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```									  Main idea of the trend analysis
forecasting method:
• a forecast is calculated by inserting a time
value into the regression equation. The
regression equation is determined from the
time-series data using the “least squares
method”

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Prerequisite: Correlation

There should be a sufficient correlation
between the time parameter and the
values of the time-series data

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The Correlation Coefficient
• The correlation coefficient, R, measure the
strength and direction of linear relationships
between two variables. It has a value
between –1 and +1
• A correlation near zero indicates little linear
relationship, and a correlation near one
indicates a strong linear relationship
between the two variables
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Main idea of the trend analysis
method
• Trend analysis uses a technique called least squares to fit a
trend line to a set of time series data and then project the
line into the future for a forecast.
• Trend analysis is a special case of regression analysis
where the dependent variable is the variable to be
forecasted and the independent variable is time.
• While moving average model limits the forecast to one
period in the future, trend analysis is a technique for
making forecasts further than one period into the future.

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The trend line is the “best-fit”
line: an example
Municipal public libraries in Lithuania in 1991-2002
Number of libraries

1700
1650
1600
1550
1500
1450
1400
1350
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Year

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Statistical measures of goodness
of fit

In trend analysis the following
measures will be used:

• The Correlation Coefficient
• The Determination Coefficient

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The Coefficient of Determination R2

• The coefficient of determination, R2,
measures the percentage of variation in the
dependent variable that is explained by the
regression or trend line. It has a value
between zero and one, with a high value
indicating a good fit.

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Goodness of fit: Determination
Coefficient R2
•   Range: [0, 1]
•   R2=1 means best fitting
•   R2=0 means worse fitting
•   In Excel R2 is denoted as RSQ (“R
squared”)

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Evaluation of the trend analysis
forecasting method
• Advantages: Simple to use (if using
appropriate software)
• Disadvantages: 1) not always applicable for
the long-term time-series (because there
exist several trends in such cases); 2) not
applicable for seasonal and cyclic data
patterns.

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Using Excel to calculate linear
trend

• Select a line on the diagram (left click on
the line) 
• Right click and select Add Trend line 
• Select a type of the trend (Linear)

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Non-linear trends
Excel provides easy calculation of the following trends

•   Logarithmic
•   Polynomial
•   Power
•   Exponential

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Examples of the non-linear trends

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Logarithmic trend

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y = 4,6613Ln(x) + 1,0724
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R2 = 0,9963
8
6
4
2
0
0         2                       4                 6   8

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Trend (power)

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y = 0,4826x1,5097
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R2 = 0,9919
6
4
2
0
0         2                       4                 6        8

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Trend (exponential)

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y = 0,0509e1,0055x
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R2 = 0,9808
40

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0
0   2                       4                 6   8

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Trend (polynomial)

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y = -0,1142x3 + 1,6316x2 - 5,9775x + 7,7564
6
R2 = 0,9975
4

2

0
0           2                      4                  6        8

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Choosing the trend that fits best
• 1) Roughly: Visually, comparing the data
pattern to the one of the 5 trends (linear,
logarithmic, polynomial, power,
exponential)
• 2) In a detailed way: By means of the
determination coefficient

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