RAA602S - REGRESSION ANALSIS AND ANALYSIS OF VARIANCE - 1ST OPP - NOVEMBER 2024 :: NUST past examination papers between 2021 and 2025

Expand document

Collapse document

RAA602S - REGRESSION ANALSIS AND ANALYSIS OF VARIANCE - 1ST OPP - NOVEMBER 2024

1 Page 1

2 Page 2

3 Page 3

4 Page 4

5 Page 5

6 Page 6

7 Page 7

RAA602S - REGRESSION ANALSIS AND ANALYSIS OF VARIANCE - 1ST OPP - NOVEMBER 2024

1 Page 1

▲back to top

nAm I BI A u nlVE RSITV

OF SCIEnCEAnDTECHnOLOGY

FacultoyfHealthN, atural

ResourceasndApplied

Sciences

Schoool f NaturalandApplied

Sciences

Departmentof Mathematics,

StatisticsandActuarialScience

13JacksonKaujeuaStreet

Private Bag13388

Windhoek

NAMIBIA

T: +264612072913

E: msas@nust.na

W: www.nust.na

QUALIFICATION: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS

QUALIFICATION CODE: 07BSAM

LEVEL:6

COURSE: REGRESSION ANALYSIS AND ANALYSIS OF

VARIANCE

DATE: NOVEMBER 2024

DURATION: 3 HOURS

COURSECODE: RAA602S

SESSION: 1

MARKS: 90

EXAMINER:

MODERATOR:

FIRSTOPPORTUNITY:EXAMINATION QUESTION PAPER

MR. ANDREW ROUX

DR. J. Mwanyekange

INSTRUCTIONS

1. Answer all questions on the separate answer sheet.

2. Please write neatly and legibly.

3. Do not use the left side margin of the exam paper. This must be allowed for the

examiner.

4. No books, notes and other additional aids are allowed.

5. Mark all answers clearly with their respective question numbers.

PERMISSIBLEMATERIALS;

1. Non-Programmable Calculator

ATTACHEMENTS

1. Statistical Formulae Sheet

2. F - & T - Distribution Table

This paper consists of 5 pages including this front page

2 Page 2

▲back to top

QUESTION 1

[32]

The chairman of the accounting department at a large university undertakes a study

to relate starting salary (y) after graduation for accounting majors to grade point

average (GPA) in major courses. To do this, records of seven recent accounting

graduates are randomly selected.

Accounting

Graduate

GPA

3.26

2.60

3.35

2.86

3.82

2.21

3.47

Starting Salary (y)

(Thousands of dollars)

28.2

24.8

27.9

25.3

30.3

23.0

29.4

/J /3 1.1) Compute the least squares point estimates of

and

1.2) Write the least squares prediction equation relating y to x

(4+4 = 8)

(2)

1.3) Calculate both the Sum Squares of Error SSE and the Mean Squares of Error

MSE

(4 + 2 = 6)

1.4) Calculate the variance of x, s.~ and the standard error of the slope s b,

(4 + 4 =8)

1.5) Test the slope obtained for a direct linear relationship (using a = 0.10)

(8)

QUESTION 2

[30]

The data below shows the number of ice creams (y) sold, country-wide, at ten outlets

x of Spar Supermarkets. The table below also indicates the impact of three ( Xi ; 2 ;

x 3 )factors affecting the sales of ice creams at those different outlets

Outlet

730

152

198

760

173

201

850

166

202

840

161

202

720

152

198

730

153

205

REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)

1st opportunity November 2024

3 Page 3

▲back to top

840

166 204

730

157 204

650

136

172

850

142 218

740

151 207

720

145 209

710

147 190

SUMMARY

OUTPUT

Regression

Statistics

Multiple 0.85362

0.72868

Square

Adjusted 0.63823

Square

Standar 38.7825

d Error

ObseNa

tions

ANOVA

Regressio

Residual

Total

3 36355.51

Significance F

12118.5 8.057037 0.006439

9 13536.8 1504.089

12 49892.31

Intercept

Coefficient

-372.984

3.536757

3.734544

-2.16607

Standard

Error

242.3717

1.194784

1.10691

0.85177

t Stat

-1.53889

2.960165

3.373845

-2.54302

P-value

0.158214

0.015955

0.008207

0.031554

Lower

95%

-921.267

0.833968

1.230539

-4.09291

Upper

95%

175.2991

6.239546

6.238549

-0.23923

Lower

95.0%

-921.267

0.833968

1.230539

-4.09291

Upper

95.0%

175.2991

6.239546

6.238549

-0.23923

Consult the "EXCEL SUMMARY OUTPUT' to answer the following questions below

2.1) Discuss the "Regression Statistics"

(10)

2.2) State the multiple regression model for this data set.

