Consider the data provided in the DA2022 Assignment3 Data.xlsx file. The data pro- vides you with the historical levels (1959-1995) of consumption and income per capita in the USA. We are investigating whether a linear relationship exists between the two variables. We postulate that the consumption is the dependent variable and that income is the independent variable. 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. Write down the equation of the linear regression model we are considering, using a prob- abilistic approach. (10 points) 2. Draw the scatter plot representing the relationship between the two data sets, with the dependent variable on the y-axis. (8 points) 3. Using the formula presented in the lecture slides, compute the OLS estimates of the linear regression model you have written in the previous question. (20 points) 4. In a few sentences, explain how an increase in income changes consumption. Make sure to use the appropriate units. (10 points) 5. Calculate SST, SSE, SSR and the coefficient of determination R2(32 points) 6. Using the regression function found in Excel under Data Data Analysis, check your answers to Question 3 and 5 (R2)(10 points) 7. Ina few sentences, explain whether income is responsible for changes in consumption and why? (10 points) Submit your answer by uploading two files: a pdf document that must be typed and then converted in pdf, not scanned which summarises your answers, and one Excel file which shows the actual calculations and graph. The pdf document should NOT exceed 3 pages in length, with 11 pts font and regular spacing and margins.

Year Income Consumption 1959 8604.285 7274.925 1960 8664.368 7376.945 1961 8796.294 7475.597 1962 9079.651 7665.462 1963 9276.482 7813.804 1964 9807.232 8134.39 1965 10304.52 8460.497 1966 10717.34 8802.401 1967 11063.25 9002.979 1968 11450.58 9349.496 1969 11711.25 9618.26 1970 12024.27 9824.337 1971 12347.05 9979.727 1972 12772.04 10364.18 1973 13540.72 10675.81 1974 13312.82 10641.37 1975 13404.45 10818.95 1976 13795.95 11199.58 1977 14098.78 11481.16 1978 14664.96 11838.17 1979 14902.58 12039.28 1980 14812.98 12013.56 1981 15012.22 12047 1982 15000.78 12097.09 1983 15278.67 12468.26 1984 16255.69 12840.39 1985 16600.27 13232.91 1986 16983.1 13535.37 1987 17108.86 13863.86 1988 17623.39 14230.62 1989 17804.09 14416.48 1990 17944.64 14554.67 1991 17757.77 14422.72 1992 18063.26 14608.15 1993 18079.16 14780.91 1994 18331.16 15007.67 1995 18802.89 15202.98