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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Based on previous statistics, the dean of a business school forecasts total student attendance for this year's summer session classes: Year Enrollment Four years ago 2000 Three years ago 2200 Two years ago 2800 Last year 3000 What is the annual rate of change (slope) of the least squares trend line for these data?Q3 The following data relates to the gross value of output of a factory over the last few years:Year 2014 2015 2016 2017 2018 2019 2020Production(in ‘000 tons)60 72.5 85.6 106.8 125.5 145.4 156.2Fit a straight-line trend using the method of least squares. Calculate the parabolic trend equation to predict the average annual output. Predict the trend values using each of the model and comment on its suitability
- Compute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)The table given below indicates Small Holding Ltd.’s quarterly profits in 2019 and 2020.Time Period Profit (Thousands Of Rands)2019 Q1 2502019 Q2 2102019 Q3 1652019 Q4 1952020 Q1 2652020 Q2 2182020 Q3 1782020 Q4 204Q.6.3.1 Determine the trend regression function for this data set. In order to obtain full marks for this question, you must complete the relevanttable (template provided below) and then apply the appropriate timeseries formulae in the formulae sheet.Q.6.3.2 Given that the typical seasonal index for Q3 is 87.3, use this informationand the trend regression function obtained in Q.6.3.1 to determine theseasonally adjusted trend estimate for profits in Q3 of 2022.The table given below indicates New Holding Ltd.’s quarterly profits in 2019 and 2020.Time Period Profit (Thousands Of Rands)2019 Q1 2502019 Q2 2102019 Q3 1652019 Q4 1952020 Q1 2652020 Q2 2182020 Q3 1782020 Q4 204 Determine the trend regression function for this data set. Given that the typical seasonal index for Q3 is 87.3, use this informationand the trend regression function obtained to determine theseasonally adjusted trend estimate for profits in Q3 of 2022.
- Use a smoothing constant ALPHA = 0.8 and calculate the forecasted value and smoothing valueThe table given below indicates Small Holding Ltd.’s quarterly profits in 2019 and2020.Time Period Profit (Thousands Of Rands)2019 Q12019 Q22019 Q32019 Q42020 Q12020 Q22020 Q32020 Q4250210165195265218178204Q.6.3.1 Determine the trend regression function for this data set. In order toobtain full marks for this question, you must complete the relevanttable (template provided below) and then apply the appropriate timeseries formulae in the formulae sheet.The following time series shows the sales of supermarket chain over the last six months. Month Sales ($ 000) August 2021 250 Sep 2021 280 Oct 2021 295 Nov 2021 320 Dec 2021 380 Jan 2022 360 Develop a linear trend equation that can be used to forecast sales in Feb 2022. Forecast the sales in Feb 2021 using a three-period weighted moving average designed with the following weights: Nov 2021 weight 0.6, Dec 2021 weight 0.3 and Jan 2022 weight 0.1. Which method (A or B) is the best? Explain why.
- The following data resulted from a study commissioned by a large management consulting company to investigate the relationship between amount of job experience (months) for a junior consultant and the likelihood of the consultant being able to perform a certain complex task. (image w/ success and failure) Interpret the accompanying MINITAB logistic regression output, and sketch a graph of the estimated probability of task performance as a function of experience. (2nd image)hudson Marine has been an authorized dealer for c&d marine radios for the past sevenyears. the following table reports the number of radios sold each year.Year 1 2 3 4 5 6 7Number Sold 35 50 75 90 105 110 130a. construct a time series plot. does a linear trend appear to be present?b. Using Minitab or excel, develop a linear trend equation for this time series.c. Use the linear trend equation developed in part (b) to develop a forecast for annualsales in year 8.The sales records of a major auto manufacturer over the past years from 2005 to 2019 are shown below. Number of Cars Sold Year (In thousands of Units) 2005 195 2006 200 2007 250 2008 270 2009 320 2010 380 2011 440 2012 460 2013 500 2014 500 2015 550 2016 570 2017 600 2018 650 2019 700 Develop moving average with k=4 and compute its MSE Develop exponential model with α = 0.4 and compute its MSE Develop a linear trend model and compute its MSE Based on the MSE computed fore ach model , which model fits well to the data Based on the answer of question (4) forecast the number of cars sold for year 2020.