(3)

REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)

rt opportunity November 2024

4 Page 4

▲back to top

2.3) Test the validity of the model

( use a = 0.05)

(7)

2.4) Test to determine whether there is enough evidence to infer that there is a

linear relationship (gradient) between the maximum ice thickness (y), and the

"number of days per year of ice cover" ( x,) Use a= 0.10

(10)

QUESTION 3

[12)

A recent survey conducted by the Directorate of Rural Water Supply considered a

random sample of 49 farms in the Hardap Region , 45 farms in the Omaheke Region

and 29 farms in the Karas Region. The average rainfall recorded for September

2012 over those farms in the Hardap Region was found to be 8.36 mm, with a

standard deviation of 2.98 mm, while the average rainfall recorded over the farms in

the Omaheke Region was found to be 7.91 mm, with a standard deviation of 3.15

mm. The average rainfall recorded over the farms in the Karas Region was found to

be 9.02 mm with a standard deviation of 3.62 mm.

Use the following sample statistics to test a claim that there is NO difference in the

average rainfall over farms in these regions. ( use a = 0.05)

Question 4 [16)

A randomized block experiment produced the data below.

Blocks

Treatments

4.1) Can we infer at the 5% significance level that the treatment means differ? (8)

4.2) Can we infer at the 5% significance level that the block means differ?

(8)

XXXXXXXXXXXXXXXXXXXXENXDXXXXXXXXXXXXXXXXXXXXXXXXXX

REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)

1'1Opportunity November 2024

5 Page 5

▲back to top

FORMULAE SHEET

= n(Lxy)-(Lx)(LY)

n(Lx 2 )-(Lx) 2

= LY-.B(Lx)

MST

Fsw,= MSE

MST= SST

k-l

MSE = SSE

n-k

+ f3111X11

MSE = SSE

n-2

REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)

1st Opportunity November 2024

6 Page 6

▲back to top

F-table 0.05

Table of F-statistics P=0.05

11~1~'1'1'141'1'1'1'1'FFF~FFFFFFFFFFFFFFFFFFFFFFFo} 000 I~~/ l>lOOO

~110.1319.ss 19.2819.1219la..0914la.89la.asla.a1la.79la.76la.74la.73la.71la.70Ja.69la.6ala.67Ja.67la.66la.6sla.64la.63Ja.62la.62la.60la.s91a.s9la.sala.s7la.s7la.s6la.ss1a.s4la.s31a.s3

~17.71 16.9l46.s916.3l69.26l6.1616.o916l.6o.4ools.96ls.94ls.91ls.89ls.87ls.86ls.84ls.831s.a2ls.a1ls.aols.79ls.77ls.76ls.7sls.7sls.73ls.72ls.71ls.7ols.69ls.Gals.67ls.66ls.GsJs.64ls.63fs.63~

rs--16.61 ls.79ls.41ls.19ls.os14.9514.1a4a.8124.7714.74141.47.06184.6614.64141.46.26l04.s914.s1a4.5174.5164.5414.1543.5214.Js4o.S1O4.4814.4614.4514.41344.4124.4124.414.3914.1347.37~rs--

~ls.99 ls.1414.7614.5314.3914.2814.2114.1514.10141.o36.91841.o33.91641.o3o.9413.9213.91131.39.081731.3a.a8613.8413.8313.8213.8113.79J3.7713.7613.7513.7413.7313.7213.7113.69J3.6813.6

~15.59 14.7414.3514.1213.9713.8713.7913.674313.16308.5713.5513.5313.45193.4183.4173.4163.4413.43131.34.14103.3913.3813.3613.3413.33131.33.21931.33.10239.2713.2513.2413.23

,1815.32 14.4614.0713.8413.61931.35.10538.4413.1339.3513.1331.2183.2613.1234.2213.1230.1193.1713.1613.1513.11331.3lo.1132.0913.1o3a.o613.lo34.o313.02131.021.9192_9192.9J72.9512.9142.93[2-9313

·~15.12 14.2513.85131.35.34183.3713.29131.32.31183.1143.1103.0173.o1s3.0133.012.9192.9172.9152.91s2.9142.9122.9l02.a912.a172.al52.a412.a132.a12.8102.7192.7182.7172.7152.7132.7122.71

