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Unformatted text preview: 7MGMT 305 SAMPLE EXAM 3 .—j Fall 2009 _ Date: December 3, 2009 If x and y are negatively related in a linear regression model, then
a. y is negative
b. an is negative
c. the coefﬁcient of correlation is negative
01. the coefﬁcient of determination is negative Larger values of r2 imply that the observations are more closely grouped about the
a. average value of the independent variables b. average value of the dependent variable 0. least squares regression line d. origin Which estimated regression equation has a better ﬁt? a. with a larger SSR
b. with a larger SSE
c. with a larger SST
d. with a larger r2 Compared to the interval estimate for a particular value of y (in a linear regression
model), the interval estimate for an average value of y will be a. narrower b. wider c. the same (1. None of these alternatives is correct. Application of the least squares method results in values of the y intercept and the slope which minimizes the sum of the squared deviations between the a. observed values of the independent variable and the estimated values of the
independent variable b. actual values of the independent variable and estimated values of the
dependent variable 0. observed values of the dependent variable and the estimated values of the
dependent variable d. None of these alternatives is correct. In a regression and correlation analysis if r2 = 0.5, then
a. SSE = SST b. SSE = 1 c. SSR = SST d. SSR = SSE Exhibit 1
The following estimated regression model was developed relating yearly income (Y in
$1 ,0005) of 30 individuals with their age (X1) and their gender (Xz) (0 if male and 1 if female). if = 30 + 0.7X1+ 3X2 Also provided are SST = 1,200 and SSE = 384. 7. 10. Refer to Exhibit 1. The yearly income of a 24—year—old female individual is
a. $19.80 b. $19,800
o. $49.80
(1. $49,800 Refer to Exhibit 1. The multiple coefﬁcient of determination is
a. 0.32 b. 0.42
c. 0.68
d. 0.50 A test on the signiﬁcance of the model based on an F test, should yield which of
the following conclusion? (Based on a 5% signiﬁcance level) ANOVA df SS MS F pvalue
Regression 1 309.9516 309.9516 6.325517 0.024736
Residual 14 686.0028 49.0002
Total 15 995.9544 a. Since Pvalue < a, we do not reject the null hypothesis. b. Since PValue < a, there exists a signiﬁcant linear relationship between the
independent variable and the dependent variable. 0. Since Pvalue < a, there does not exist a signiﬁcant linear relationship
between the independent variable and the dependent variable. (1. None of the above is correct. The random errors Si in a linear regression model are assumed to be
a. dependent
b. normally distributed 0. constant
d. both b and c 11. If a 98% conﬁdence interval for ,6. is constructed as [1.75, 3.92] in a simple linear regression model, we conclude that
a. At o.=0.02, there exists a negative linear relationship between the variables
b. At o.=0.20, there is no evidence of a signiﬁcant linear relationship between the variables
0. At (1:002, there exists a signiﬁcant linear relationship between the variables (1. None of the above Use the following model to answer questions 13, 14, and 15. Model: S = BO + 81E +
a, where E is the number of hourly employees/week and S is equal to the totai weekly
payroll for hourly employees. SUMMARY
OUTPUT
Regression
Statistics
Mutt. R 0.91
R Sq. 0.82
Adj. R Sq, 0.81
SE 760.83
Obs 15
ANOVA
df 88 MS F Sig. F
Regression 1 3407661826 3407661826 <A> 0.00
Residual 13 752530832 578869.87
Total 14 4160192658
Coef. SE tStat Pvafue Lower 95% Upper 95%
Intercept 4806.83 1071.44 1.69 0.12 4121.52 507.87
E 428.33 55.83 7.67 0.00 307.73 548.94 12. The percent of the weekly variation in S (= weekly payroll) explained by the
estimated regression equation is equal to
a. 91 %
b. 82 "/0
c. 9 %
d. 100 % 13. We conclude that
a. B] is equal to 0 since b1 has a t—statistic of 7.67 which is close to 1.96 statistically. b. B] is not equal to 0 since b; has a tstatistic which is equal to 7.67 which is
close to 2.58 statistically. c. At OL = 0.02, [3. is not equal to 0 since b1 has a pvalue less than 0.02. d. At a risk 0!. i 0.025, B] is equal to 0 since b1 has a p—value less than 0.025. 14. 15. 16. What is the answer for <A>?
