THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
Assignment 2 – Trend Projection (Part 2)
Goal
To use several types of trend projection procedures to fit an appropriate curve to
historical data and to critically evaluate the output.
Data
The data for this exercise are provided to you in an Excel spreadsheet:
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.
Using the Template
To fit a linear curve, compute the coefficients using formulas, use the LINEST array
function, run the regression tool (Tools>Data analysis>Regression) routine on index X
and raw Y values, and use the trend line procedure after you have graphed the data
(question 4) (Chart>Add trend line). Compute the projected values using the coefficients
calculated above (they should all be the same!) and check your results using the TREND
array function.
To fit a geometric curve, compute the coefficients using formulas, use the LOGEST array
function, run the regression data analysis routine on index X and log (Y) values and use
the trend line procedure after you have graphed the data (question 4) (Chart>Add trend
line). Compute the projected values using the coefficients calculated above and check
your results using the GROWTH array function.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
To fit a modified exponential curve, compute the coefficients using formulas and run the
regression data analysis routine on index X and log (c-Y) values. (Note that it will return
logs of the a and b coefficients.) Use the antilogs of these coefficients to compute
projected values and check your work using the GROWTH array function using cfunction (c-Y).
To fit a logistic curve, compute the coefficients using formulas and run the regression
data analysis routine on index X and log (1/Y-1/c) values. Use the antilogs of these
coefficients to compute projected values and check your work using the GROWTH array
function using c-function (1/c-1/Y).
Instructions
1. Using the Excel template provided, fit each of the four curves to the population data
for the University of Lethbridge Full-time Fall Students data up to 2010.
2. Display and examine population projections, regression coefficients, and evaluation
statistics. Create a table that shows the observed data and the projected data according
to each curve, a summary measure for input evaluation, and a measure of goodness of
fit.
3. Using a hand calculator, calculate YC values for 2010 and show your handwritten
work– remember to use the index numbers not the actual years!
a. Were you able to independently verify that the model is working properly?
b. Why bother with this step?
4. Create a single X,Y graph that plots the observed points (without connecting lines)
and the four curves (omitting the markers). Print your graph.
5. While you printed all four curves (just for practice), you should have selected only
one.
a. What factors led to your choice of curve?
b. Discuss the results of your projection.
6. It is now Fall 2006. We know that the University of Lethbridge fall enrolment figures
show a total enrolment of 8,000 students.
a. With the clarity of hindsight, was your projection entirely satisfactory?
b. How can you explain the differences?
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2006
7. Using data for Ridgewood Heights displayed in Table 3 in Part 1, imagine that the
year is 2000 thus you only have data for 1984-1999 (***For a moment, ignore all
population values after 1999***). Project Ridgewood’s population forwards to
2006. Use the Excel regression procedure to determine the a and b parameters and a
spreadsheet to tabulate and graph your results. Remember, begun in 1984, the
subdivision was planned for a total of approximately 530 dwelling units.
8. Think about the sort of process that underlies population growth in Ridgewood
Heights.
a. Is it really a demographic process up to 1999?
b. Is this exercise pointless in some respects? Why or why not? (It may help to
take a walk, drive or bike ride through Ridgewood Heights. Look for empty
lots and space for future development.)
9. The municipal census of 2002 indicated that Ridgewood’s population dropped to
1,741 while its dwelling count increased to 536. By 2006 the population declined
further to 1,615 while the number of dwellings increased to 538. Is the observed
population consistent with your projection? Why or why not? As a forecaster, what
additional factors might you have taken into account to adjust your projection when
you were doing this work, way back in 1999?
10. Using the same procedure, project yearly average CO2 emissions at the Mauna Loa
Observatory in Hawaii forward to the year 2025. Using your measures of input
evaluation and goodness of fit, which curve is shown to be most appropriate in
modelling this phenomenon? Present the projected yearly average CO2 emissions
and the summary statistics for the most likely curve in a summary table.
11. Conclude by reflecting on the difference between a forecast and a projection. Based
on your own judgement, would you discount any of the projections that you have
produced? Why? How might you allow for these factors to arrive at a more probable
forecast?
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.
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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 4 of 5
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
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Dwelling Units
2
65
112
185
312
477
499
519
533
536
537
538