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In this paper of Business Statistics, you are required to present a report examining the problem. In your report you must demonstrate competence in the production and presentation of results from Microsoft EXCEL ad include methods of employed, provide appropriate analysis and interpretation of results and finally, structure and present a clear report.
International College Portsmouth
Coursework 1 2018/01 LIBU105 -
Business Statistics
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, using ICP house style. Advice about writing the report:
Assessment Criteria
Section (A) Simple Linear Regression Model [40 marks]
1). Plot a separate scatter diagrams of demand for coffee, Y, against, 𝑋1, 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, 𝑋1, 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] 𝑌𝑖 = 𝐸(𝑌𝑖) + 𝜀𝑖 = 𝛼𝑖 + 𝛽𝑖𝑋1𝑖 + 𝜀𝑖 [1]
3). Estimate the coefficient of determination - 𝑅 2 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, 𝑋2 are linked by a linear relationship, estimate this regression by Ordinary Least Squares (OLS) method using Excel: [10 marks] 𝑌𝑖 = 𝐸(𝑌𝑖) + 𝜀𝑖 = 𝛼2 + 𝛽2𝑋2𝑖 + 𝜀𝑖 [2]
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. [4 marks] Section (B) Multiple Regression Analysis [60 marks] It is reasonable to assume that demand for coffee depends on both the real price of coffee and real disposable income. Use multiple regression analysis to investigate the relationship between 𝑌 𝑎𝑛𝑑 𝑋1 𝑎𝑛𝑑 𝑋2.
6). Estimate the following linear regression model using the data set: [12 marks] 𝑌𝑖 = 𝐸(𝑌𝑖) + 𝜀 = 𝛼3 + 𝛽3𝑋1 + 𝛽4𝑋2 𝜀𝑖 [3] 7). Compare the estimated coefficient for the real price of coffee, 𝑋1, 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. [15 marks]
8). Tabulate the value of the coefficient of multiple determination, 𝑅 2 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 in section B - regression equation (3). [10 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). [10 marks]
10). What other variable(s) in your opinion could influence the demand for coffee in United Kingdom. Provide a clear thought explanation for your reason. [13 marks]
