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The U.S. Department of Agriculture tracks prices and sales of numerous food commodities. Consider the weekly sales volume (thousands of pounds) of butter sold in the United States starting with the first week of January 2007 and ending with the second week of December 2008.22

(a) Use software to make a time series plot of the butter sales time series. Describe the basic features of the time series. Be sure to comment on whether a trend or significant shifts are present or not in the series.

(b) Calculate 1-week, 2-week, 3-week, 4-week, 5-week, and 6-week moving averages for the butter sales time series.

(c) Compute the residuals for the 1-week, 2-week, 3-week, 4-week, 5-week, and 6-week moving-average models fitted in part (b). (Note: Given the different spans, you will find a different number of residuals for each of the models. In particular, you will find 101 residuals for the 1-week moving-average model, 100 residuals for the 2-week moving-average model, and so on.)