a)Outline the diffences between simple, double and triple exponential smoothing? b) Consider the following time series 100 100 100 110 120 130 140 150 160 170 180 190 Using alpha=0.2 and beta=0.5, compute the forecasts up to period 12 and also calculate the

The following linear trend expression was estimated using a time series with 17 time periods. Tt = 129.2 + 3.8t. What is the trend projection for time period 18 ?

A consumer interest group is tracking the percentage of household income spent on gasoline over the past 30 years. Which graphical display would be more useful, a histogram or a time-series graph. Why? a. A histogram because the change in data over time is the most relevant issue.b. A time-series graph because the change in data over time is the most relevant issue.    c. A time-series graph because the range of values for the data is the most relevant issue.6. A histogram because the range of values for the data is the most relevant issue.

The LawnPlus Fertilizer Company distributes fertilizer tovarious lawn and garden shops. The company must base itsquarterly production schedule on a forecast of how manytons of fertilizer will be demanded from it. The companyhas gathered the following data for the past three yearsfrom its sales records. a. Compute a three-quarter moving average forecast forquarters 4 through 13 and compute the forecast errorfor each quarter.b. Compute a five-quarter moving average forecast forquarters 6 through 13 and compute the forecast errorfor each quarter.c. Compute a weighted three-quarter moving averageforecast using weights of 0.50, 0.33, and 0.17 for the most recent, next recent, and most distant data, respec-tively, and compute the forecast error for each quarter. d. Compare the forecasts developed in parts (a), (b), and(c) using cumulative error. Which forecast appears tobe most accurate? Do any exhibit any bias?

Refer to the gasoline sales time series data in the given table. Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places. Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 12.89.

Compute the MAE for the data below: Time series Forecast 16 19.6 20 19 18 19.14 22 19

For the Philippines Basketball Association (PBA) 2013-2014 season, San Mig James Yap was the scoring leader with an average of 33 points per game. The following data shows the average of points per game for the scoring leader from the 2008-2009 season to the 2013-2014 season. Season Average 2008-2009 25                               2009-2010       35 2010-2011 29 2011-2012 34 2012-2013 35 2013-2014 33   Use exponential smoothing to forecast this time series. Consider smoothing constant of ɑ = 0.20 and ɑ = 0.30. What value of the smoothing constant provides the best forecast/ What is the forecast of the leading scoring average for the 2014-2015 season? Graph the forecast at ɑ = 0.30.

A local bank is using Winters' method with a = 0.2, B = 0.1, and y = 0.5 to forecast the number of customers served each day. The bank is open Monday through Friday. At the end of the previous week, the following seasonal indexes have been estimated: Monday, 0.95; Tuesday, 0.90; Wednesday, 0.80; Thursday, 1.25; Friday, 1.10. Also, the current estimates of level and trend are 20 and 1. After observing that 30 customers are served by the bank on this Monday, forecast the number of customers who will be served on each of the next five business days. Round your answers to one decimal place, if necessary. Tuesday Wednesday Thursday Friday Monday Forecast 22 25 23 29 31 X X X X

3) U.S. Health care expenditures. Because the over-65 population is growing more rapidly in the next few decades health care spending is expected to increase significantly in the next few decades. The following table gives the projected US health care expenditure (in trillions) from 2008 to 2013 Year 2008 2009 2010 2011 2012 2012 Expenditure 2.34 2.47 2.57 2.70 2.85 3.02 a) Draw a scatter diagram for this data. Use “Years since 2008” on the x-axis. Make sure the scatter diagram includes all required elements (axes labels, title, and appropriate scale) b) Use the points for 2009 and 2011 to find an equation of a line modeling this situation c) Use linear regression to find an equation of a line modeling this situation d) Use the equation in b to predict expenditures in 2016 and do this again for the equation in part c. What is the absolute and percentage difference between the two equations (use the equation in c as the base equation in the % calculation) e) Now use…

Table 1. Number of children diagnosed with ASD in each NI Health Trust during the time periods stated (per quarter year). Health Trust Belfast Northern South Eastern Southern Western Total for Northern Ireland Quarter to Jun 2020 34 13 9 54 24 134 Quarter to Sept 2020 2 5 32 115 29 183 Quarter to Dec 2020 10 107 84 121 65 387 Quarter to Mar 2021 44 123 124 127 71 489 describe the pattern of change over time in total Nl cases? Quarter to Jun 2021 58 171 125 171 96 621 Quarter to Jun 2021 103 178 92 135 101 609 Quarter to Dec 2021 83 225 129 131 114 682 Quarter to Mar 2022 90 193 111 114 143 651