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"I always avoid prophesying beforehand because it is much better to prophesy after the event has already taken place. "
--Winston Churchill
Quantitative forecasting methods in library management
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Forecasting using trend analysis
• Part 1. Theory
• Part 2. Using Excel: a demonstration.
• Assignment 1, 2
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Learning objectives
• To compute a trend for a given time-series data using Excel
• To choose a best fitting trend line for a given time-series
• To calculate a forecast using regression equation
To learn how:
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Main idea of the trend analysis forecasting method
• Main idea of the method: a forecast is calculated by inserting a time value into the regression equation. The regression equation is determined from the time-serieas data using the “least squares method”
Quantitative forecasting methods in library management
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Prerequisites: 1. Data pattern: Trend
Trend (close to the linear growth)
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Prerequisites: 2. 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 general equation for a trend line
F=a+bt Where:• F – forecast,• t – time value,• a – y intercept,• b – slope of the line.
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Least Square Method
• Least square method determines the values for a and b so that the resulting line is the best-fit line through a set of the historical data.
• After a and b have been determined, the equation can be used to forecast future values.
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The trend line is the “best-fit” line: an example
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Statistical measures of goodness of fit
• The Correlation Coefficient
• The Determination Coefficient
In trend analysis the following measures will be used:
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The Coefficient of Determination
• The coefficient of determination, R2, measures the percentage of variaion 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 fitt: Determination Coefficient RSQ
• Range: [0, 1].
• RSQ=1 means best fitting;
• RSQ=0 means worse fitting;
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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 ternds in such cases); 2) not applicable for seasonal and cyclic datta patterns.
Part 2. Switch to Excel
Open a Workbook trend.xls, save it to your computer
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Working with Excel
• Demonstration of the forecasting procedure using trend analysis method
• Assignment 1. Repeating of the forecasting procedure with the same data
• Assignment 2. Forecasting of the expenditure
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Using Excel to calculate linear trend
• Select a line on the diagram • Right click and select Add Trendline • Select a type of the trend (Linear)
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Part 3. Non-linear trends
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Non-linear trends
• Logarythmic
• Polynomial
• Power
• Exponential
Excel provides easy calculation of the following trends
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Logarithmic trend
y = 4,6613Ln(x) + 1,0724
R2 = 0,9963
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Trend (power)
y = 0,4826x1,5097
R2 = 0,9919
02468
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Trend (exponential)
y = 0,0509e1,0055x
R2 = 0,9808
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Trend (polynomial)
y = -0,1142x3 + 1,6316x2 - 5,9775x + 7,7564
R2 = 0,9975
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Choosing the trend that fitts best
• 1) Roughly: Visually, comparing the data pattern to the one of the 5 trends (linear, logarythmic, polynomial, power, exponential)
• 2) In a detailed way: By means of the determination coefficient
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