Year Income Consumption 1973 4356 2312 1974 5056 2816 1975 5828 3256 1976 6724 3812 1977 7252 4192 1978 8100 4604 1979 9084 5072 1980 10116 5656 1981 11512 6428 1982 12324 7264 1983 13592 7776 1984 14728 8140 1985 16256 9124 1986 17416 9960 1987 19488 10820 1988 21688 11804 1989 23756 13012 1990 24228 13752 1991 24228 14248 1992 25116 14640 1993 26056 15080 1994 27512 15832 1995 28968 16724 1996 30052 17180 1997 31688 18140 1998 33060 19156 1999 34596 20136 2000 36588 21448 2001 38584 22324 2002 40736 23788 2003 43148 25044 2004 45636 26328 2005 48832 27568 2006 52204 29524 2007 55284 31584 2008 58932 31736 2009 58552 33096 2010 63320 34600 2011 66324 35884 2012 66684 36920 2013 68524 37928 2014 68492 38836 2015 68728 39772 2016 71740 40452 2017 73724 41412 2018 76688 42176

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.

1. State the equation of the linear regression model that you are considering here, using a probabilistic approach. Explain each element of the equation.

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.

3. Compute the OLS estimates of the linear regression model, which you have written in Q1, using the formulas presented in the lecture slides.

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.

5. Calculate SST, SSE, SSR and the coefficient of determination R2 using the given formulas in the lecture

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.

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.