a. about 37
b. about 48
c. about 52
(1. about 59 About analysis of variance (ANOVA), which statement is not true? a. ANOVA is used to test the “equality of population means”. b. To do ANOVA, we must assume that all the populations are normally
distributed. 0. To do ANOVA, we must assume that all the population variances are equal. (1. If the null hypothesis is rejected, we have sufﬁcient evidence to conclude that
all the means are different. In an analysis of variance problem involving 3 populations and 10 observations
from each population, SSE = 270. The MSE for this situation is a. 9.0 b. 10.0 c. 38.6 d. 90.0 Exhibit 2: Test H0: #1 zyz z #3 = #4 2 ,us 18. Source of Degrees of
Mean Square
Varlatlon Squares Freedom —
—— 17. Ha : Not all the population means are equal Sum of Refer to Exhibit 2. The value of the F statistic is
a. 7.23
b. 5.50
c. 3.33
d. 2.87 Refer to Exhibit 2. If at 5% level of signiﬁcance, we want to determine whether
or not the means of all the pOpulations are equal, the critical value of F is a. 1.645 b. 2.53 c. 3.01 d. 5.69 Exhibit 3
The following data show the overall vacancy rates (%) and the average rental rates (per square foot) for the central business district for 7 selected markets. Market Vacancy Average Ragzziggage Sicilagz (1:13:31? Rate (0%) RRaZEtg) Rental Rate) Rate ($)) 2
WW Boston 6 34 204 36 1 156 Chicago 16 24 3 84 256 576 New York 11 37 407 121 1369 Philadelphia 15 19 285 225 3 61 San Francisco 7 32 224 49 1024 Sum 77 165 1922 1171 4847 19. Refer to Exhibit 3. The estimated regression equation that could be used to predict
the average rental rate given the overall vacancy rate is Average Rental Rate = 41.22—1.069*Vacancy Rate Average Rental Rate = 41 .22+1 .069*Vacancy Rate
Average Rental Rate = —41.22—1.069*Vacancy Rate
Average Rental Rate = 41.221.069*Vacancy Rate 99.7!” 20. Refer to Exhibit 3. The F test statistic and critical F value at oc m 0.05 are a. 8.32 and 3.85
b. 8.32 and 7.71
c. 7.93 and 7.71
d. 7.93 and 7.71 21. Refer to Exhibit 3. The conclusion at the 0.05 level of signiﬁcance is a. There is no signiﬁcant relationship between vacancy rate and average rental
rate b. There is a cause and effect relationship between vacancy rate and average rental rate There is signiﬁcant relationship between vacancy rate and average rental rate None of the above 99 22. Refer to Exhibit 3. The overall vacancy rate in the central business district in Detroit
is 20%. The expected rental rate for Detroit. a. 18.94
b. 11.84
c. 13.84
d. 19.84
Exhibit 4 In order to determine whether or not the sales volume of a company (Y in millions of
dollars) is related to advertising expenditures (X1 in millions of dollars) and the number
of salespeople (X2), data were gathered for (n=10) years. Part of the regression results is
shown below. Coefﬁcient Standard Error
Constant 7.0174 1.8972
X1 8.6233 2.3968
X2 0.0858 0.1845 Analysis of Variance Source of Degrees Sum of Mean
Variation of Freedom Squares Square F
Regression 321.1 1 Error 63.39 23. Refer to Exhibit 4. The estimated regression equation that can be used to predict sales is
a. X" = 7.0174 + 8.6233X1+ 0.0858X2
b. Y = 7.0174 + 8.6233X1+ 0.0858X2 + e
c. Y = 1.8972 + 2.3968X,+ 0.1845X2
d. Y =1.3972 + 2.3968X.+ 0.1345X2 + s 24. Refer to Exhibit 4. The numerator and denominator degrees of freedom
respectively are a. 2 and 9
b. 2 and 7
c. 1 and 9
d. 1 and 8 25. Refer to Exhibit 4. The F test statistic and the critical value of F at 0!. = 0.01
respectively are a. 17.73 and 8.55
b. 15.73 and 9.55
c. 16.73 and 8.55
d. 17.73 and 9.55 26. Refer to Exhibit 4. At or = 0.01, the ﬁtted regression equation
a. does not represent a signiﬁcant relationship between independent variables
and the dependent variable.
