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
|
|