THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
Assignment 2 – Trend Projection (Part 1)
Introduction
Curve-fitting and extrapolation techniques provide well-defined scientific methods for
quantitative modellers to understand past trends and make educated predictions about
future trends. Initially, one must perform input evaluation – that is, the curve ‘fitting’
procedure – to select an appropriate mathematical model that encompasses the past data.
Goal
To become familiar with the input evaluation phase of the trend projection procedures
and to apply input evaluation to historical time series to evaluate which series best
represents the data. Next week, Assignment 2 (Part 2) will explore fitting curves to the
series and assess goodness of fit.
Data
The data for this exercise are provided to you in an Excel spreadsheet. Note that your
workbook contains five worksheets – four containing data, and an additional input
evaluation template where you can see how the methods are applied.
University of Lethbridge Full-time Fall Students –
Source: University Statistics and Fact Book publications, University of
Lethbridge Archives.
Yearly Average Carbon Dioxide Emissions –
Source: C. D. Keeling, T.P. Whorf, and the Carbon Dioxide Research Group,
Scripps Institution of Oceanography (SIO), University of California.
Ridgewood Heights –
Source: City of Lethbridge Planning Department, Municipal Census, various
years.
Alberta Urbanization –
Source: Statistics Canada, Censuses of Population, 1901 - 2001.
Page 1 of 6
THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
Instructions
University of Lethbridge Full-time Fall Students
1. Use historical data from the University archives (Table 1) and the methods
learned in Lab 1, generate a growth curve for the school.
2. Describe the pattern of change in student enrolment that is revealed through the
growth curve – you may want to examine the growth curve different scales to help
you answer the question.
3. Note that many of the cells in the Input Evaluation Template spreadsheet are
empty. Following the pattern provided for you, copy and paste the university
enrolment data and insert appropriate formulae to complete the template. Display
and examine the ‘differences’.
4. Based on a visual examination of the differences, can you detect which of the four
series is most like the input data? Why or why not?
5. At the base of each of the four columns, complete the three rows to compute the
mean, standard deviation, and coefficient of relative variation (CRV) for each
curve type. These statistics are important and you will discuss them in subsequent
questions – make sure that the table of summary statistics is inserted into your lab
report.
6. Which of the three statistics (mean, standard deviation, or CRV) is the best
measure of dispersion for input evaluation and why?
7. Using your judgment as a population forecaster, which curve would you select to
project the current trend in University of Lethbridge enrolments?
8. Attach a single-page copy (File > Page Setup > Fit to 1 page wide by 1 page tall)
of your input evaluation calculations for the University data to the end of your lab
report.
Yearly Average Carbon Dioxide Emissions, Mauna Loa, Hawaii
Perform the input evaluation procedure using the yearly average CO2 concentration
(ppmv) in air samples from the Mauna Loa Observatory in Hawaii (Table 2). You
may have to adjust the number of rows in the input evaluation template.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
9. Which curve would you select to project the current trend in carbon dioxide levels
at this location? Explain why you chose this curve; and what the trend might
suggest as far as natural hazards and environmental issues in the area.
10. Attach a single-page copy (File > Page Setup > Fit to 1 page wide by 1 page tall)
of your input evaluation calculations for the CO2 to the end of your lab report.
Ridgewood Heights
Repeat the input evaluation procedure using data for Ridgewood Heights (Table 3).
Begun in 1984, this subdivision was planned for a total of approximately 530
dwelling units. You will discover that these data are not well suited to the
differencing method for input evaluation. Welcome to the frustrations of real world
data problems! There are several ways of solving this problem, none is perfect and
none will necessarily be graded as wrong – but it is important to consider the
implications of manipulating data sets!
11. Explain the problem, how you chose to handle it and why (you may find that
growth curves may help you to understand and solve the problem).
12. Using your judgment as a population forecaster, which curve would you select to
project the current trend in this urban neighbourhood?
13. Attach a single-page copy (File > Page Setup > Fit to 1 page wide by 1 page tall)
of your input evaluation calculations for the Ridgewood Heights to the end of
your lab report.
Alberta Urbanization through the Past Century
Perform the input evaluation procedure using the proportion of the Alberta population
that is urbanized which you calculated and plotted in Assignment 1 (or Table 4). You
may have to adjust the number of rows in the template.
14. Identify any issues present in your data that might affect the application of the
differencing method for input evaluation (again, you may find that growth curves
may help you to understand and solve the issues). How will you handle any
problems?
15. Using your judgment as a population forecaster, which curve would you select to
project the current trend in urbanization in Alberta? Explain why you chose this
curve; and why it might or might not truly be the best fitting curve.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
16. Attach a single-page copy (File > Page Setup > Fit to 1 page wide by 1 page tall)
of your input evaluation calculations for the Alberta urbanization data to the end
of your lab report.
Your laboratory report should be typed with a cover sheet and submitted to your lab
instructor on or before October 5, 2006. Reports should be submitted only in person OR
through the geography assignment drop box; no email submissions please.
You may format your lab report with numbers indicating the answers to each of the
questions. For ‘discussion’-type questions, please respond in paragraph form, using
correct spelling, grammar and punctuation. For ‘action’-type questions, please make use
of the Copy/Paste functions in Microsoft office to insert your work into the lab report. If
a table or chart does not easily fit into the page, then attach them as clearly labelled
appendices. Following the format used in your textbook and using the Guide to Term
Papers on the course web page note that graphs and tables should be numbered with
titles, axis labels, and a source to indicate where you obtained the data.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
Table 1
University of Lethbridge
Full-time Fall Semester Students, 1967 - 2004
Year
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
Full-Time
Students
638
1024
1261
1409
1218
1076
1086
1154
1340
1474
1531
1439
1419
Year
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
Full-Time
Students
1502
1771
2208
2442
2633
2692
2763
2717
2937
3165
3548
3659
3776
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Full-Time
Students
3710
4247
4250
4447
4611
4725
5187
5544
5945
6175
6512
6847
Table 2
Yearly Average Carbon Dioxide Emissions, 1958 - 2004
Mauna Loa, Hawaii
Year
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
CO2 Concentration
(ppmv)
315.33
315.98
316.91
317.65
318.46
318.99
319.15
320.03
321.37
322.18
323.05
324.62
325.68
326.32
327.46
329.68
Year
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
CO2 Concentration
(ppmv)
330.25
331.15
332.15
333.9
335.5
336.85
338.68
339.93
341.13
342.78
344.42
345.91
347.15
348.93
351.48
352.91
Page 5 of 6
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
CO2 Concentration
(ppmv)
354.19
355.59
356.37
357.04
358.89
360.88
362.64
363.76
366.63
368.31
369.48
371.02
373.1
375.64
377.38
THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
Table 3
Ridgewood Heights Subdivision, Lethbridge
Population and Dwelling Counts, Selected Census Years
Year
1984
1985
1986
1987
1989
1992
1994
1997
1999
2002
2005
2006
Population
6
216
347
544
1006
1,617
1717
1766
1802
1741
1649
1615
Dwelling Units
2
65
112
185
312
477
499
519
533
536
537
538
Table 4
Alberta, Canada
Proportion of Urbanized Population, 1901 - 2001
Year
1901
1911
1921
1931
1941
1951
1956
1961
1966
1971
1976
1981
1986
1991
1996
2001
Urban Proportion
0.254
0.368
0.379
0.381
0.385
0.479
0.566
0.633
0.688
0.735
0.75
0.772
0.794
0.798
0.795
0.809
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