b. represents a signiﬁcant relationship between the independent variables and the dependent variable.
0. Represents a causal relationship between the independent variables and the dependent variable.
d. None of the above. 27. Refer to Exhibit 4. At or = 0.05, the appropriate test for the signiﬁcance of [his
t= 3.59 > 2.365; [31 is signiﬁcant.
t= 3.59 < 2365;131is signiﬁcant.
F = 3.59 > 2.365; [31 is signiﬁcant.
F = 3.59 < 2.365; [31 is signiﬁcant. 9.05793 Exhibit 5 Three universities decided to administer the same comprehensive examination to the
recipients of MBA degrees from the three institutions. From each institution, MBA
recipients were randomly selected and were given the test. The following table shows the
scores of the students from each university. Northern Central Southern
University University University 75 85 80
80 89 81
84 86 84
85 88 79
81 83
85
Sample Mean 81 87 82
Sample Variance 15.5 3.33 5.6 We want to develop a test to see if there is any signiﬁcant difference in the average
scores of the students from the three universities. 28. Refer to Exhibit 5. The appropriate null and alternative hypotheses are:
a. H0: in =u2 at m, and Ha: Not all the population means are equal
b, H0: u; = u; = pg and Ha: Not all the population means are equal
0. H0: (51 ﬂ 02 = 63 and Ha: Not all the population standard deviations are equal
d. Both (b) and (c) 29. The value of F statistic is a. 10.20
b. 5.04
c. 5.40
d. 4.40 30. At 5% level of signiﬁcance, a. there is no signiﬁcant difference in the average scores of the students from the
three universities. b. there is signiﬁcant difference in the average scores of the students from the
three universities 0. there is a signiﬁcant relationship between average scores and the universities. d. students from central university have higher scores than students from south
and north universities. MGMT 305 Fall 2008  Key to Samgle Final Exam Multiple Choices:
1. C O PWHQMPP’P [\JNNNNMNNNNF‘Hb—IO—Il—lb—II—II—ll—‘H
FWHP‘MPP’PT‘PF’WSQP‘FWPi—‘P
00:1:9UJUUJ>UOW>UJOUUUUOWOUJUJOUUO>U 30. B 6. W \l' 5: MGMT 305 Spring 2009 Sample Final Exam M If x and y are negatively related in a linear regression model, then a. y is negative _
’{xﬁzcsﬁgh 0% bi J Y2. b. be is negative @ the coefﬁcient of correlation is negative
d. the coefﬁcient of determination is negative Larger values of r2 imply that the observations are more closely grouped about the
a. average value of the independent variables
b. average value of the dependent variable
@ least squares regression line (1. origin Which estimated regression equation has a better ﬁt? ii. Z izger 2. ggfz ﬂ Expiajneai Whirl
. K : damT"?  _ _ '
c. with a larger SST 5351“ T04, 1/52 Mahan @ with a larger r‘2 Compared to the interval estimate for a particular value of y (in a linear regression
model), the interval estimate for an average value of y will be narrower , .. 1
b. wider p]? #5 sudden {ham CI
c. the same
(1. None of these alternatives is correct. Application of the least squares method results in values of the y intercept and the slope which minimizes the sum of the squared deviations between the a. observed values of the independent variable and the estimated values of the
independent variable @ [Xi * 55;) b. actual values of the independent variable and estimated values of the dependent variable wafx; ﬁj
