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The Census Bureau tracks a variety of retail and service sales using the Monthly Retail Trade Survey. Consider the monthly sales (in millions of dollars) from January 2014 through April 2018 for office supply and stationery stores. 1. Create a time plot for monthly sales for office supply and stationary stores with the months labeled \"1 \" for January, \"2\" for February, and so on. Show your plot in the space provided below: (21') 2. Interpret the characteristics of monthly sales for this sector in terms of time series component, such as trend, seasonality, cyclical pattern etc. over the time. Do you observe any pattern from the data that repeats itself at a regular interval? (411-) 3. In which month do you observe a dramatic increase or decrease for the sales? Explain the reason very briey. 4. Regress the monthly sales to a time variable and show the regression output in the space provided below. Interpret the results in terms of explained variability and the significance of the model. (611-) 5. Create indicator variables to represent each month as a category. Consider December data as a baseline model, How many indicator variables do we need to recode months as different categories? (39-) 6. Explain very briey the reason why we need indicator variables, in other words why we need to recode each month as a different category and include in the regression analysis? (411-) 7. Regress the monthly sales to a time variable along with all indicator variables. The new model captures the linear trend along with the seasonal pattern in the time series. Showthe output of the trend-and-season model and the multiple regression equation including all indicator variables in the space provided below. Interpret the results in terms of model fit which is reected in explained variability and the significance of the trendandseason model. 8. Compare and contrast the model fits of trend-only model and trend-and-season model in terms of explained variability and the significance of the model. (4p.) 9. Test the significance of each indicator variable and report if there is any insignificant variable exists in the trend-and-season model. (2p.) 10. Explain very briefly the reason why some coefficients of the indicator variables are negative from trend-and-season model. (2p.) 11. Report the indicator variable that shows the highest coefficient in the trend-and- season model and explain very briefly why one of the coefficients is quite high relative to other coefficients of indicator variables. (3p.) 12. What are the predicted monthly sales for the month of August using the trend-and- season model? Explain the results very briefly. (3p.)