and several dependent dependent variables " A dependent variable and several independent independent variables  !everal dependent variables variables and several independent independent variables D !everal regression e'uations and a single sample sample Difficulty: Difficulty: Easy Goal: 1 Answer: "

Fill-in-the-Blank

)+. ?iolating ?iolating the need for successive observations observations of the dependent variable to be uncorrelated is called  . . Difficulty: Difficulty: Medium Goal: , Answer: autocorrelation

),. Multiple R # measures the proportion of . . Difficulty: Difficulty: Medium Goal: % Answer: e*plained variation

)0. -n multiple regression analysis& analysis& a variable whose possible outcomes are coded as a 515 or a 525 is called a7n   . Difficulty: Difficulty: Easy Goal: 0 Answer: dummy variable

). -f a dependent variable and one or more independent variables are inversely inversely related& what is the sign for the regression coefficients of the independent variables<  Difficulty: Difficulty: Easy Goal: 1 Answer: negative

+2. A fre'uent use of a correlation matri* is to chec for . . multicollinearity Difficulty: Difficulty: Easy Goal: , Answer: multicollinearity

+1. -n a multiple multiple regression regre ssion analysis A=>?A A=>?A table& what determines determine s the number of degrees of freedom associated with the the regression sum of s'uares< s'uares<   . Difficulty: Difficulty: Medium Goal: # Answer: the number of independent variables


#(+

+#. -f the null hypothesis& hypothesis& 6 2 : β ( = 2 & is not reected& what effect does the independent variable& X (& have when predicting the dependent variable<  Difficulty: Difficulty: Easy Goal: ) Answer: no effect

+%. hat is the proportion of total variation variation in the dependent variable that is e*plained by the independent variable for a multiple R # J 2.2<  Difficulty: Difficulty: Easy Goal: % Answer: 2@ or 2.2

9 J ).1 B #.# X 1 3 %.) X #& what will a unit increase in the +(. Given a multiple multiple linear regression regression e'uation Y independent variable& X #& & mean in the change of Y 9 assuming other things are held constant< 

Answer: 4%.)

Difficulty: Difficulty: Easy

Goal: 1

+). hen the variance of the differences between the the actual and the predicted values of the dependent variable are appro*imately the same& the variables are said to e*hibit  . . Difficulty: Difficulty: Medium Goal: + Answer: homoscedasticity

++. A method for selecting the best subset of variables in a multiple multiple regression e'uation is:  Answer: !tepwise Kegression Difficulty: Difficulty: Easy Goal:  AA!": A!

9 = a + b ( + b ( + b 7 ( ( & 7 ( (  is the  +,. -n the following following regression e'uation& Y 1 1 # # % 1 # 1 # Answer: -nteraction of * 1 and * #

Difficulty: Medium

Goal: 12

AA!": A!

Multiple Choice

Cse the following to answer 'uestions +04,1: The following correlations were computed as part of a multiple regression analysis that used education& ob& and age to predict income. income.

-n c o m e E d u c a tio n Lob A ge

#(,

-n c o m e 1 .2 2 2 2 .+ , , 2 .1 , % 2 .% + 

E d u c a tio n 1 .2 2 2 3 2 .1 0 1 2 .2 , %

Lo b

A ge

1 .2 2 2 2 .+ 0 

1 .2 2 2


+0. hat is this table called< A =et regression regression coefficients coefficients " oefficients of nondetermination nondetermination  Analysis Analysis of variance D orrelation matri* Difficulty: Difficulty: Medium Answer: D

Goal: ,

+. hich is the the dependent variable< variable< A -ncome " Age  Education D Lob Difficulty: Difficulty: Medium Answer: A

Goal: 1

,2. hich independent variable variable has the strongest association with with the dependent variable< A -ncome " Age  Education D Lob Difficulty: Difficulty: Medium Goal: , Answer: 

,1. hich independent variable variable has the weaest association with the dependent dependent variable< A -ncome " Age  Education D Lob Difficulty: Difficulty: Medium Goal: , Answer: D

Fill-in-the-Blank

Cse the following to answer 'uestions ,#4,0: -t has been hypothesi;ed that overall academic academic success for college freshmen as measured by grade point average 7GFA is a function of - scores ( N 1 ) & hours spent studying each wee ( N # ) & and oneIs high

9 = +. + 2.2)) X + 2.12, X + 2.20)% X . school average ( N % ) . !uppose the regression e'uation e'uation is: Y 1 # % The multiple standard error is +.%1% and R # J 2.0#+.