© observed values of the dependent variable and the estimated values of the dependent variable a y;  d. None of these alternatives is correct. In a regression and correlation analysis if r2 = 0.5, then a. SSE=SST
b. SSE=1 ~65": ﬂ: ()5
c. SSR=SST SST
SSR SSE 59R = 0.5SST E)
558% :1 O‘ECSSR + sg
+ 05555 Exhibit 1
The following estimated regression model was developed relating yearly income (Y in
$1,0005) of 30 individuals with their age (XI) and their gender (X2) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384. 7. 8. 10. Y = 30+ 0.7X1‘l‘ 3X2 = Refer to Exhibit 1. The yearly income of a 24yearold female individual is
a. $19.80 b. $19,800 949490489938 4 g I c. $49.80 .. . .2 q, x 000
430+ estater— 3(0) @ $49,800 5 was“: Refer to Exhibit 1. The multiple coefﬁcient of determination is
a. 0.32 o . l
b. 0.42 R1 _1:aﬂgzlnnl ___. j_([_0.6‘3)('3£03—:2—£ © 0.68 a.“ ‘ _
d. 0.50 “"1” z: 0.56 A test on the signiﬁcance of the model based on an F test, should yield which of
the following conclusion? (Based on a 5% signiﬁcance level) ANOVA df SS MS F pvalue
Regression 1 309.9516 309.9516 6.325517 0.024736
Residual  14 686.0028 49.0002
Total 15 995.9544 a. Since Pvalue < a, we do not reject the null hypothesis.
® Since Pvalue < 0., there exists a signiﬁcant linear relationship between the
independent variable and the dependent variable.
0. Since Pvalue < 0., there does not exist a signiﬁcant linear relationship
between the independent variable and the dependent variable.
(1. None of the above is correct. The random errors Si in a linear regression model are assumed to be
a. dependent ® normally distributed 6 = N [0, U‘) c. constant—1
d. both b and c  I , a; =i= CW9" [553.2] ‘ . 1:353:55 =0 8
521;. 55383815 , R SST [200 Z] 11. If a 98% conﬁdence interval for [31 is constructed as [1.75, 3.92} in a simple linear regression model, we conclude that
a. At 0t=0.02, there exists a negative linear relationship between the variables
b. At 0t=0.20, there is no evidence of a signiﬁcant linear relationship between the variables
At u=0.02, there exists a signiﬁcant linear relationship between the variables
. None of the above Use the following model to answer questions l3, l4, and 15. Model: S = Bo + 01E +
e, where E is the number of hourly employees/week and S is equal to the total weekly
payroll for hourly employees. SUMMARY
OUTPUT
Regression
Statistics
Mult. R 0.91
R Sq. 0.82
Adj. R Sq, 0.81
SE 760.83
Obs 15
ANOVA
df 88 MS F Sig. F
Regression 1 3407661826 3407661826 <A> 0.00
Residual 13 752530832 578869.87
Total 14 4160192658
Coef. SE tStat Pvalue Lower 95% Upper 95%
Intercept 4806.83 1071.44 —1.69 0.12 4121.52 507.67
E 428.33 55.83 7.67 0.00 307.73 548.94 12. The percent of the weekly variation in S (= weekly payroll) explained by the
estimated regression equation is equal to a. 91 % . '
© 82 % R2: 0.82 SlmPLe Lnan Regveﬂrmn .2?
c. 9 % h J 3.,” a. 100% Hairlth 13. We conclude that
a. 01 is equal to 0 since b1 has a t~statistic of 7.67 which is close to 1.96
statistically.
b. [31 is not equal to 0 since b; has a tstatistic which is equal to 7.67 which is
close to 2.58 statistically.
@ At OL = 0.02, B; is not equal to 0 since b1 has a p—value less than 0.02.
d. At a risk 0!. : 0.025, B] is equal to 0 since b1 has a pvalue less than 0.025. 14. What is the answer for <A>? a. about 37
b. about 48 F :ﬂéfé :3 5‘?
