5. Problem 5(20%). Follow the instructions below, create the needed outputs, attach the outputs where required, and explain what is required. Do not attach the full R-screen. If I cannot read your output, the question will receive zero credits. Attach the required plots and tables only. When attaching tables use courier new font, size 8 . Do not leave the question blank. Please start each problem on a new page. If the answer is not related to what the question asks, the question will receive zero credits. Do not share your answers or mistakes. If the instructor finds out that students have shared their answers or mistakes, the students will receive zero credits and the academic honesty policies and procedures will apply (as suggested by the Student Handbook which may be found at Handbook). 5.1. Use the data set us change to estimate a regression of consumption on the first lags of income, production, savings and unemployment. You have to create the first lags of the explanatory variables. Attach the regression output here. (Use courier new font, size 8) 5.2. Generate residual diagnostics and explain them. Attach the plot here. 5.3. Conduct a Ljun-box test of autocorrelation of the residuals and explain it. Explain why dof =5. Attach the results here. (Use courier new font, size 8) 5.4. Create the data set us_change 2016 from the data us change that covers the period 1970Q1-2016Q2. Create the data set us_change2017 that covers the period from 2017Q1 to the end of the series. Use the data us_change2016 to estimate a regression of consumption on income, savings, production, and unemployment. Attach the regression output here. (Use courier new font, size 8) 5.5. Generate forecasts of consumption given the regression model you estimated in subsection 5.4 and the data us_change2017. Attach the fable that shows the forecasts here. (Use courier new font, size 8) 7 NAME: 5.6. Generate a plot that shows the actual consumption data and its forecasts. Attach the plot here. Do not include the confidence intervals in the plot