,#. hat is the predicted GFA for a student with an - of 120& %# hours spent studying stud ying per wee and a high school average of 0#<  Difficulty: Difficulty: Medium Goal: 1 Answer: %.1((+


#(0

,%. hat is the predicted GFA GFA if the - is 120& the number of hours spent studying is %2& and the high school average is 0#<  Difficulty: Difficulty: Medium Goal: 1 Answer: #.%2+

,(. Assuming Assuming other independent variables are held constant& what effect on the GFA will will there be if the numbers of hours spent studying per wee increases from %# to %+<  Difficulty: Difficulty: Medium Goal: 1 Answer: B2.(#0

,). $or which independent variable variable does a unit change have the least effect on GFA< GFA<  

Answer: high school average ( N % )

Difficulty: Difficulty: Medium

Goal: 1

,+. $or which independent variable variable does a unit change have the greatest effect on the GFA< GFA<   Difficulty: Difficulty: Medium Goal: 1 Answer: hours spent studying per wee ( N # )

,,. 6ow many dependent variables variables are in the regression regression e'uation<  Difficulty: Difficulty: Medium Goal: 1 Answer: one

,0. 6ow will a studentIs GFA be affected if an additional hour is spent studying each weenight< weenigh t<  Difficulty: Difficulty: Medium Goal: 1 Answer: increases by 2.)%)

Multiple Choice

Cse the following to answer 'uestions ,40,: Twenty4one Twenty4one e*ecutives in a large corporation were randomly selected for a study to determine the effect of several factors on annual salary 7e*pressed in O222Is. O222Is. The factors selected were age& seniority& seniority& years of college& number of company divisions they had been e*posed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output:

 o n s ta n t ! t d E r r o r o f Y e s t i m a t e # R = o . o f > b s e r v a t i o n s D e g re e s o f $ r e ed o m

X  o e f f i c i e n t s ! t d E rr o f  o e f

#(

# % .2 2 % , # . 1  % 2 . 1 ( 2 # 1 A ge 3 2 .2 % 1 2 .1 0 %

1 % ( 1 )

!en 2 .% 0 1 2 .1 ) 0

Educ 1 .( ) # 2 .% 0 ,

P o f D iv 3 2 .2 0  2 .) ( 1

Qevel % .) ) ( 2 .0 % %


,. hich one of the following following is the dependent dependent variable< A Age " !eniority  Qevel of of responsibility responsibility D Annual salary E E*perience in number of company company divisions Difficulty: Medium Goal: 1 AA!": A! Answer: D

Fill-in-the-Blank

02. rite out out the multiple regression regression e'uation. 

Answer:

9 = #%.22( − 2.2%1 X + 2.%01 X + 1.()# X − 2.20 X + %.))( X Y 1 # %. ( )

Difculty:

Medium Goal: 1 Kefer To: 1(2%

01. hich of the following has the most influence influence on salary 44 #2 years of seniority& ) years years of college or attaining )) years of age<  Difficulty: Difficulty: Medium Goal: % AA!": A! Answer: #2 years of seniority

0#. -f the other variables are held constant& how does an increase of one level of responsibility responsibility affect salary<  Difficulty: Difficulty: Medium Goal: 1 Answer: BO%&))(

0%. -f other variables are held constant& how does an increase in age of two years affect salary< salary<   Difficulty: Difficulty: Medium Goal: 1 Answer: 4O+#

0(. hat proportion of the total variation variation in salary is accounted for by the set of independent variables<  Difficulty: Difficulty: Medium Goal: % Answer: 1.(@

0). hat is the value of the denominator in the calculation of the multiple multiple standard error of estimate<  Difficulty: Difficulty: 6ard Goal: % Answer: 1)

0+. Test Test the hypothesis that the regression regression coefficient for age is e'ual to 2 at the 2.2) significance level.  Difficulty: Difficulty: 6ard Goal: ) Answer: d.f. J 1)& t J 4 2.#%0& t4critical J R #.1%1& fail to reect.


#)2

0,. Test Test the hypothesis that the regression regression coefficient for education is e'ual to 2 at the 2.2) significance significance level.  hypothesis and conclude that that Answer: d.f. J 1)& t J %.,)#& t4critical J ± #.1%1& reect the null hypothesis education and salary are significantly related. Difficulty: Difficulty: 6ard Goal: )

Cse the following to answer 'uestions 004%: The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. !uppose our econometric model resulted in the following following data.

