BRUNEL UNIVERSITY Master of Science Degree examination Specimen Exam Paper 2005-2006 EC5002: Modelling Financial Decisions and Markets EC5030: Introduction to Quantitative Methods Time allowed: 1.5 hours Answer all of question 1 and at least two other questions

1. COMPULSORY Provide brief answers to all the following: (a) A sample of 20 observations corresponding to the model: Y = + X + u, gave the P P P following data: (X X)2 = 215:4, (Y Y )2 = 86:9, and (X X)(Y Y ) = 106:04. Estimate . (5 marks) (b) Prove that r2 = byx bxy , where byx is the least-squares (LS) slope in the regression of Y on X , bxy is the LS slope in the regression of X on Y , and r is the coe¢ cient of correlation between X and Y . (5 marks) (c) Present four alternative in‡ ation/unemployment regressions. (5 marks) (d) Give one reason for autocorrelated disturbances. (5 marks) (e) Explain how we might use the Breusch-Godfrey statistic to test estimated residuals for serial correlation. (5 marks) (f) The following regression equation is estimated as a production function for Q: lnQ = 1:37 + 0:632 lnK + 0:452 lnL, cov(bk ; bl ) = 0:055;

(0:257) (0:219)

where the standard errors are given in parentheses. Test the hypothesis that capital (K ) and labor (L) elasticities of output are identical. (5 marks) Continued (Turn over)

1

ANSWER TWO QUESTIONS FROM THE FOLLOWING: 2. (a) Economic theory supplies the economic interpretation for the predicted relationships between nominal (in‡ ation) uncertainty, real (output growth) uncertainty, output growth, and in‡ ation. Discuss …ve testable hypotheses regarding bidirectional causality among these four variables. (25 marks) + yt

(b) An investigator estimates a linear relation for German output growth (yt ): yt = 1 + ut , t = 1850; : : : ; 1999. The values of …ve test statistics are shown in Table 1: Discuss the results. Is the above equation correctly speci…ed? (10 marks)

3. (a) i) Show how various examples of typical hypotheses …t into...

...part unexplained by the regression equation:
Standard error of prediction for a single Y:
Standard error of prediction for the mean Y:
Chapter 12, Time Series Analysis and Forecasting
Mean Absolute Error:
Root Mean Square Error:
Mean Absolute Percentage Error:
All forecasting models have the general form of the equation: Yt = Fitted Value + Residual
Linear trend model is given by: Yt = a + bt + et
Appropriate regression equation contains a multiplicative error term: ut: Yt = cebtut.
Equation for the random walk: Yt = Yt-1 + m + et.
Simple Exponential Smoothing: Formula: Ft+k = Lt = αYt + (1 – α)Lt-1
Formulas for Holt¡¦s exponential smoothing method:
Winters’ Exponential Smoothing Method :
Bayes’ Rule:
Chapter 13: Introduction to Optimization Modeling
No formulas there.....

...sExam Quantitative Research Methods I, IB&M, 2011-2012
Friday, April 27th , 2012, 9:00-12:00 hours.
Name: Student number:
Each correctly answered multiple choice question yields 3 points. The remaining 55 points are alotted to the essay question.
The last question of this exam is on page 12.
Regarding the multiple choice questions: Use the scrap form. Please mark the box associated with the answer you deem to be correct. Do not forget to write your name on the scrap form and mark the right student number boxes. Regarding the open questions: Explain every single step in your reasoning. Answers without explanation never yield any points.
Good luck!
Multiple Choice Questions 1. Sixty percent of the pupils of some very large secondary school own a mobile phone. A group of 8 randomly chosen pupils of this school is asked whether they own a mobile phone. What is the probability that exactly 5 of them own a mobile phone? a. That probability is approximately 0.005. b. That probability is approximately 0.124. c. That probability is approximately 0.279. d. That probability is approximately 0.625. 2. The operation manager of a company that manufactures shirts wants to determine whether there are diﬀerences in the quality of workmanship among the three daily shifts. She randomly selects 600 recently made shirts and carefully inspects them. Each shirt is classiﬁed as either perfect or as ﬂawed and the shift that produced the shirt is also...

...Introduction
The hospital manager is studying and evaluating some options of Blood bank services to be more efficient as he has three options; each one is different in terms of cost, benefits and efficiency, and he is trying to evaluate which one will most suitable for making this service more efficient our role is to develop a multi criteria model for his problem and options he has, to help him taking the right decision Utilizing the multi attribute value analysis supported by V.I.S.A software.
Problem structuring:
The checklist cause criteria, alternatives, uncertainties, stakeholders and environmental factors or constraints will help to ensure that all the important facets of the problem have been considered.
Expanding briefly on these aspects in relation,
Stakeholders: is the hospital manger however there are some other stakeholder including as the senior medical staff and other department managers
Alternatives: there are three alternatives:
1. Keep the Blood Bank as it is without changing. And we will call it Option A
2. Expand the Blood Bank to content more blood supply. And we will call it Option B
3. Implementing an IT inventory system with automatic supply order. And we will call it Option C
The criteria: different between the available options.
The external factor is often considered as a source of uncertainty, as traffic or weather problems is a factor to be taken into consideration
Building Value Tree...

