Description

LIAF105 – Quantitative Methods
This coursework is worth 40% of the overall grade.
The submission date is Friday, 24/07/2020, 4:00 PM
You should do the assignment individually.

Aims:
The aim of this assessment is to develop and evaluate data-driven models based on bivariate and multivariate
regression models, and to demonstrate ability to apply the coefficient of variation to given data.
The coursework allows students to:
(1) develop and demonstrate the application of the methods of ordinary least squares using Excel.
(2) show an understanding of the importance of the coefficient of variation.
The assessment will consist of graphs and statistical analysis within a written report, fully explaining results and
findings for each question. This should be no more than 1700 words and should be typed, using ICP house style.
Report writing requirements:
• There are 11 questions and you should answer all of these separately.
• Type your answers to each question in a word document, and number the questions clearly.
• Show all relevant Excel calculations / regression summary output within your answers and include relevant
analysis / findings / conclusions for each question.
• Use references based on all the literature you have used in compiling this report. Use the APA referencing
system.
• Pay attention to the overall presentation and structure, ensuring logical development of ideas.
SECTIONS A and B:
• Use an introduction to set your aims, explaining the problem you are examining.
• Structure the main body of work, which should comprise a discussion of your findings within each question,
including the following:
• Summarise the main regression results including the estimated regression coefficients and model, t-ratios,
coefficient of determination and regression summary analysis.
• Explain your regression line graphs and statistical results clearly.
• Show an understanding of the coefficient of determination.
• Carry out hypothesis tests on regression coefficients and interpret your findings.
SECTION C:
• Show an understanding of the coefficient of variation and decisions based upon it.

Assessment Criteria
• Demonstration of competence in the production and presentation of results from Microsoft EXCEL.
• Providing appropriate analysis, explanation and interpretation of results.
• Showing understanding of methods employed in analysis of data.
• Structuring and presenting the report clearly (including labelling of graphs and tables).

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Coursework Brief
SECTIONS A and B:
You are required to examine a time series data set for demand for coffee in from 1990 to 2018. You will examine the
relationship between market demand of coffee, and two variables, price and income. You will evaluate the significance
of the variables within your models with a view to influence on consumer behaviour.

In section A, use a bivariate regression model to investigate the following relationships separately:
(1) Demand for coffee and Price of coffee.
(2) Demand for coffee and Income.
You are expected to analyse the regression results, and comment on your findings.

In section B, you are expected to use multivariate regression analysis for Demand, Price and Income, and comment on
your findings.

In section C, you are expected to use the coefficient of variation to analyse the given data, and comment on your
findings.

For all sections (A, B and C), you may give your answers to 2 decimal places when appropriate; otherwise,
use your judgement to give a suitable degree of accuracy.

Data
Download the data from the MS Excel file in moodle to answer the questions in Sections A and B.
The table shows time series data for demand for coffee, the price of coffee, and the personal disposable income of
consumers over the years (1990 to 2018).
Remember you are expected to conduct descriptive statistics and inferential statistics for both sections A and B.

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COURSEWORK QUESTIONS:

Answer each question separately, clearly showing the relevant question number.

Section (A): Bivariate Linear Regression Model [40 marks]

1). Plot separate scatter diagrams for the following:
(i) Demand for coffee (Y), against Price of coffee (X1).
(ii) Demand for coffee (Y), against Income (X2).
Note that Demand should be plotted on the y axis for all graphs in this coursework.
Comment on the relationship between the variables in graphs (i) and (ii). [6 marks]
2). Assuming that Demand for coffee (Y), and Price of coffee (X1), are linked by a linear relationship, by using
the Ordinary Least Squares (OLS) method, estimate a model for this regression: Y = α1 + β1X1 , and interpret
the value of the gradient.
Show all calculations clearly (The regression summary output in Excel can used). [10 marks]
3). Find the coefficient of determination, R
2
, and comment on its value.

State whether there is a significant relationship between Demand and Price by carrying out an appropriate
test at a 5% significance level.
(The regression summary output in Excel can used). [7 marks]
4). Assuming that Demand for coffee (Y), and Income (X2), are linked by a linear relationship, by using the
Ordinary Least Squares (OLS) method, estimate a model for this regression: Y = α2 + β2X2 , and interpret
the value of the gradient.
Show all calculations clearly. (The regression summary output in Excel can used). [10 marks]
5). Find the coefficient of determination, R
2
, and comment on its value.

State whether there is a significant relationship between Demand and Income by carrying out an appropriate
test at a 5% significance level.
(The regression summary output in Excel can used). [7 marks]

Section (B) Multivariate Regression Analysis [50 marks]

It is reasonable to assume that Demand for coffee depends on both Price of coffee and Income.
Use multivariate regression analysis to investigate the relationship between Demand (Y), and Price (X1)
and Income (X2
) .

6). Estimate the linear regression model for Demand (Y), and Price (X1) and Income (X2
):

Y = α3 + β3X1 + β4X2 .
Interpret the values of the gradients.
Show all calculations clearly (The regression summary output in Excel can used). [10 marks]

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7). Compare the estimated coefficient (β1) for Price of coffee (X1), in the bivariate regression equation in
Section A (in Question 2), to the estimated coefficient (β3) for Price of coffee (X1), in the multivariate
regression equation in Section B (in Question 6).
Are the coefficients different? If so, why? Explain your answer. [10 marks]

8). State and discuss the value of the coefficient of determination for the multivariate regression analysis
for Demand (Y), and Price (X1) and Income (X2

), and compare it to the value of R
2
in the bivariate
regression analysis found in Question 3, Section A. [10 marks]

9). Provide a conclusion based on all your findings in this assignment and hence comment on the validity of
the regression models used in Section A and B. [10 marks]
10). What other variable(s) do you think could influence the demand for coffee in the United Kingdom.
Provide clear explanations for your reasons. [10 marks]

Section (C) Coefficient of Variation [10 marks]

11). You are asked by an investor to analyse the stock risk of two companies: Ori and Luna. You are
provided with the sample mean (X) and standard deviation (S) over a 5 year period for the stock of both
companies, as shown in the table below:

Year Stock: Ori Stock: Luna
X1 S1 X2 S2
2011 7.02 1.22 6.23 2.5
2012 8.63 1.52 6.7 2.31
2013 7.06 1.03 6.9 1.15
2014 7.4 1.5 7.55 1.3
2015 8.3 1.75 7.66 1.4

State which stock was riskier for each year. Show all your working and explain your answers.