Quantitative Methods

Aims and Objective
The aim of this assessment is to develop and evaluate data-driven models based on simple and multiple regression models. It allows students to develop and demonstrate the application of the methods of ordinary least squares using Excel. Also to show an understanding of the importance of coefficient of variation. The assessment will consist of statistical analysis, graphs, analysis and written report explaining your results and findings.

Advice about writing the report:
• Use an introduction to set the aim of the report explaining the problem you are examining.
• Structure the main body which should comprise of a discussion of your results.
• Summarise the main regression results including the estimated regression line, estimated regression coefficients, standard errors, t-ratios, coefficient of determination and present regression summary analysis.
• Carry out hypothesis tests on regression coefficients and interpret your findings.
• Explain your graphs of regression line and statistical results clearly in the report.
• Show an understanding of coefficient of variation and decisions based on it
• Summarise your findings/conclusion at the end of the report.
• Answer all the questions.
• Use references based on all the literature you have used in compiling this report. Use APA referencing system.
• Pay attention to the overall presentation, structure and ensure logical development of ideas.

Assessment Criteria
• Demonstrating competence in the production and presentation of results from Microsoft EXCEL
• Understanding of methods employed,
• Providing appropriate analysis, explanation and interpretation of results.
• Structuring and presenting the report clearly.

Section (A) Simple Linear Regression Model [40 marks]
1). Plot a separate scatter diagrams of demand for coffee, Y, against, X,, real price of coffee
and for demand for coffee Y, and real personal disposable income, X2. Comment on kind of
relationship that exit? [6 marks)
2). Assuming that the demand for coffee, Y, and real price of coffee, X;, are linked by a linear
relationship, estimate this regression by Ordinary Least Squares (OLS) method, clearly
showing all your calculations (Excel can used for all the computations). (10 marks]
¥, = BY) + 6 = a + BX + &; [4]
3). Estimate the coefficient of determination – R? and comment on its value. Carry out an
appropriate test at 5% significance level for the explanatory power of the model.
[10 marks]
4). Assuming that annual demand for coffee, Y, and real personal disposable income level, X,
are linked by a linear relationship, estimate this regression by Ordinary Least Squares (OLS)
method using Excel: [10 marks]
¥, = B(Y,) + €) = 2 + BoX2; + & (2]