110l4.96 J4.1013.713.4J83.3313.2213.1134.0713.1022.9J82.9412.912.8192.8162.als2.a3l2.a112.a1o2.7192.7172.71s2.7J42.7212.712.7J02.6a12.6J62.6512.5142.6122.612.6l02.s9J2.s612.ssl2.s4~jlO

11114.84 13.91B3.s913.36131.32.00913.102l.9152.9012.la2s.a212.7912.75J2.741122..772012.6912.6712.G515s2.6132.6J12.s912.sa12.5712.1525.s312.5l22.s112.4192.4182.4712.1426.4132.4J22.41lz.41111

11214.75 13.8193.4193.2613.1131.o1o2.912.8152.a1o2.71s2.7122.6192.6162.5142.6122.6102.sa12.5172.5l62.s412.5122.512.4l92.4a12.4172.4142.4132.412.4102.3182.3172.3l62.3s12.3122.312.30~112

11314.67 13.813.4l13.1B13.0132.9l22.a312.7172.712.6172.6132.6102.sa12.ssJ2.s3l2.s112.so12.4182.4172.4162.4142.4122.412_3J92.3BJ2.3612.3142.3132.312.3102.21a2.2172.2162.2J32.2212.21ju1113

~J4.60 J3.74J3.3413.112.9162.8152.7162.7102.G1s2.Gl2o.s712.5132.s1l2.4a12.4162.4142.4132.412.4102.3192.3l72.3s12.3132.3122.312.21a2.2172.21s2.2142.2122.212.2102.1J92.1GJ2.1412.14

j15J4.S4 13.6J83.29l3.0612.9102.7192.7J12.64J2.5912.5l42.s1J2.4aJ2.4s12.4122.4J02.3aJ2.3712.3152_34121.323.312.2192.2J72.2G12.21s2.2122.2102.1l92.1a12.1l62.1s12.1142.1J22.1012.o1a2.07~115

j16J4.49 13.6J33.24l3.0112.a1s2.7142.Gl2G.s9J2.s412.4192.4162.4J22.4o12.3l72.3s12.3J32.3212.3102.2192.2la2.2s12.2142.2122.212.1192.1172.11s2.1142.1122.112.0192.0182.0172.0142.0122.02~116

11714.45 13.5913.1220.9l62.a112.7102.612.ssJ2.49l2.4s12.412.3182.3152.3J32.312.2192.2172.2162.2142.2132.212.1192.1172.1512.112s.1122.1102.0192.o1a2.0162.o1s2.0132.0211.l9t.997lt.97 ~117

~14.41 13.ss13.1612.1923.7712.1626.5182.5J12.4612.412.3J72.3412.312.2192.2172.2152.2132.2122.2102.1J92.17l2.1sJ2.1312.1J22.112.o1a2.0162.0152.0412.0212lt..0909l1.9alt.95Jt.9311.92

11914.38 13.5213.J123.9o12.7412.l623.s4l2.4a12.4122.3182.3142.3l12.2a12.2J62.2312.212.2l02.1a12.1172.1162.1132.112.1102.o1a2.0172.o1s2.0132.012.0l0t.98lt.97lt.96lt.94Jt.91l1.a911.aa[1.ss119

rus-~ !2014.35 13.4913.l120.a712.7112.6102.5l12.4s12.3J92.3s12.312.21a2.2Js2.23J2.20l2.1a12.1J72.1s12.1142.1J22.1012.o1a2.0712.1o2s.0J42.011.9191.9l8t.97l1.9s11.9131.9121.911.ala1.a6Ji.as f1.ii4!20

~14.30 13.4413.1o2s.8122.6162.ssJ2.4612.4102_3142.3J02.2612.2132.2102.1172.11s2.1J32.112.1102.o1a2.0J72.os12.0132.0J12.oo11.9181.9J6t.94Jt.92Jt.91l1.a9Ji.as11.aJGi.asl1.a2Ji.soJ1.79

~14.26 J3.40J3.012.71a2.6l22.s112.4J22.3612.3102.21s2.2l22.1aJ2.1s12.1132.1J12.09J2.0712.o1s2.0142.0132.0l0t.9811.9l71.9s11.9141.9l11.a911.ala1.a6l1.a4l1.a3l1.a2It.solt.7711.71s1.74

12614.23 J3.37J2.9B12.7l42.s912.4172.3192.3122.2172.2l22.1al2.1s12.1122.0192.0J72.os12.0132.0J22.ooJ1.99lt.97l1.9s11.9131.9J11.90l1.a711.als1.a4l1.a211.alot.79l1.7a11.7161.7J31.711.70~126

