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eliminated An illustration of the application of simple linear regression analysis is presented in Example Problem 5-3
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Example Problem 5-3 The historical data shown in Table 5-1 could also be used to prepare a forecast of the annual passenger enplanements at the study airport in the design years 2010 and 2015 using a simple regression analysis In applying simple regression analysis to these data, let us assume that a relationship between the study airport annual enplanements (ENP) and the study area population (POP) is to be examined Therefore, it is assumed that a linear relationship of the form shown in Eq (5-1) exists between the variables ENP = a0 + a1(POP) Using a standard regression analysis computer program the relationship is found to be ENP = 3,047,032 + 138633(POP) where the coefficient of determination R2 is 0983815, the coefficient of correlation is 0991874, and the standard error of the estimate, yest is 55,5209 The regression line and the data points upon which this regression line is based are shown in Fig 5-5 The coefficient of determination indicates that there is an extremely good relationship between the annual enplanements at the study airport and the study area population, that is, 984 percent of the variation in the study airport annual enplanements is explained by the variation in the study area population The standard error of the estimate, however, indicates that there is a large range of error associated with forecasting with this equation, that is, there is a 68 percent probability that the forecast of annual enplanements at the study airport will have an error range of 55,5209 annual enplanements This may
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ENP = 3047032 + 138633 POP
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FIGURE 5-5 Trend line forecast of study area population for Example Problem 5-3
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or may not be too high depending on the level of annual operations forecast in the future and the sensitivity of various components of the airport system to such variations Using a trend projection, it is forecast that the area population in the year 2010, as shown on Fig 5-6, is expected to be 363,000 The forecast of the annual enplanements at the airport in the year 2010 can be found by substitution into the regression equation yielding 1,985,300 annual enplanements Similarly, if the forecast of the area population in the year 2015 is expected to be 410,000, then the forecast of the annual enplanements at the airport in the year 2015 is found to be 2,636,900 Given the range in the standard error of the estimate, it could be expected that in the year 2010 there is a probability of 68 percent that the forecast could range between 1,985,300 55,500, or from 1,929,800 to 2,040,800 annual enplanements about 68 percent of the time Similarly, it could be expected that in the year 2015 the forecast could range between 2,636,900 55,500, or from 2,581,900 to 2,692,400 It is likely that this range in the forecasts is acceptable since it represents about a 2 to 3 percent error
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It is interesting to compare the results found by the three different techniques used in Example Problems 5-1 through 5-3 The results compare very well and it gives one some degree of confidence in the results when the three forecasts compare well This is called redundancy in forecasting Based upon the results found in these example problems, a preferred forecast would be developed If there is no reason to suspect
600 Historical Data Study Area Population (Thousands) Forecast
410 400 363
200 2000 2005 Year 2010 2015
FIGURE 5-6 Trend line forecast of study area population for Example Problem 5-3
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that one technique is better than another, then a simple average might be used to develop the preferred forecast If this is done in these examples, then the preferred forecast for the year 2010 is about 2,000,000 annual enplaned passengers and in the year 2015 is 2,600,000 annual enplaned passengers The Federal Aviation Administration utilizes econometric models to determine national forecasts of US aviation demand The FAA Aerospace Forecast [8] provides a 12-year outlook and view of the immediate future for aviation It is updated in March each year and includes aggregate level forecasts of the following: Passenger enplanements, revenue passenger miles, fleet, and hours flown for large carriers and regional commuters Cargo revenue ton miles and cargo fleet for large air carriers Fleet, hours, and pilots for general aviation Activity forecasts for FAA and contract towers by major user category The FAA Long Range Aerospace Forecasts [9] is a long range forecast that extends the 12-year forecast to a longer time horizon, typically for a period of 25 years This forecast contains projections of aircraft, fleet and hours, air carrier and regional/commuter passenger enplanements, air cargo freight revenue ton-miles, pilots, and FAA workload measures The success in applying mathematical modeling techniques to ascertain the level of future activity depends to a large extent on the certainty associated with the independent variables and the relative influence of these variables on the dependent variable Simple and multiple regression analysis methods are often applied to a great variety of forecasting problems to determine the relationships between transport related variables and such explanatory factors as economic and population growth, market factors, travel impedance, and competitive forces Table 5-2 lists many of the variables required for various purposes in aviation planning studies
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