Business Statistics

Instructions to students:

This is a take-home examination.
Attempt all problems. Each problem contains 10 marks.
Solve problems in separate tabs of a single Excel file, and mail the Excel file to. The file name should be .xls
Do not forget to highlight the final answers with yellow colour.
This question paper comprises of 2 pages (including this page).

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

Year Revenue (billions)
2001 1.44
2002 1.58
2003 1.55
2004 1.47
2005 1.39
2006 1.41
2007 1.40
2008 1.39
2009 1.42
2010 1.34
2011 1.28
2012 1.36
2013 1.15
2014 1.27
(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 school GNP per capita
Cuba 18 98 98 2000
Sri Lanka 20 85 92 3300
Costa Rica 19 94 84 5800
Vietnam 44 85 58 600
China 54 80 86 2400
South Africa 56 76 68 4000
Saudi Arabia 38 59 68 11000
Brazil 60 78 56 5600
Zimbawe 68 82 76 1800
Morocco 68 42 76 3400
Pakistan 98 36 38 2100
Nigeria 86 44 56 1600

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

Year Revenue (millions USD)
2009 70
2010 183
2011 340
2012 649
2013 1243
2014 1979
2015 4096
2016 6440
2017 8459
2018 12154
The file xls contains the annual incomes of a representative sample of people in the years 1975, 1985, 1995 and 2005 of USA.
What is the sample size?
How does the average income change over time?
Which income should represent the sample and why?
Which year shows more variability in income? Why do you think so?
Which year’s income is most asymmetrical? Give reason.
Find the pairs of years, the income of which varied directly.
1+1+2+2+2+2 = 10

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?
(4+4) + 2 = 10

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