Statistics

LIBU105_Business Statistics_201702

International College Portsmouth

Coursework 1 2017/02

LIBU105 - Business Statistics

Lecturers: Ifeanyichukwu Nworie & Chinedu Dibia

This coursework is worth 30% of the overall grade.

The submission date is Friday, 14/07/2017, 4:00 PM

You should do the assignment individually.

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. The assessment will consist of statistical analysis, graphs, analysis and written report explaining your results and findings. This should be no more than 1500 words and should be typed.

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 the discussion of your results very clearly.

· Summarise the main regression results including 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.

· 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,

Coursework Brief

You are required to examine a time series data of demand for coffee in United Kingdom from 1990 to 2010. As part of this assignment you are required to examine the market demand of coffee model and evaluate the significance of variables influencing consumer behaviour. In section A, you are required to use a simple two variable model to investigate the relationship between demand and real price of coffee and real disposable income separately. You are expected to analyse the regression results and comment on your findings. In section B, you are expected to use multiple regression analysis and comment on your findings.

Data

The following data is provided in an excel file and can be downloaded. The table show time series data on demand for coffee, real price of coffee, and real personal disposable income over the years (1990 to 2010) in the UK. Download the data from M.S Excel file in module and answer the following questions in part A and B.

Section (A) Simple Linear Regression Model [50 marks]

1). Plot 2 separate scatter diagrams of demand for coffee, Y, against, , real price of coffee and real personal disposable income, . What kind of relationship does each scatter diagram present? Explain. [6 marks]

2). Assuming that demand for coffee, , and real price of coffee, , 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). [15 marks]

= + = + + [1]

3). Calculate the coefficient of determination, = 1- 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, and real personal disposable income level, are linked by a linear relationship, estimate this regression by Ordinary Least Squares (OLS) method using Excel:

= + = + + [2]

[12 marks]

5). Carry out an appropriate test at 5% significance level for the explanatory power of the model, using the information in the regression summary output. [7 marks]

Section (B) Multiple Regression Analysis [50 marks]

It is reasonable to assume that demand for coffee depends on both real price of coffee and real disposable income. Use multiple regression analysis to investigate the relationship between .

6). Estimate the following linear regression model using the data set: [12 marks]

= + = + + [3]

7). Compare the estimated coefficient for real price of coffee, , from the regression equation (1) in section A and multiple regression equation (3) in section (B). Are they different? If so, why? Explain your answer. [12 marks]

8). What is the value of the coefficient of multiple determination, for the multiple regression model? Explain the difference between the co-efficient of determination from the first estimated linear regression (1) in section A and the one calculated in section B, regression equation (3). [13 marks]

9). Provide a conclusion based on all your findings in this assignments and hence comment on the validity of the above regression models used in section (A and B). [13 marks]

Total 100 marks