THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
Assignment 2 – Input Evaluation and 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 and describe:
Mauna Loa, Hawaii, USA 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.
Taber, Alberta Official Population –
Source: Alberta Municipal Affairs, Official Populations, 1901 - 2001. Available
online at http://www.municipalaffairs.gov.ab.ca/ms_official_pop_lists.htm
Calgary, Alberta Official Population –
Source: Statistics Canada, Census of Population.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
General Instructions for Perfoming
Input Evaluation Analysis using SPSS
Part A: Create the 7 Required Variables for Input Analysis

Create two variables—“year” and “pop”. Enter the appropriate data for your
problem into these two columns. In the Variable View, make sure to set the
appropriate data type, column width and number of decimals, and variable label.

Using Transform > Compute, create a new variable called “logpop”. Use the
arithmetic function LG10 as shown below:


Using Transform > Compute, create a new variable called “recippop”. To
calculate this variable, use the inverse of the population as shown below, and
format this new variable to show 6 decimal places.


Using Transform > Create Time Series, create a new variable called
“diff_recippop” that calculates the 1st difference of the values in the “recippop”
variable. When setting up this variable, make sure to use the Change button to
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
rename the variable appropriately; select the Difference function from the list;
and specify the Order as 1 to get a ‘1st’ difference, as shown below:


Using Transform > Create Time Series, create a new variable called “diff_pop”
that calculates the 1st difference of the values in the “pop” variable. When setting
up this variable, make sure to use the Change button to rename the variable
appropriately; select the Difference function from the list; and specify the Order
as 1 to get a ‘1st’ difference, as shown below:


Using Transform > Create Time Series, create a new variable called
“diff_logpop” that calculates the 1st difference of the values in the “logpop”
variable. When setting up this variable, make sure to use the Change button to
rename the variable appropriately; select the Difference function from the list;
and specify the Order as 1 to get a ‘1st’ difference, as shown below:


Using Transform > Compute, create a new variable called “ratio_diff_pop”. To
calculate this variable, you will divide the respective value(s) of the 1st difference
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
variable (“diff_pop”) by the previous value in the time series (obtained by SPSS
through the LAG function), as shown below:


Using Transform > Compute, create a new variable called “ratio_diff_recippop”.
To calculate this variable, you will divide the respective value(s) of the reciprocal
1st difference variable (“diff_recippop”) by the previous value in the time series
(obtained by SPSS through the LAG function), as shown below:

Part B: Calculate Descriptive Statistics for Input Evaluation

Using the Analyze> Descriptive Statistics > Descriptives option, calculate the
basic descriptive statistics of mean and standard deviation for the last four
variables – “diff_pop”, “diff_logpop”, “ratio_diff_pop”, and
“ratio_diff_recippop”. Note that you may need to adjust the width of the columns
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
and/or the Cell Properties in your Descriptives output table so that the means are
displayed as decimal numbers to the right level of precision.

The summary measure of CRV is not available through the SPSS Analyze>
Descriptive Statistics options. You will have to calculate this manually –
remember that the CRV is the standard deviation of a variable expressed as a
percentage of the mean. (Hint: divide first, then multiply by 100 to convert this to
a ‘percentage’…then the measures are truly comparative!)
1. Using Microsoft Excel and the graphic techniques that you explored in Lab 1,
generate growth curves for each of the three data sets.
2. Describe the patterns of change that are apparent with each of these curves – you
may want to examine the growth curves different scales to help you answer the
question. Do the increments stay constant over time; or does the growth rate stay
constant over time?
3. Complete the ‘General Instructions for Performing Input Evaluation using SPSS’
for each of your data sets to enable you to explore the ‘differencing’ method of
Input Evaluation and Curve Fitting. Using the Analyze > Reports > Case
Summaries option in SPSS, create table(s) that summarize the input data and the
‘differences’ and format these neatly to include in your lab report.
4. Based on a simple visual examination of the differences, can you detect which of
the curve models is most like the input data? Why or why not?
5. Which of the three descriptive statistics (mean, standard deviation, or CRV) used
to assess the ‘differences’ is the best measure of dispersion for input evaluation
and why?
6. Using your judgment as a population forecaster, which curve would you select to
project the current trend in population growth for Taber? Explain why you chose
this curve; and its future implications for the community.
7. Using your judgment as a population forecaster, which curve would you select to
project the current trend in population growth for Calgary? Explain why you
chose this curve; and its future implications for the community.
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THE UNIVERSITY OF LETHBRIDGE
DEPARTMENT OF GEOGRAPHY
GEOGRAPHY 3235: Quantitative Models for Geographic Analysis
Fall 2007
8. Which curve would you select to project the current trend in carbon dioxide levels
at the Mauna Loa volcano? Explain why you chose this curve; and what the trend
might suggest as far as natural hazards and environmental issues in the area.
Your laboratory report should be typed with a cover sheet and submitted to your lab instructor on or before
October 4, 2007. 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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