Example 18.15 The trend equation for annual sales of a product is- Y = 102 + 36 X %3D with 1st January 1990 as origin. (i) Determine the monthly trend equation with 1 July 1992 as origin. (ii) Compute the trend values of sales in October 1994.
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Statistics: Forecasting
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- The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data forseveral years is given in Table 4[14]. Determine whether the trend appears linear. If so, and assuming the trendcontinues. in what year will the percentage exceed 35%?What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
- Does Table 1 represent a linear function? If so, finda linear equation that models the data.The median home value in Mississippi and Maryland (adjusted for inflation) are shown below: If we assume that the house values are changing linearly,a) In which state have home values increased at a higher rate? b) If these trends were to continue, what would be the median home value in Mississippi in 2010?$An economist at Nedbank ran a study of the relationship between FTSE/JSE All Shares index return (JALSH) and consumer price index (CPI) from 2006 to 2017, the data collected is shown in the Table 1 below. FTSE/JSE All Shares index return (JALSH) and consumer price index (CPI) from 2006 to 2017. Year JALSH (Y) CPI (X) 2006 0.41 4.7 2007 0.19 7.1 2008 -0.23 11.5 2009 0.32 7.1 2010 0.19 4.3 2011 0.03 5.0 2012 0.27 5.6 2013 0.21 5.7 2014 0.11 6.1 2015 0.05 4.6 2016 0.00 6.4 2017 0.21 5.3 The estimated regression…
- What does the following graph suggest? No suggestion of linear relationship between the two variables A medium positive correlation between the two variables A medium negative correlation between the two variables A curvilinear relationship between the two variablesThe median home value in Michigan and New York (adjusted for inflation) are shown below. Year Michigan New York 1950 45400 61500 2000 115600 148700 If we assume that the house values are changing linearly,a) In which state have home values increased at a higher rate? New York, Mich., or equal rates: b) If these trends were to continue, what would be the median home value in Michigan in 2010?$ :c) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)The year :Monthly sales have been found to follow a linear trend of y = 10 + 8x, where y is the number of items sold and x is the number of the month. Monthly deviations from the trend have been calculated and follow an additive model. In month 12, the seasonal variation is estimated to be -6. What is the forecasted number of items to be sold in month 12?
- The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle. Sales also exhibit seasonal variations. Using the information given, prepare a forecast of sales for each quarter of next year (not this year), and the first quarter of the year following that. Ft = 30 – 5.5t + 2.5t2 Where Ft = Unit Sales t = 0 at, the first quarter of this year Quarter Relative 1 1.1 2 1.0 3 0.7 4 1.2The equation of the trend line for the data based on sales (in $1000) of a local restaurant over the years 2005-2010 is Sales= -265575+132.571*year. Using the trend line, the forecast sales for the year 2012 is ________ a. $1,157.85 b. $1,157,850 c. $132,571 d. $2,673,304 e. $1,000,327