Question 4

Question 4 (this question has four parts, (a), (b), (c) and (d)) We obtain monthly data on retail sales of supermarket and grocery stores in Victoria measured in millions of Australian dollars from January 2010 to January 2021. Figure 1: Retail sales of supermarket and grocery stores (mil) in Victoria 3000 Supermarket and grocery sales (mil) 2500 2000 1500 2010 2012 2014 2016 2018 2020 (a) Comment on the time series features of retail sales of supermarket and grocery stores data shown in Figure 1. (3 marks) (b) We fit the following model to the retail sales of supermarket and grocery stores (Sales.). Here the variable t denotes a linear time trend, and Dect denotes a dummy variable for December. Interpret the coefficient on t. Salest = Bo + B1Salest-1 + Bat + ByDect + ut (2 marks) (c) Given the sample regression function below with standard errors in the parentheses, test for overall significance of the model at 5% level of significance. 9Sales, = 1232.766 + 0.185Salest-1 + 6.263t + 291.489Dect (103.47) (0.067) (0.560) (31.494) n = 132, R2 = 0.908. (4 marks) (d) To examine if the panic buying during COVID-19 lockdowns has any effect on Sales, we create a dummy variable COVID, for the months of March and July 2020 for the first and second COVID lockdowns in Victoria. We add COVID, to the model from part (c) above and obtain the following sample regression function. The standard errors are in parentheses. Interpret the coefficient on COVID,, and test if the panic buying behaviour is statistically significant at 1% level of significance. Sales, = 1218.724 + 0.201 Salest-1 + 5.866 t (86.636) (0.056) (0.472) +299.784 Dect + 452.464 COVID. (26.387) (60.646) n = 132, R2 = 0.936. (3 marks) (3+ 2 + 4 + 3 = 12 marks)