Chapter 3
Forecasting II
3-1
Techniques for Trend
• Linear trend equation
– Linear Regression
• Non-linear trends
– Parabolic trend equation
– Exponential trend equation
– Growth curve trend equation
3-2
Simple Linear Regression
• Regression - a technique for fitting a line to a
set of data points
– Simple linear regression - the simplest form of
regression that involves a linear relationship between
two variables
• The object of simple linear regression is to obtain an
equation of a straight line that minimizes the sum of
squared vertical deviations from the line (i.e., the least
squares criterion)
3-3
Least Squares Line
y c a bx
where
y c Predicted (dependent) variable
x Predicted (independent) variable
b Slope of the line
a Value of y c when x 0 (i.e., the height of the line at the y intercept)
and
n xy
x y
b
n x x
y b x
a
or y bx
2
2
n
where
n Number of paired observations
3-4
Simple Linear Regression Assumptions
1. Variations around the line are random
2. Devaiations around the average value (the
line) should be normally distributed
3. Predictions are made only within the range of
observed values
3-5
The implication of the regression models in
forecasting is called the The Time-series
Approach
3-6
Time Series Forecasting Methods
• Static methods
– Assumes that the estimates of level, trend, and
seasonality within systematic components do not vary
as new demand is observed
– Estimate the value of parameters and use these value
for future forecasts
• Adaptive forecasting
– Estimates of level, trend, and seasonality are updated
after each demand observation
– Moving average, exponential smoothing
3-7
The Time Series Approach: Static
Methods
• A simple data plot can reveal the existence and
nature of a trend
Simply replace x by t
• Linear trend equation
Ft a bt
where
Ft...