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Question 1 - Improved global competitiveness was a factor in increasing exports of Canadian resource-based products during the period 2011 to 2015, as shown:                                                           

Year

Exports ($ billions)

2011

104.9

2012

105.3

2013

156.1

2014

188

2015

216.1

a) Draw a scatter diagram (1)                                                     

b) Obtain the least squares equation and plot the trend line

c) Estimate Canadian resource-based exports for (i) 2017 and (ii) 2019

d) What was the average annual change in exports

Question 2 - Warranty repairs for J.R. Electronics Canada were as follows:            

2008

2929

2009

2633

2010

2418

2011

2163

2012

1916

2013

1711

2014

1549

2015

1434

a) Construct a scatter diagram   

b) Determine the trend line equation and plot the line  

c) Forecast warranty repairs for (i) 2017 and (ii) 2019       

Question 3 - From the trend line equation yp = 520 + 30x, where y represents annual unit sales and 2008 is the first year (x=1), determine

a) The expected sales for 2011

b) The average annual change in unit sales

c) The estimated sales for 2014

Question 4 - Investment spending for the years 2011 to 2015 in billions of dollars IS LISTED BELOW. The least squares equation best describing the data is yp = 56.6 + 8x, with 2011 as the first year (x=1)                                                         

Year

 

INVESTMENT

SPENDING

2011

66

2012

73

2013

78

2014

87

2015

99

a) Plot the observed values on a line graph                                         

b) Plot the trend line on the graph in part (a)                                     

c) Compute the trend values for the years 2011 to 2015                                

d) Compute the percent of trend for the time period                                    

e) Construct a graph depicting the percent of trend                                        

Year

x

y

C)

D)

yp = 56.60 + 8.00x

Percent trend

yp =

y/yp(100)

2011

1

66

 

 

2012

2

73

 

 

2013

3

78

 

 

2014

4

87

 

 

2015

5

99

 

 

Question 5 - The equation yp = 2.29 + 1.08x represents the least squares equation for the following data:

Year

2010

2011

2012

2013

2014

2015

Cell phone use (in millions)

3

4.1

6.2

7.1

7.9

8.1

Let 2007 be x=1                                                                                

a) Plot the observed values of y and join the points                                                                                        

b) Plot the trend line                                                                                     

c) Compute the trend value for each year yp = 2.29 + 1.08x                         

d) Calculate the cyclical relatives                                                                                              

e) Construct a graph of the cyclical relatives                                                                                        

Year

x

y

yp (c)

Cyclical relative (d)

2010

1

3

 

 

2011

2

4.1

 

 

2012

3

6.2

 

 

2013

4

7.1

 

 

2014

5

7.9

 

 

2015

6

8.1

 

 

Question 6 - The number of corporate tax returns processed by a tax accountant for the period 2000 to 2015 is listed below:               

a) Compute the five-year moving averages        

2000

65

2001

51

2002

65

2003

70

2004

60

2005

97

2006

69

2007

50

2008

42

2009

46

2010

41

2011

37

2012

24

2013

22

2014

36

2015

40

b) Plot the time series and the moving averages               .

Question 7 - Monthly restaurant sales in the clubhouse of a local vacation resort offering golfing and skiing were are listed in the following table.                                                                   

Determine the 12-month moving average.                                                                         

Year

Month

Sales

12-month moving totals

12-month moving averages


2011

January

31,800

 

 


February

40,200

 

 


March

29,100

 

 


April

19,500

 

 


May

16,200

 

 


June

21,900

 

 

Jan to Dec 2011

July

27,900

 

 

Feb-11 to Jan-12

August

31,500

 

 

Mar-11-Feb-12

September

25,500

 

 

And so on

October

15,300

 

 


November

8,100

 

 


December

10,200

 

 


2012

January

32,100

 

 


February

40,500

 

 


March

28,800

 

 


April

16,500

 

 


May

19,200

 

 


June

22,200

 

 


July

30,300

 

 


August

31,800

 

 


September

22,500

 

 


October

14,400

 

 


November

8,700

 

 


December

8,400

 

 


2013

January

34,500

 

 


February

42,900

 

 


March

26,700

 

 


April

19,500

 

 


May

21,900

 

 


June

20,700

 

 


July

33,900

 

 


August

34,200

 

 


September

25,500

 

 


October

19,500

 

 


November

10,500

 

 


December

11,700

 

 


2014

January

37,800

 

 


February

47,400

 

 


March

27,900

 

 


April

22,800

 

 


May

24,300

 

 


June

24,300

 

 


July

23,700

 

 


August

31,600

 

 


Question 8 - The following data summarize the overnight guests at a bed and breakfast operation from 2011-2014:

Year

II

III

IV

2011

190

270

250

2012

210

285

250

2013

220

300

260

2014

190

250

250

Seasonal index

85

120

115

a) Compute the quarterly moving average i.e. quarter 1-4, 2-5etc                                            

b) Construct a graph of the time series                                 

c) Depersonalize the data                                           

d) Plot the seasonally adjusted values on the graph in (b)                                            

Reorganize data as follows and complete blank columns                                              

Year/Quarter

Guests

Quarterly moving totals

Quarterly moving averages (a)

Seasonal indexes

Seasonally adjusted quarterly values (c)

2011 -I

180

 

 

80

 

2011 -II

190

 

 

85

 

2011 -III

270

 

 

120

 

2011 -IV

250

 

 

115

 

2012 -I

190

 

 

80

 

2012 - II

210

 

 

85

 

 2012 -III

285

 

 

120

 

2012 -IV

250

 

 

115

 

2013 - I

210

 

 

80

 

2013 - II

220

 

 

85

 

 2013 - III

300

 

 

120

 

 2013 - IV

260

 

 

115

 

2014 - I

200

 

 

80

 

 2014 - II

190

 

 

85

 

 2014 - III

250

 

 

120

 

 2014 - IV

250

 

 

115

 

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