Coe X 1 J A u t o m X # J A u t o m X % J A u t o m X ( J A u t o m X ) J A u t o m  o n s ta n t M u l t i p l e R

o b ile s o b ile s o b i le s o b i le s o b i le s

produ ced produ ced produced produced produced

th is y e a r la s t y e a r # y e a rs a g o % y e a rs a g o ( y e a rs a g o

) .2 2 2 .# ) 2 .+ , # .1 # % .( ( 3 ) 2 &2 2 2 2 .0 %

t'ratio 1 2 .( 2 .+ 1 .( # ., + .)

00. hich variable in the the model is the most significant significant predictor of of tire production<  Goal: ) Answer: N 1 Difculty: Medium

0. hat is the proportion of variation in tires produced produced by our predictor variables in the model<  Difficulty: Difficulty: Medium Goal: % Answer: 2.+

2. hich variable in the model is the least significant significant in predicting tire production< production<  Goal: ) Answer: N # Difculty: Medium

1. hat is the e'uation for our model<   

Answer: number of tires produced J 4 )2&222 + ).22 X 1 + 2.#) X # Difficulty: Difficulty: Medium

+ 2.+, X % +

#.1# X (

+ %.(( X )

Goal: 1

#. 6ow much does tire production increase for every thousand thousand cars produced two years ago<  Difficulty: Difficulty: Medium Goal: 1 Answer: +,2

%. 6ow much does tire production change for every thousand thousand cars produced three years ago<  Difficulty: Difficulty: Medium Goal: 1 Answer: #&1#2

#)1


Cse the following to answer 'uestions (4122: A real estate agent developed a model to relate a houseIs selling price 7 Y  to the area of floor space 7 X  and the area of floor space s'uared ( X # ) . The multiple regression regression e'uation for this this model is:

9 = 1#) − % X + X # Y 9 J selling price 7times O1222 where: Y J s'uare feet of floor space 7times 122 X J

(. hat is the the intercept 7a<   Difficulty: Difficulty: Medium Answer: O1#) 7in thousands

Goal: 1

). hat is the selling selling price of a house with 1222 1222 s'uare feet<  Difficulty: Difficulty: Medium Goal: 1 Answer: O1)&222

+. hat is the selling selling price of a house with 1)22 1)22 s'uare feet<  Difficulty: Difficulty: Medium Goal: 1 Answer: O%2)&222

,. hat is the selling selling price of a house with #222 #222 s'uare feet<  Difficulty: Difficulty: Medium Goal: 1 Answer: O(+)&222

0. hat is the difference in selling prices prices of a house with 1+22 s'uare feet and one with 1,22 s'uare feet<  Difficulty: Difficulty: 6ard Goal: 1 Answer: O%2&222 7O%+%&222 4 O%%%&222

. hat is the difference in selling prices prices of a house with 1,22 s'uare feet and one with 1022 s'uare feet<  Difficulty: Difficulty: 6ard Goal: 1 Answer: O%#&222 7O%)&222 4 O%+%&222

122. hat is the difference in selling prices prices of a house with 1+)2 s'uare feet and one with 1,)2 s'uare feet<  Difficulty: Difficulty: 6ard Goal: 1 Answer: O%1&222 7O%,0&,)2 4 O%(,&,)2


#)#

Multiple Choice

Cse the following to answer 'uestions 121412+: A manager at a local ban analy;ed the relationship between monthly salary and three independent variables: length of service 7measured in months& months& gender 7 2 J female& 1 J male and ob type 72 J clerical& clerical & 1 J technical. technical . The following A=>?A A=>?A summari;es summari; es the regression results:

A = > ? A K e g r es sio n K e s id u a l T o t al

- n te r c e p t ! e rv i ce G ender Lob

df % #+ #

!! 1 2 2 ( % ( + ., , 1 1 ( + 1 1 % ( .)  + # ( + ) ( 0 1 .% + ,

M ! % % ( , 0 # .# ) , ) +1  , .( 0( ( )

$ ) . +

 o e f f ic i e n t s , 0 ( . #  .1  # # # ., 0 4# 0 .# 1

! ta n d a r d E r ro r % # # .# ) % .# 2 0  .2 2 0  .+ 1

t ! ta t # .( ( # .0 , # .) 2 42 .% 1

F 4 v a lu e 2 .2 # 2 .2 1 2 .2 # 2 ., +

121. "ased on the A=>?A A=>?A and a 2.2) significance level& leve l& the global null hypothesis test of the multiple regression model A ill ill be reected and conclude that monthly salary is related to all of the independent independent variables " ill ill be reected and conclude that monthly salary is related to at least one of the independent independent variables.  ill ill not be be reected. D ill ill show a high multiple coefficient of determination determination Difficulty: Difficulty: Medium Goal: ( Answer: "

