For the following data find the linear trend (the equation). Then improve the trend by first taking 3 yearly and then 5 yearly moving averages (Specify R2 values for the 3 scenarios). Also predict the revenue for the year 2015 considering the random fluctuations using both additive and multiplicative model.

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  1. For the following data find the linear trend (the equation). Then improve the trend by first taking 3 yearly and then 5 yearly moving averages (Specify R2 values for the 3 scenarios). Also predict the revenue for the year 2015 considering the random fluctuations using both additive and multiplicative model.

2+2+2+(2+2) = 10

YearRevenue (billions)
20011.44
20021.58
20031.55
20041.47
20051.39
20061.41
20071.40
20081.39
20091.42
20101.34
20111.28
20121.36
20131.15
20141.27
  1. (a) Establish an MLR model to predict Infant Mortality based on the given data considering adult literacy %, finishing primary school % and GNP per capita. Find which of these predictors are not significant at 5% significance level (give reason).

3+2 = 5

(b) Drop that predictor and run MLR again. Write the predictive model again. Could you improve the prediction? Explain in terms of standard error and adjusted R2

3+2 = 5

Infant Mortality(deaths per thousand births)%age adult literacy%age finishing primary schoolGNP per capita
Cuba1898982000
Sri Lanka2085923300
Costa Rica1994845800
Vietnam448558600
China5480862400
South Africa5676684000
Saudi Arabia38596811000
Brazil6078565600
Zimbawe6882761800
Morocco6842763400
Pakistan9836382100
Nigeria8644561600

 

  1. Run all kinds of regression possible to predict the revenue for 2019 and list down the equations. Write the best-fit regression equation giving the reason why it is best-fit. Then predict the revenue for 2019.

5+2+3 = 10

YearRevenue (millions USD)
200970
2010183
2011340
2012649
20131243
20141979
20154096
20166440
20178459
201812154
  1. The file xls contains the annual incomes of a representative sample of people in the years 1975, 1985, 1995 and 2005 of USA.
    1. What is the sample size?
    2. How does the average income change over time?
    3. Which income should represent the sample and why?
    4. Which year shows more variability in income? Why do you think so?
    5. Which year’s income is most asymmetrical? Give reason.
    6. Find the pairs of years, the income of which varied directly.

1+1+2+2+2+2 = 10

  1. Develop a frequency distribution table for the incomes of 2005 with 10 classes and draw a histogram on separate tabs of Incomedata.xls. Which one is the modal class and why?