Consider the data provided in the DA2022_Sem2_Ass3_Data.xlsx file. The data provides you with historical values (1973-2018) of consumption and income per capita in Australia, given in Australian Dollars. Some believe that there is a linear relationship between the two variables, so in this assignment you will explore that. They also postulate that consumption is the dependent variable and that income is the Independent variable, so you will start with that particular structure of the relationship. Using the sample data provided to you, please do the following and make sure to provide explanations (e.g details of calculations) for each answer: 1. State the equation of the ligear regression model that you are considering here, using a probabilistic approach. Explain each element of the equation. (10 points) 2. Draw a scatter plot representing the relationship between the two data sets that follows standard conventions. Make sure to correctly label and title your plot. ( 8 points) 3. Compute the OLS estimates of the linear regression model, which you have written in Q1, 1ising the formulas presented in the lecture slides, ( 20 points) 4. In a few sentences, explain what the estimated coefficients tell you about how changes in income are related to changes in consumption in Australia. Make sure to include and use the appropriate units for your variables. (10 points) 5. Calculate SST, SSE, SSR and the coefficient of determination R2 using the given formulas in the lecture ( 32 points) 6. Using the "regression" function found in Excel under Data Data Analysis, check your answers to Question 3 and 5(R2). Make sure to highlight the relevant results of the regression function output. ( 10 points) 7. Discuss shortly what the results of Q5 tell you about the relationship between income and consumption in Australia as well as what all the results tell you about the causality between them. ( 10 points) Submit your answer by uploading two files: a pdf document that must be typed and then saved or converted to pdf, not scanned which provides your answers to the questions, and one Excel file which shows the actual calculations and graph. Make sure that you indicate on the Excel sheet what you are calculating. The pdf document should NOT exceed 3 pages in length, with 11 pts font and regular spacing and margins.1. Consider the data provided in the DA2022_Sem2_Ass3_Data.xlsx file. The data provides you with historical values (1973-2018) of consumption and income per capita in Australia, given in Australian Dollars. Some believe that there is a linear relationship between the two variables, so in this assignment you will explore that. They also postulate that consumption is the dependent variable and that income is the Independent variable, so you will start with that particular structure of the relationship. Using the sample data provided to you, please do the following and make sure to provide explanations (e.g details of calculations) for each answer: 1. State the equation of the ligear regression model that you are considering here, using a probabilistic approach. Explain each element of the equation. (10 points) 2. Draw a scatter plot representing the relationship between the two data sets that follows standard conventions. Make sure to correctly label and title your plot. ( 8 points) 3. Compute the OLS estimates of the linear regression model, which you have written in Q1, 1ising the formulas presented in the lecture slides, ( 20 points) 4. In a few sentences, explain what the estimated coefficients tell you about how changes in income are related to changes in consumption in Australia. Make sure to include and use the appropriate units for your variables. (10 points) 5. Calculate SST, SSE, SSR and the coefficient of determination R2 using the given formulas in the lecture ( 32 points) 6. Using the "regression" function found in Excel under Data Data Analysis, check your answers to Question 3 and 5(R2). Make sure to highlight the relevant results of the regression function output. ( 10 points) 7. Discuss shortly what the results of Q5 tell you about the relationship between income and consumption in Australia as well as what all the results tell you about the causality between them. ( 10 points) Submit your answer by uploading two files: a pdf document that must be typed and then saved or converted to pdf, not scanned which provides your answers to the questions, and one Excel file which shows the actual calculations and graph. Make sure that you indicate on the Excel sheet what you are calculating. The pdf document should NOT exceed 3 pages in length, with 11 pts font and regular spacing and margins.1