12#. "ased on the A=>?A& A=>?A& the multiple coefficient of determination determina tion is A ).),@ " ).%@  (2.,@ D cannot be computed Difficulty: Difficulty: Medium Goal: % Answer: 

12%. "ased on the hypothesis tests for the individual individual regression coefficients& coefficients& A All the regression regression coefficients are are not e'ual to ;ero. " 5ob5 is the only significant significant variable in the model model  >nly months of service and gender are significantly related related to monthly salary. salary. D 5service5 is the only significant significant variable in in the model Difficulty: Difficulty: Medium Goal: ) Answer: 

#)%


12(. -n the regression model& model& which of the following are dummy variables< A -ntercept " !ervice  !ervice and and gender gender D Gender and ob E !ervice& gender& gender& and and ob Difficulty: Easy Goal: 0 AA!": A! Answer: D

12). The results for the variable variable gender show that that A males average O###.,0 more more than females in monthly salary salary " females average O###.,0 more more than males in monthly salary salary  gender is not related to monthly monthly salary D Gender and months months of service are are correlated. Difficulty: Medium Goal: 0 Answer: A

12+. "ased on the hypothesis tests for individual individual regression coefficients& coefficients& A All regression coefficients should remain in the regression e'uation " "ased on the standard errors& the variable& service& should not be included in the regression e'uation.  "ased on the p4values& the variable& ob& should not be included in the regression regression e'uation. D The relationship relationship between monthly salary salary and gender is linear. linear. Answer:  Difficulty: Medium Goal  AA!": A!

Essay

12,. hat are the five assumptions assumptions of linear multiple multiple regression< Answer: 1 A linear relationship relationship between the dependent variable and the independent variables& # the

9 & % the residuals are normally variation of the residuals is the same for small and large values of Y distributed& ( the independent variables should not be correlated& ) The residuals are independent. Difficulty: Difficulty: Easy Goal: + 120. 6ow are scatter diagrams used to evaluate the assumptions assumptions of linear regression< Answer: A scatter diagram can be used used to evaluate the assumption assumption of linearity. linearity. $or each independent variable& the dependent variable can be plotted against against the independent variable. These plots provide evidence of linear relationships. Difficulty: Difficulty: Medium Goal: + AA!": A

12. 6ow are residual plots drawn and used to evaluate the assumptions assumptions of linear regression< Answer: A residual plot graphs the residuals against the values of one of the independent variables. A residual plot is graphed for each independent independent variable. To support the assumptions assumptions of e'ual variation for small and large values of the independent variable& the points should be evenly distributed above and below ;ero and evenly distributed distributed over all values values of the independent independent variable. Difficulty: Difficulty: 6ard Goal: +


#)(

112. hat statistic is used to assess multicolinearity in multiple regression analysis< analysis< Answer: ?ariance ?ariance inflation factor 7?-$ Difficulty: Difficult y: Easy Goal: ,

Fill-in-the-Blank

Cse the following to answer 'uestions 111411): -t has been hypothesi;ed that overall academic success for college freshmen as measured by grade point average 7GFA is a function of - scores ( N 1 ) & hours spent studying each wee ( N # ) & and oneIs high school average ( N % ) . !uppose the regression e'uation e'uation is:

9 = +. − 2.2)) X Y 1

+ 2.12, X # + 2.220% X %. − 2.222( X # X %

The multiple standard error is +.%1% and K # J 2.0#+.

111. hat is the predicted GFA for a student with an - of 120& %# hours spent stud ying per wee and a high school average of 0#<  Difficulty: Difficulty: Medium Goal: 12 Answer: %.#(

11#. hat is the predicted GFA if the - is 120& the number of hours spent spen t studying is %2& and the high school average is 0#<  Difficulty: Difficulty: Medium Goal: 12 Answer: %.2#

11%. Assuming other independent independe nt variables are held constant& constant & what effect on the GFA GFA will there be if the numbers of hours spent studying per wee increases from %# to %+<  Difficulty: Difficulty: 6ard Goal: Answer: The answer depends on the value of hours studied per wee 12

11(. 6ow many independent variables variables are in the regression e'uation<  Difficulty: Difficulty: 6ard Goal: 12 Answer: four

11). 6ow will a studentIs GFA be affected if the studentSs high school average was 02 and an additional hour is spent studying each weenight<  Difficulty: Difficulty: 6ard Goal: 12 Answer: increases by 2.))1

#))


Chapter14 Multiple Regression and Correlation Analysis

Recommend Documents