LIAF105 - Quantitative Methods
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 (where relevant) the estimated regression coefficients and model, p-values/t-ratios/significance of F values, 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).
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
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.
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 (π1).
(ii) Demand for coffee (Y), against Income (π2).
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 (π1), are linked by a linear relationship, use Excel with the Ordinary Least Squares (OLS) method to estimate a model for this regression: π = πΌ1 + π½1π1, 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, π 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 (π2), are linked by a linear relationship, use Excel with the Ordinary Least Squares (OLS) method to estimate a model for this regression: π = πΌ2 + π½2π2 , 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, π 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] Use multivariate regression analysis to investigate the relationship between Demand (π), and Price (π1) and Income (π2 ):
6). Estimate the linear regression model for Demand (π), and Price (π1) and Income (π2 ):
π = πΌ3 + π½3π1 + π½4π2 .
Interpret the values of the gradients.
Show all calculations clearly (The regression summary output in Excel can used). [10 marks]
7). Compare the estimated coefficient (π½1) for Price of coffee (π1), in the bivariate regression equation in Section A (in Question 2), to the estimated coefficient (π½3) for Price of coffee (π1), in the multivariate regression equation in Section B (in 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 coffee depends on both Price of coffee and Income. [10 marks]
8). State and discuss the value of the coefficient of determination for the multivariate regression analysis for Demand (π), and Price (π1) and Income (π2 ), and compare it to the value of π 2 in the bivariate regression analysis found in Question 3, Section A. Give all values to 4 significant figures. [10 marks]
9). Discuss the validity of the regression models used in Section A and B, and use the evidence you have found to provide a conclusion. [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: Sirius PLC and Orion Ltd. 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:
Stock: Sirius Stock: Orion
Year X1 S1 X2 S2
2015 13.99 5.94 6.43 2.59
2016 14.12 3.88 12.86 2.50
2017 11.68 7.14 5.37 3.59
2018 13.66 2.78 11.14 3.18
2019 13.72 5.05 12.06 5.78
Use the coefficient of variation to state which stock was less risky for each year. Show all your work and explain your answers.
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