12814.20 13.3l42.9s12.712.sG12.4152.3162.2192.2142.1l92.1s12.1122.0192.0152.0142.0122.0101.9191.9171.9161.9131.911.9101.ala1.a7l1.a4l1.a211.a1o1.7191.7l7t.75lt.74lt.7311.6l9t.6711.66fl.66128

!3014.17 13.3122.9122.6l92.s312.4122.3132.2172.212.1162.1132.0192.0162.0142.011.9l91.9a11.9l61.9s11.9131.9l11.a9l1.a7l1.a5l1.a4l1.a111.7191.7171.7611.7411.17.2711.7101.6161.6141.63f1.6213D

13514.12 13.2172.a172.6412.4912.3712.22912.16121.21.1oJa2.0412.011.9191.9161.9411.9211l1.9.a1911.a1a1.als1.a3l1.a211.8101.79J1.7611.7411.7J211.16.81710.GJG1.6s11.6131.6l01.s7J1.s7~135

~14.08 13.2132.a142.6l12.4s12.3l42.2sl2.1a12.1122.o1a2.0142.0101.9l71.9s11.9121.9l01.a9l1.a711.al1s.a4l1.a111.7191.7711.1716.7141.7121.6191.6171.6161.6141.6121.6l11.s9l1.5sl1.s3l1.s21151~

~14.06 13.2l02.a1J2.saJ2.42J2.31J2.22l2.1s12.1J02.osJ2.011.9J7l.9411.9l21.a9J1.a7J1.aGl1.a4J1.a2l1.a111.7181.7161.7J4i.7311.711.6181.6J61.64lt.6311.6101.5911.1517.5J5t.51Jt.49l1.4a

rso-14.03 13.1182.7l92.s6J2.4D12.2192.2102.1132.0172.0131.9l91.9sJ1.92l1.a9l1.a711.als1.a3l1.a111.alo1.7al1.7611.7411.lnt.7011.6191.6611.1613.611.6011.ls1a.s6l1.s4l1.s2J1.4al1.4Gfvis["L44""rso-

16Dl4.00 J3.1512.7J62.s312.3l72.2s12.1172.1102.0141.9l91.9s11.9J21.a9J1.aGl1.a4l1.a211.alo1.7a11.7l61.7sl1.72l1.70J1.6B11.6l61.6sJ1.62l1.s911.5171.sGJ1.s3l1.s211.sol1.4a11.4J41.41J1.40fu9!60

~J3.98 13.1J32.7412.5102.3152.2132.1142.0172.0121.9171.9J31.a9Ji.BGJ1.a4J1.a111.7191.7171.7l5t.7411.7121.7101.6J7t.6511.6141.6121.5J91.5711.5J51.5311.soJ1.4911.4171.4151.4J0l.37J1.36[Lis~

fsol3.96 13.112.7122.4192_3132.212.1132.0162.0l01.9s11.9J11.aal1.a4l1.a211.7J9i.7711.71s1.7131.7211.1710.G1a1.G1s1.6131.6121.Gl1o.s7l1.s4l1.s2l1.s111.4181.4l6t.4511.4J31.3Blus lu4 ~[so

j[loo13.94 13.0192.7102.4J62.31J2.1912.1J02.0311.9171.9J31.a911.als1.a211.7191.7J71.7sJ1.7311.7J11.69J1.6B11.G1s1.5131.6J11.59J1.s711.5l41.s211.4l9t.48J1.4s11.4311.1411.3J9l.34lu1 luo ~[loo

1J2ool3.89 13.0142.61s2.4122.2162.1142.0l61.9a11.9J3i.asJ1.a411.aJo1.7711.7141.n11.5J9l.6711.6161.6J41.G121.6l01.s711.5l51.s3l1.s2l1.4a11.4161.4J31.41lu9 11.3J61.3s11.3121.2161.2J21.21~jzoo

fsool3.a6 13.012.6212.1329.2132.1122.0311.1916.9101.als1.a111.7J7t.74lu1 11.6191.6161.6141.6121.6l11.s9l1.5611.s4111.512.5101.4Ja1.4511.4121.4101.3laus J1.3211.3J01.2aJ1.211.1161.14fu2Tsoo

J 100013.as13.o1o2.6J12.3a12.2122.112.0121.9l51.a9l1.a411.a1o1.7161.7131.7101.6l81.6s11.6311.1611.6l01.sal1.ssJ1.s3J1.s111.4191.4171.4131.4l1ua lu6 lu3 11.311.2J91.2G11.1J91.13

