RAA602S - REGRESSION ANALYSIS AND ANOVA - 1ST OPP - NOVEMBER 2023 :: NUST past examination papers between 2020 and 2024

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RAA602S - REGRESSION ANALYSIS AND ANOVA - 1ST OPP - NOVEMBER 2023

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RAA602S - REGRESSION ANALYSIS AND ANOVA - 1ST OPP - NOVEMBER 2023

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nAml BIA un IVERS ITY

OF SCIEnCEAnDTECHn0L0GY

Facultyof Health,Natural

ResourceasndApplied

Sciences

Schoolof NaturalandApplied

Sciences

Department of Mathematics,

Statistics and Actuarial Science

13JacksonKaujeuaStreet

Private Bag13388

Windhoe~

NAMIBIA

T: +264612072913

E: msas@nust.na

Vi/;wwv,.nust.na

QUALIFICATION: BACHELOR OF SCIENCE IN APPLIED MATHEMATICS AND STATISTICS

QUALIFICATION CODE: 07BSAM

LEVEL: 6

COURSE:REGRESSION ANALYSIS AND ANOVA

COURSECODE: RAA602S

DATE: NOVEMBER 2023

SESSION: 1

DURATION: 3 HOURS

MARKS: 100

EXAMINER:

MODERATOR:

FIRST OPPORTUNITY: QUESTION PAPER

Simon Pombili Kashihalwa

Prof Rakesh Kumar

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.

PERMISSIBLE MATERIALS:

1. Non-Programmable Calculator

ATTACHEMENTS

1. t- Table

This paper consists of 4 pages including this front page

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QUESTION 1 [60)

1.1

For each of the following indicates the Statistical tools to be applied:

(a) Examining how the level of employee training impacts customer satisfaction ratings

[2]

(b) Predict weight if we know an individual's height.

[2]

time.

[2]

(d) Measuring the relationship between two securities.

[2]

(e) Predicting whether a patient has a particular disease or not.

[2]

1.2

What is the effect of putting additional predictor variables in the model on each of

the following?

[2]

Adj R 2

[2]

SSE

[2]

Estimated standard deviation of the errors

[2]

1.3 A biologist is comparing the intervals (m seconds) between the mating calls of a certain species

of tree frog and the surrounding temperature (t 0C). The following results were obtained.

t 0c

m secs

13 I

6.5

4.5 I

a) Calculate the coefficient of correlation and interpret it

[6]

b) Test the significance of the coefficient of correlation at 5%

[8]

c) Find the equation of the regression line

(4]

d) Use your regression line to estimate the time interval between mating calls when the

°c surrounding temperature is 10

[2]

1.2 A multiple regression model of the following form is fitted to a data set.

Yi= /Jo+/J1X1 + /J2X2 + /33X3 + /34X4 + Ei,Ei~N(O, cr2) i. i. d.

Variables

Cons

Coefficients

5.3036

4.0336

-9.3153

Std. Error

0.196

2.5316

2.4657

2.2852

t value

8.438

1.627

0.257

Pr(>ltl

3.57

0.03

0.107

0.002

0.7973

a) Find the missing values in the output.

[5]

b) Write down the estimated regression model.

[2]

c) Test the significance of x4.

[5]

d) Interpret the coefficients of all variables.

[5]

e) Test the significance of x3.

[SJ

Regression Analysis and ANOVA (RAA602S)

l' t Opportunity November 2023

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Question 2(40)

2.1 Study the ANOVA output and answer the questions that follow

Source of

Variation

Between Groups

Within Groups

Total

86049.55

10254

96303.55

43024.78

1709

p-value F crit

0.001

5.14

a) Mathematically state the two assumption of ANOVA (No mark for plain English).

[4]

b) Formulate the hypothesis for treatment means and make a decision.

(4]

c) Find the sample size used in this experiment.

[1]

d) Find the total df, df for Between group and Within group.

[3]

e) Calculate the test statistics.

[3]

f) Write down the general format of the effects and Means model.

(4]

Study the output below based on political election campaign, where the dependent variable

is won a seat or not regressed by incumbency (O=challenger, l=incumbent), spending

measures in N$ and spending total*c (interaction of spending and incumbency)

wonseat

Coef

Std.Err.

P> IZI 95% Cl

lncumb

3.200883 0.8391721 0.00 ....................................

spend_total

0.0001604 0.0000232

0.00 0.001149 ; 0.0002058

spend_total*c

-.0000649 0.000428 0.130 .....................................

cons

-3.901699 0.429417

0.00 -4.743341; -3.060057

a) Explain why OLS is unsuitable for binary dependent variable.

[2]

b) Calculate the 95% Cl for incumb (/31 ) and the 95%CIfor OR.

[8]

c) If a challenger spent N$10 000 more, what will be his or her odds of winning.

[2]

d) Write down the estimated probability of winning a seat for the challenger.

[3]

e) Calculate the 95% Cl for spend_total*c(/33) and comment on the significance of

spend_total*c, using 95% Cl.

[6]

END

RegressionAnalysis and ANOVA (RAA602S)

l51Opportunity November 2023 3

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Regression Analysis and ANOVA (RAA602S)

l' t Opportunity November 2023