3. The following data show estimates of the population of Liberia in selected years between 1960 and 2010: Year 1960 1970 1980 1990 2000 2010 Population (millions) 1.1 1.4 1.9 2.1 2.8 4 Calculate the rate of growth of the population in millions per year for 2010. (a) Use two-point backward difference formula.
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- Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.
- 5 Quarterly data from 1960Q1 to 2009Q4, stored in the file consumptn.dat, were used to estimate the following relationship between growth in consumption of consumer durables in the U.S. (DURGWTH) and growth in personal disposable income (INCGWTH); DURGWTHt = 0.0103 - 0.163 DURGWTHt-1 + 0.7422 INCGWTHt + 0.3479 INCGWTH t-1 Given that DURGWTH 2009Q4 = 0.1, INCGWTH 2009Q4 = 0.9, INCGWTH 2010 Q1= 0.6, and INCGWTH 2010 Q2= 0.8, forecast DURGWTH for 2010Q1 and 2010Q2The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuingto decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?With the gasoline time series data from table 17.1, show the exponential smoothing forecasts using a = .1.a. applying the MSe measure of forecast accuracy, would you prefer a smoothing constant of a = .1 or a = .2 for the gasoline sales time series?b. are the results the same if you apply Mae as the measure of accuracy?c. What are the results if Mape is used?
- The following table shows the daily receipts in millions of dollars of the movie "The Hunger Games" after its opening on 23 March 2012. Days $Receipts 0 152.535 14 33.111 28 14.666 42 5.587 56 2.95 70 1.567 84 0.852 98 0.397 112 0.279 126 0.518 Estimate the instantaneous rate of change of the daily receipts on day 70.The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for January 2018 to December 2020 period: a. Calculate the Seasonal Index for every quarter. b. If the trend is described by the trend line T^ = 1,000 + 30 t, what is the forecast for the fourth quarter of 2021?Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.9 Q2 84.1 Q3 107.1 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,964 Time 50.7 What is the trend projection of the series for period 119? (please round your answer to 1 decimal
- By what percentage is salary predicted to increase if ros increases by 50 points? Does ros have a practically large effect on salary?Look at the four plots in Figure 14.2—the US unemployment rate, thedollar-pound exchange rate, the logarithm of the index of industrial production, and the percentage change in stock prices. Which of these seriesappears to be non-stationary? Which of them appears to resemble a randomwalk?Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 70.3 Q2 81.4 Q3 107 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,345 Time 62.4 What is the forecast for period 104, if period 104 is a Q4? (please round your answer to 1 decimal place