0. about 52 H5 @ about 59 15. About analysis of variance (AN OVA), which statement is n_ot true?
a. ANOVA is used to test the “equality of population means”.
b. To do ANOVA, we must assume that all the populations are normally
distributed.
0. To do ANOVA, we must assume that all the population variances are equal.
@ If the null hypothesis is rejected, we have sufﬁcient evidence to conclude that
all the means are different. 16. In an analysis of variance problem involving 3 populations and 10 observations
from each population, SSE = 270. The MSE for this situation is a. 9.0
@100 MﬁEﬁgﬁﬁ gigg;m 10.0
313313 1‘7"“ 3°” Exhibit 2: Test Ho! #1 = M2 = #3 = [.14 = #5 Ha : Not all the population means are equal Source of Degrees of
Mean Square F
Variation Squares Freedom
1900 m.— 17. Refer to Exhibit 2. The value of the F statistic is
a. 7.23
b. 5.50
6:) 3.33
d. 2.87 Sum of 18. Refer to Exhibit 2. If at 5% level of signiﬁcance, we want to determine whether
or not the means of all the populations are equal, the critical value of F is a. 1.645 
c. Fol [K”, n'r’K) 5 FOSUi/ 60) '12—'53
d. 5.69 Exhibit 3 The following data show the overall vacancy rates (%) and the average rental rates (per square foot) for the central business district for 7 selected markets. Market Vacancy Average Ragga2:33 e gage32c)? (11:2:de
Rate (%) 1:: ital) Rental Rate)g Rate ($)) 2 W Boston 6 34 204 36 1156 Chicago 16 24 384 256 576 New York 11 37 407 121 1369 Philadelphia 15 19 285 225 361 San Francisco 7 32 224 49 1024
W 19. Refer to Exhibit 3. The estimated regression equation that could be used to predict
the average rental rate given the overall vacancy rate is
196:: Lil99. b g 1 ﬁzz—mmsfllé
i ——"'_;/6 Average Rental Rate = 41.221.069*Vacancy Rate 6"
I I?! '7?  . Average Rental Rate = 41.22+1.069*Vacancy Rate b. s #149 bI —_ ._  .06“! 0. Average Rental Rate = 41.221.069*Vacancy Rate
[657+ [.069 g d. Average Rental Rate = 41 .221.069*Vacancy Rate
b0”? # b0
20. Refer to Exhibit 3. The F test statistic and critical F value at on = 0.05 are
6 8.32 and 3.85 = .53; :83
8.32 and 7.71 ———I
c. 7.93 and7.71 I: [l “‘12) = F05(l,tli) 31;?!“
d. 7.93 and 7.71 d ’ 21. Refer to Exhibit 3. The conclusion at the 0.05 level of signiﬁcance is a. There is no signiﬁcant relationship between vacancy rate and average rental
rate
b. There is a cause and effect relationship between vacancy rate and average
rental rate
(9 There is signiﬁcant relationship between vacancy rate and average rental rate d. None of the above T
gamma $32] > 22. Refer to Exhibit 3. The overall vacancy rate in the central business district in Detroit
is 20%. The expected rental rate for Detroit. ii. 1“]: 4122—1069):
0: 13:84 : 4122.. 1.069(29) .— 19.53:;
@ 19.84 Exhibit4 In order to determine whether or not the sales volume of a company (Y in millions of
dollars) is related to advertising expenditures (X; in millions of dollars) and the number
of salespeople (X2), data were gathered for (n=10) years. Part of the regression results is
Shown below. Coefﬁcient Standard Error i2. Constant 7.0174 : be 1.8972. .   ;_ gasp/1.8932. = 3.70 ‘/
X1 86233 :1): 2.3968    s.sm/a.3958 = 3, 59
X2 00353 = b1 0.1845.     0.98581016q5 = o. ’11? Analysis of Variance Source of Degrees Sum of Mean Variation of Freedom Squares Square F Regression kg; 321.11 150.56 1?)?!‘23 s HTS153 Error “4.4:; 63.39 9. 06  «—— ____________‘
3 23. Refer to Exhibit 4. The estimated regression equation that can be used to predict
sales is (29 if = 7.0174 + 8.6233X1+ 0.0858X2 be = 7‘ 9 ' 1? g
b. if = 7.0174 + 8.6233X1+ 0.0858X2 + a b, = 8 5733
c. = 1.8972 + 2.3968X1+ 0.1845X2 bl = o. 0858
d. Y x 1.8972 + 2.3968X;+ 0.1845X2 + e 24. Refer to Exhibit 4.
