Business Statistics Assignment
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.
Section (A) Simple Linear Regression Model [50 marks]
1). Plot 2 separate scatter diagrams of demand for coffee, Y, against, X_1, real price of coffee and real personal disposable income, X_2. What kind of relationship does each scatter diagram present? Explain.
2). Assuming that demand for coffee, Y, and real price of coffee, X_1, 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).
Y_i = E(Y_i) + ε_i = α_i + β_i X_1i + ε_i [1]
3). Calculate the coefficient of determination, R^2 = 1- ESS/TSS and comment on its value. Carry out an appropriate test at 5% significance level for the explanatory power of the model.
4). Assuming that annual demand for coffee, Y, and real personal disposable income level, X_2 are linked by a linear relationship, estimate this regression by Ordinary Least Squares (OLS) method using Excel:
Y_i = E(Y_i) + ε_i = α_2 + β_2 X_2i + ε_i[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.
Section (B) Multiple Regression Analysis
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 Y and X_1 and X_2 .
6). Estimate the following linear regression model using the data set:
Y_i = E(Y_i) + ε = α_3 + β_3 X_1 + β_4 X_2 ε_i[3]
7). Compare the estimated coefficient for real price of coffee, X_1, 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.
8). What is 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 the one calculated in section B, regression equation (3).
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).
Attachment:- Database.rar