...Quantitative Research MethodsQuantitative means quantity which implies that there is something that can be counted. Quantitative research has been defined in many ways. It is the kind of research that involves the tallying, manipulation or systematic aggregation of quantities of data (Henning, 1986)
John W. Creswell defined quantitative research as an inquiry into a social or human problem based on testing a theory composed a theory composed of variables, measured with numbers, and analysed with statistical procedures in order to determine whether the predictive generalisations of the theory holds true. (Creswell, 2003)
On the other hand, another author defined quantitative research as the collection of numerical data in order to explain, predict and/or control phenomena of interest. Quantitative research is explaining phenomena by collecting numerical data that are analysed using mathematically based methods (Aliaga & Gunderson, 2000)
Quantitative research can also be said to be a research based on traditional scientific methods, which generates numerical data and usually seeks to establish causal relationships (or association) between two or more variables, using statistical methods to test the strength and significance of the relationships (A dictionary of Nursing, 2008)
Simply put, quantitative...

...multi-dimensional analysis.
4. Explain ‘Options’ trading. State their significance in modern day
trading.
5. Comment on the business models of private equity funds.
6. Comment on valuation of ‘distressed companies’.
7. Illustrate with an example any three capital structure ratios.
8. Illustrate with an example any three profitability ratios.
9. State and explain ‘time value of money’.
10. Explain with an example, the ‘if-then’ analysis & features in excel
enabling it.
11. Explain any three significant financial analysis features of
excel.
12. Explain ‘derivatives’ trading. State its significance in modern day
trading.
13. Comment on the business valuation through the ‘build-up’ method.
14. State & Explain and two methods of appraisal of a company or
project.
15. Illustrate with an example any three liquidity ratios.
16. Illustrate with an example any three capital market ratios.
This article describes the formula syntax and usage of the VLOOKUP function in Microsoft Excel.
Description
You can use the VLOOKUP function to search the first column of a range of cells, and then return a value from any cell on the same row of the range. For example, suppose that you have a list of employees contained in the range A2:C10. The employees' ID numbers are stored in the first column of the range, as shown in the following illustration.
If you...

...
Quantitative Research
Research Methods in Criminal Justice and Security
Professor Beshears
27 February 2014
Quantitative research collects numerical data through surveys, questionnaires, and polls. Quantitative research main purpose is to find the relationship between two variables. According to Babbie (2010) a descriptive study establishes only associations between variables while experimental defines the casualties (pg. 1). The data that is collected from the research is usually used for bigger representation of a population. The data can also be repeated if it was considered to be very accurate and reliable. Every part of quantitative research is scrutinized very carefully before the data is actually collected. The data that is collected is always in a statistics form or number form. Quantitative research can be used to investigate causal relationships, tell the future, or generalize concepts more widely. According to Babbie (2010) to the main purpose of quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed (pg. 1). There are four approaches under the Quantitative research and they are descriptive research, correlation research, causal-comparative research, and experimental research.
The research that gathers the information to test the...

...QuantitativeMethods
BITS Pilani
Pilani Campus
Course handout
BITS Pilani
Pilani Campus
Session-1
Instructor Details
Dr. Remica Aggarwal 1214 C ; FD-1 Department of Management Email: remica_or@rediffmail.com
Mobile: 09772054839
BITS Pilani, Pilani Campus
Course Details
• • • • • • •
Management Science Use of QM/QA Modelling Techniques Data Analysis Techniques MS Excel QM for Windows Test
BITS Pilani, Pilani CampusQuantitativeMethods
• • • • • • • Operations Research Statistics Management Science Data IT & QM Business intelligence Theory Vs. Use?
BITS Pilani, Pilani Campus
Operational Research
...is concerned with scientifically deciding how best to design and operate man-machine systems under conditions requiring allocation of scarce resources
BITS Pilani, Pilani Campus
Definition of OR
–T.L. Saaty:
A collection of tools and techniques which provide bad answers to problems ………………………….…………….. which otherwise have ………………… worse answers
BITS Pilani, Pilani Campus
Evolution of OR
• History –U.S. Navy –Naval Research Forum –P.M.S. Blackett –Naval Research Logistics • Need – civilian applications • OR – Blend of art and science
BITS Pilani, Pilani Campus
Application Areas
• • • • • • • • Allocation (product-mix) Scheduling & Sequencing Routing Replacement Inventory Queueing Search Competitive
BITS Pilani, Pilani Campus
Application …(contd.)
•...

...1. How you would use the concept of probabilities to apply to profiles for hiring more satisfied individuals and
2. Other ways that probability is used in business (Use the Business Source Elite Database in the Cybrary, research how probability is used in business).
Begin your email to AIU by first providing an overview of the database, i.e., a story.
Include the following pieces of information.
Part I
a) What is the gender distribution (%females and %males)?
Solution. From the database, we know that there are 168 female people, 120 male people
among 288 people. So,
168/288=58.33% is female,
120/288=41.67% is male.
b) What is the “tenure with company” distribution by gender?
We look at all males. You can do that for females similarly. We get the following table.
From this table, we know that there are 120 males:
26 with code 2 meaning they stay in the company for 2 to 5 years.”
14 with code 3 meaning they stay in the company over 5 years”
80 with code 1 meaning they stay in the company for less than 2 years
So, the “tenure with company” distribution by male is
26/120=21.67% among 120 males stays in the company for 2 to 5 years.
14/120=11.67% among 120 males stays in the company over 5 years;
80/120=66.66% among...