respectively are The numerator and denominator degrees of freedom 21. 2 and 9 (1) 2and7 c. land9
d. land8 k=2,' mic1:? 25. Refer to Exhibit 4. The F test statistic and the critical value of F at OL = 0.01
respectively are a. 17.73 and 8.55 F: 17.153 J
b. 15.73 and9.55 _ 2, ‘7'! = c355
c. 16.73 and 8.55 PM?» "‘f‘g " Fo'l: 17.73 and 9.55 .1, 1)
© (mmdie) (Dzé‘HA'ﬂ)
26. Refer to Exhibit 4. At OL = 0.01, the ﬁtted regression equation
a. does not represent a signiﬁcant relationship between independent variables and the dependent variable.
@ represents a signiﬁcant relationship between the independent variables and the
dependent variable. g, smre F:l'—I?~3 7 Hot ('12?) 5155'
c. Represents a causal relationship between the independent variables and the
dependent variable.
d. None of the above. 27. Refer to Exhibit 4. At ct = 0.05, the appropriate test for the signiﬁcance of [his
@ t—_~ 3.59 > 2.365; [31 is signiﬁcant. t _ b! 3 8.6233 =. 3.56!
b. w 3.59 < 2.365; [31 is signiﬁcant. " 52;“ "3.3963 *‘
c. F = 3.59 > 2.365; [3115 Signlﬁcant. 15‘ 05/2 ("'1‘4) : tags (3) = 2.35; d. F = 3.59 < 2.365; 01 is signiﬁcant. ‘ I blank
Ii {7: 3.5"! > Eta/1 = 2.3551, 5, )5 Sign: Exhibit 5 Three universities decided to administer the same comprehensive examination to the
recipients of MBA degrees from the three institutions. From each institution, MBA
recipients were randome selected and were given the test. The following table shows the scores of the students from each university. Northern Central Southern
University University University
75 85 80
80 89 81
84 86 84
85 88 79
81 83 85 SmpLSrEe 71,:5 z=Ll‘ 14325 n
SampleMean 52, = 81 E
1 = 87 "2,: 32
Sample Variance 5,1 = 15.5 5; = 3.33 5: .—= 5.6 We want to develop a test to see if there is any signiﬁcant difference in the average
scores of the students from the three universities. iSE38 I 28. Refer to Exhibit 5. The appropriate null and alternative hypotheses are:
a. H0: in =u2 74 [43 and H3: Not all the population means are equal
Ho: u1 = m = ug and Ha: Not all the population means are equal
c. H0: 0. = 62 z 03 and Ha: Not all the population standard deviations are equal d. Both (b) and (c) : M : M :11
“Vladhes” =55“) Ho 1 2 53 1n. means are 6742:!
29. The value of F statistic is Ha" I No+ d” H1 POP
a. 10.20
b. 5.04
5.40
. 4.40 30. At 5% level of signiﬁcance, a. there is no signiﬁcant difference in the average scores of the students from the
three universities. ® there is signiﬁcant difference in the average scores of the students from the
three universities Sime, F: 5. km} '7 F; [ 151, n'ka) : 3.89 c. there is a signiﬁcant relationship between average scores and the universities. d. students from central university have higher scores than students from south
and north universities. of Sum of Mean F
Van’ah'an Scyuares "5'
.45 5. 4 0 i . . go ..K._§1I:._a . .
'C'Tr'sza '  ' '833 W 130 ﬁlm1:14 Fczucpi, nT—K) = 1705(2, 12) = 3'39 Smu, F: 5401 3, E0512, 12323.31 Fejed Ho: ...
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