Trend SALES Year 1 4.8 1985 2 4 1986 3 5.5 1987 4 15.6 1988 5 23.1 1989 6 23.3 1990 7 31.4 1991 8 46 1992 9 46.1 1993 10 41.9 1994 11 45.5 1995 12 53.5 1996 13 48.4 1997 14 61.6 1998 15 65.6 1999 16 71.4 2000 17 83.4 2001 18 93.6 2002 19 94.2 2003 20 85.4 2004 21 86.2 2005 22 89.9 2006 23 89.2 2007 24 99.1 2008 25 100.3 2009 26 111.7 2010 27 108.2 2011 28 115.5 2012 29 119.2 2013 30 125.2 2014 31 136.3 2015 32 146.8 2016 33 146.1 2017 34 151.4 2018 35 150.9 2019

The file name SALES35.csv contains annual sales ($ million) of 35 years for a sporting store from 1985 to 2019. Use different methods to model the time series data and compare the forecast results. Questions: 1. Plot the sales data over time (T) and clearly label the axes to identify the scale and units. Discuss the components you see: trend, seasonal, cyclical, and irregular Ans.____________________________________________________________ ____________________________________________________________ 2. Run a simple regression model: Sales = b0 + b1T. Discuss your regression outcome and provide residual plot. Do you see any problems for ZINE assumptions? Explain. Ans. __________________________________________________________________ ______________________________________________________________________ 3. Conduct Durbin-Watson test. Is there evidence that the residuals are correlated following AR(1) process? Explain your answer with alpha=0.05. Ans. _______________________________________________________________ ____________________________________________________________________ 4. Based on your answer to question 3, what is wrong with the regression in question 2? Explain. 5. Recommend a new model to estimate Sales = b0 + b1T with AR(1) process.

6. Compare your regression results from questions 2 and 5. What are the differences in estimated intercept, slope, and the standard errors of the intercept and slope?