Coursework 2025/01

LIAF105 - Quantitative Methods

This coursework is worth 40% of the overall grade.

The deadline for submission on Turnitin is Friday, 28 March, 4:00 PM

You must 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 regression 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 between 1000 and 1500 words (excluding figures) and must be typed and submitted as a Word Document, with Excel figures and tables inserted appropriately.

You DO NOT have to reach the maximum word count and you may lose marks for forcing your word count up with irrelevant information.

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 answers clearly.

• Show all relevant Excel regression summary outputs 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:

• DO NOT simply copy and paste AI answers to the questions, as this will be obvious and receive 0 marks.

• Structure your work, which should comprise a relevant discussion of your findings within each question, which will include the following over the entire coursework:

Summary of the main regression results including (where relevant) the estimated regression coefficients and models, p-values and significance ofF value, coefficients of determination and regression summary analysis.

Clear explanation of your regression line graphs and statistical results.

Understanding of the coefficient of determination.

Hypothesis tests using regression coefficients and interpretation of 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, without dependence on AI.

• Showing understanding of methods employed in analysis of data.

• Structuring and presenting the report clearly in Microsoft Word (including labelling of graphs and tables).

Coursework Brief

SECTIONS A and B:

Samples of consumers in the UK who buy bottled water were surveyed over the course of a year, and this data was condensed. You are required to investigate the corresponding data set, examining the relationship between market Demand for bottled water, and two variables, Price of bottled water and Income of consumers. You will evaluate the significance of the variables within your models with a view to understanding influences on consumer behaviour.

In section A, use a bivariate regression model to investigate the following relationships separately:

(1) Demand for bottled water and Price of bottled water.

(2) Demand for bottled water and Income of consumers.

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 for bottled water, Price of bottled water and Income of consumers, 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, or follow the stated accuracy requirements.

Data

Download the data from the MS Excel file in Moodle to answer the questions in Sections A and B.

The table shows condensed data for demand for bottled water, the price of bottled water, and the personal disposable Income of consumers. Units are not given for the data, and this will not affect analysis.

COURSEWORK QUESTIONS:

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

No marks will be given for non-specific, generic answers obtained through use of AI Chat services.

Give your answers to 2 decimal places when appropriate; otherwise, use your judgement to give a suitable degree of accuracy or follow the stated accuracy requirements.

Section (A): Bivariate Regression Analysis [40 marks]

1). Using Excel, plot separate scatter diagrams for the following:

(i) Demand for bottled water (Y), against Price of bottled water (x1).

(ii) Demand for bottled water (Y), against Income of consumers (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 each of the graphs (i) and (ii). [6 marks]

2). Assuming that Demand for bottled water (Y), and Price of bottled water (x1), are linked by a linear relationship, use the regression summary output in Excel to estimate a model for this regression in the form Y = α1 + β1x1, and interpret the value of the gradient.

(The full regression summary output should be presented to support your answers). [10 marks]

3a). Find the coefficient of determination, R2, for demand for bottled water and price of bottled water, and comment on its value.

b). State whether  there is a significant relationship between Demand and Price by carrying out an appropriate test, using the p-value at a 5% significance level.

(The regression summary output in Excel should be used). [7 marks]

4). Assuming that  Demand for  bottled water  (Y), and  Income of consumers  (x2), are  linked  by a  linear relationship, use the regression summary output in Excel to estimate a model for this regression in the form Y = α2 + β2x2 , and interpret the value of the gradient.

(The full regression summary output should be presented to support your answers). [10 marks]

5a). Find the coefficient of determination, R2, for demand for bottled water and Income of consumers, and comment on its value.

b). State whether there is a significant relationship between Demand and Income by carrying out an appropriate test, using the p-value at a 5% significance level.

(The regression summary output in Excel should be used). [7 marks]

Section (B) Multivariate Regression Analysis [50 marks]

Use multivariate regression analysis to investigate the relationship between Demand for bottled water

(y), Price of bottled water (x1) and Income of consumers (x2) :

6). Use the regression summary output in Excel to estimate the linear regression model for Demand for bottled water (y), Price of bottled water (x1) and Income of consumers (x2) in the form.

y = α3   +  β3x1  + β4x2  . Interpret the values of the gradients

(The full regression summary output should be presented to support your answers). [10 marks]

7). State and compare the estimated coefficient (β1 ) for Price of bottled water (x1 ), in the bivariate

regression equation in Section A, Question 2, to the estimated coefficient (β3 ) for Price of bottled water (x1 ), in the multivariate regression equation in Section B, Question 6.  Are the coefficients different? If so, why? Explain your answer, stating whether or not you think it is reasonable to assume that Demand for bottled water depends on both Price of bottled water and Income of consumers. [10 marks]

8). State and discuss the value of the coefficient of determination for the multivariate regression analysis for Demand for bottled water (y), Price of bottled water (x1) and Income of consumers (x2), and compare it to the value of R2  in the bivariate regression analysis found in Question 3, Section A. You must give your values to four significant figures.

Giving reasons, state which coefficient of determination is best to use. [10 marks]

9). Perform. an overall significance test to check validity of the coefficients in the multivariate regression in Section B.

Briefly discuss the suitability of the regression models used in Section A and B with reference to the appropriate evidence, and hence state which model provides the best fit to the data. Were your findings as expected? (Note: Do not simply re–state all your findings). [10 marks]

10). Apart from Price of bottled water and Income of consumers, what other variables do you think could influence the demand for bottled water in the United Kingdom? Provide factual reasons (rather than personal opinions), with in-text citations and references (APA format) to support your answers. [10 marks]

Section (C) Coefficient of Variation [10 marks]

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

Use the coefficient of variation to state which stock was less risky in each year. Show your method and explain your answers. [10 marks]

TOTAL: 100 MARKS