I 1000

[I>1000J1.0413.oJo2.612.3172.212.1102.0J1l.94Ji.asl1.a311.7l91.7s11.n11.5191.5171.6411.1612.6l11.s9l1.s7l1.s4l1.s211.sol1.4a11.4161.4121.4l0u7 lus lu2 luo l1.2al1.2sJ1.1711.111.oa~I> 1000

1~~/

j'j'l3l4l5l5l7l5l5FFFFFFFFFFFFFFFFFFFFFFF

11001200isoo110001>1000

7 Page 7

▲back to top

t Table

cum. prob

one-tail

two-tails

100

1000

f.50

0.50

1.00

0.000

t .75

0.25

0.50

1.000

0.816

0.765

0.741

0.727

0.718

0.711

0.706

0.703

0.700

0.697

0.695

0.694

0.692

0.691

0.690

0.689

0.688

0.687

0.686

0.685

0.684

0.683

0.681

0.679

0.678

0.677

0.675

0.674

50%

t .80

0.20

0.40

t .85

0.15

0.30

1.376

1.061

0.978

0.941

0.920

o.i:fo6

0.896

0.889

0.883

0.879

0.876

0.873

0.870

0.868

0.866

0.865

0.863

0.862

0.861

0.860

0.859

0.858

0.857

0.856

0.855

0.854

0.851

0.848

0.846

0.845

0.842

60%

1.963

1.386

1.250

1.190

1.156

1.134

1.119

1.108

1.100

1.093

1.088

1.083

1.079

1.076

1.074

1.071

1.069

1.067

1.066

1.064

1.063

1.061

1.060

1.059

1.058

1.057

1.056

1.055

1.050

1.045

1.043

1.042

1.037

1.036

70%

t .90

0.10

0.20

t .95

0.05

0.10

t .975

0.025

0.05

3.078

1.886

1.638

1.533

1.476

1.440

1.415

1.397

1.383

1.372

1.363

1.356

1.350

1.345

1.341

1.337

1.333

1.330

1.328

1.325

1.323

1.321

1.319

1.318

1.316

1.315

1.314

1.313

1.311

1.310

1.303

1.296

1.292

1.290

1.282

6.314

2.920

2.353

2.132

2.015

1.943

1.895

1.860

1.833

1'.812

1.796

1.782

1.771

1.761

1.753

1.746

1.740

1.734

1.729

1.725

1.721

1.717

1.714

1.711

1.708

1.706

1.703

1.701

1.699

1.697

1.684

1.671

1.664

1.660

1.646

12.71

4.303

3.182

2.776

2.571

2.447

2.365

2.306

.2.262

2.228

2.201

2.179

2.160

2.145

2.131

2.120

2.110

2.101

2.093

2.086

2.080

2.074

2.069

2.064

2.060

2.056

2.052

2.048

2.045

2.042

2.021

2.000

1.990

1.984

1.962

1.282 1.645 1.960

80% 90% 95%

Confidence Level

t .99

0.01

0.02

t.995

0.005

0.01

t .999

0.001

0.002

t .9995

o.ooosl

0.001

31.82

6.965

4.541

3.747

3.365

3.143

2.998

2.896

2.821

2.764

2.718

2.681

2.650

2.624

2.602

2.583

2.567

2.552

2.539

2.528

2.518

2.508

2.500

2.492

2.485

2.479

2.473

2.467

2.462

2.457

2.423

2.390

2.374

2.364

2.330

2.326

98%

63.66

9.925

5.841

4.604

4.032

3.707

3.499

3.355

3.250

3.169

3.106

3.055

3.012

2.977

2.947

2.921

2.898

2.878

2.861

2.845

2.831

2.819

2.807

2.797

2.787

2.779

2.771

2.763

2.756

2.750

2.704

2.660

2.639

2.626

2.581

2.576

99%

318.31

22.327

10.215

7.173

5.893

5.208

4.785

4.501

4.297

4.144

4.025

3.930

3.852

3.787

3.733

3.686

3.646

3.610

3.579

3.552

3.527

3.505

3.485

3.467

3.450

'3.435

3.421

3.408

3.396

3.385

3.307

3.232

3.195

3.174

3.098

3.090

99.8%

636.62

31.599

12.924

8.610

6.869

5.959

5.4081

5.041

4.781

4.587

4.437

4.318

4.221

4.140

4.073

4.015

3.965

3.922

3.883

3.850

3.819

3.792

3.768

3.745

3.725

3.707

3.690

3.674'

3.659

3.646

3.551

3.460

3.416

3.390

3.300

3.291

99.9%

t-table.xls 7/14/2007