3 (4%) (Due: Thursday, July 21, 2016) 1. The following data represent the annual sales (in millions of dollars) for a food-processing company for the years 1999 - 2015. YEAR SALES YEAR SALES 1999 2000 2001 2002 2003 2004 2005 2006 2007 53.2 53.3 51.6 49.0 38.6 37.3 43.8 41.7 38.3 2008 2009 2010 2011 2012 2013 2014 2015 36.4 38.4 42.6 34.8 28.4 23.9 27.8 42.1 a) Compute the 5-year moving averages and forecast the Sales for 2016. (please keep the answers to 3 decimal places for all parts in question 1) [2 marks] b) Compute the 3-year weighted moving averages, using 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods respectively. Calculate the forecast for 2016. [2 marks] c) Using a smoothing coefficient of = 0.25, compute the exponentially smoothed values for the data. Calculate the forecast for 2016. [2 marks] d) Calculate the Mean Absolute Deviation error for each method in parts a) b) and c). Which method would be most accurate based on the MAD criterion? [3 marks] 2. (Modified from question 1, textbook, page 312) The data for this question come from a study of ice cream consumption that spanned the springs and summer of three years. (Please see the Excel file under Data for question 2 tab for the data set). a) Use Excel to find the multiple regression equation of the form = b0 + b1X1 + b2X2+ b3X3 where Y represents the ice-cream consumptions, X1 represents price, X2 represents income, and X3 represents temperature. Any comments about the model you have just constructed? [2 marks] b) Interpret the values of the regression coefficient for Temperature. [3 marks] c) Report the coefficient of determination. What does this statistic tell us about the model? [2 marks] d) Predict the ice-cream consumptions for Price = $2.99; Income = 1200$/week and Temperature = 22 degree Celsius. [2 marks] 1 3. The owner of a dry cleaning business, in an effort to measure the quality of the services provided, would like to study the number of dry-cleaned items that are returned for rework per day. Records were kept for a 4-week period (the store is open Monday - Saturday) with the results indicated as follows: DAY ITEMS RETURNED FOR REWORK 1 2 3 4 5 6 7 8 4 6 3 7 6 8 6 4 DAY 9 10 11 12 13 14 15 16 ITEMS RETURNED FOR REWORK 8 6 5 12 5 8 3 4 DAY 17 18 19 20 21 22 23 24 ITEMS RETURNED FOR REWORK 10 9 6 5 8 6 7 9 Construct a c-chart for the number of items per day that are returned for rework. Do you think that the process is in a state of statistical control? Why? [4 marks] 4. The manager of a branch of a local bank wants to study waiting times of customers for teller service during the peak 12 noon to 1 p.m. lunch hour. A subgroup of four customers is selected (one at each 15-minute interval during the hour), and the time in minutes is measured from the point each customer enters the line to when he or she begins to be served. The results over a 4-week period are as follows: DAY 1 2 3 4 5 6 7 8 9 10 7.2 5.6 5.5 4.4 9.7 8.3 4.7 8.8 5.7 1.7 TIMES IN MINUTES 8.4 7.9 4.9 8.7 3.3 4.2 7.3 3.2 6.0 8.0 5.4 7.4 4.6 4.8 5.8 8.9 9.1 6.2 6.6 5.3 5.8 5.5 8.4 6.9 4.7 4.1 4.6 4.0 3.0 5.2 DAY 11 12 13 14 15 16 17 18 19 20 2.6 4.6 4.9 7.1 7.1 6.7 5.5 4.9 7.2 6.1 TIME IN MINUTES 3.9 5.2 2.7 6.3 6.2 7.8 6.3 8.2 5.8 6.9 6.9 7.0 6.3 3.2 5.1 3.2 8.0 4.1 3.4 7.2 4.8 3.4 8.7 5.5 7.0 9.4 4.9 7.6 5.9 5.9 a. Construct an R-chart for the range and an X-bar chart for the arithmetic means. [6 marks] b. On the basis of the results in (a), interpret the charts and indicate whether the process is in statistical control. [2 marks] Instruction: You can work in a group of two or work on your own. Remember to include a cover page with your name(s) on it. You can use Excel to do this assignment. You can print out the charts and Excel output with your answers to submit or just submit your Excel file. For all decimal answers, please keep 2 decimal places. 2 Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Sales 53.2 53.3 51.6 49 38.6 37.3 43.8 41.7 38.3 36.4 38.4 42.6 34.8 28.4 23.9 27.8 42.1 Consumption 0.219 0.212 0.223 0.241 0.231 0.195 0.186 0.164 0.153 0.145 Price 4.0 2.5 2.5 2.5 2.4 2.3 2.4 2.4 2.4 2.5 Income 1100 1120 1132 1118 1050 1090 1200 1120 1045 1300 Temperature 6 13 19 20 22 19 16 8 0 -5 The icecream consumption is in literes per capita per week Price of the icecream is in dollars Family income of consumers is in dollars per week Temperature is in degrees Celsius Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Items returned for rework 4 6 3 7 6 8 6 4 8 6 5 12 5 8 3 4 10 9 6 5 8 6 7 9 Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 7.2 5.6 5.5 4.4 9.7 8.3 4.7 8.8 5.7 1.7 2.6 4.6 4.9 7.1 7.1 6.7 5.5 4.9 7.2 6.1 Time (in minutes) 8.4 7.9 8.7 3.3 7.3 3.2 8.0 5.4 4.6 4.8 8.9 9.1 6.6 5.3 5.5 8.4 4.7 4.1 4.0 3.0 3.9 5.2 2.7 6.3 6.2 7.8 6.3 8.2 5.8 6.9 6.9 7.0 6.3 3.2 5.1 3.2 8.0 4.1 3.4 7.2 X-bar 4.9 4.2 6.0 7.4 5.8 6.2 5.8 6.9 4.6 5.2 4.8 3.4 8.7 5.5 7.0 9.4 4.9 7.6 5.9 5.9 Range