[Solved] 1). Plot a separate scatter diagrams of demand for coffee, Y, against, 𝑋1, real price of coffee and for demand for cof

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[Solved] 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?

This paper revolves around business statistic, you are required to present a clear structured report. Your report must answer the following questions:

• Plot a separate scatter diagrams of demand for coffee against real price of coffee and Comment on kind of relationship that exit?
• Estimate regression by ordinary least square and the coefficient of determination
• ·          Significance level, and multiple regression analysis
• ·          Tabulate the value of the coefficient of multiple determination
• ·          Conclusion based on all your findings and ). What other variable(s) in your opinion could influence the demand for coffee in United Kingdom

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:

• · 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, the coefficient of determination and present regression summary analysis.
• · Carry out hypothesis tests on regression coefficients and interpret your findings.
• · Explain your graphs of the 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,

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]