Statistics

JGU Id. No. __________

End Term Examination Spring 2021

Programme & Batch: IBM 2020

Course Name: Business Statistics

[Course Code: BS-DSC-165]

MAXIMUM MARKS: 50 TIME: 24 HOURS

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 [email protected]. The file name should be <Student ID>.xls

· Do not forget to highlight the final answers with yellow colour.

· This question paper comprises of 2 pages (including this page).

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

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

2. (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

3. 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

4. The file Incomedata.xls contains the annual incomes of a representative sample of people in the years 1975, 1985, 1995 and 2005 of USA.

a. What is the sample size?

b. How does the average income change over time?

c. Which income should represent the sample and why?

d. Which year shows more variability in income? Why do you think so?

e. Which year’s income is most asymmetrical? Give reason.

f. Find the pairs of years, the income of which varied directly.

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

5. 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

End Term Examination – Spring 2021, JGBS Page 1