IT-390Forecasting

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IT-390 Forecasting
2
Introduction

• Forecasting is a future calculation
• Not an exact science
• Forecasting involves extrapolation
• This is based on the theory that past data
  follows some particular pattern

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Graphic Analysis of Data

• Understanding of data organization
• Raw data ? Frequency Distribution
• Grouping data into categories
• Count number of observations in each class
• Gives Range (largest smallest values), apparent
  patterns, what values the data may group around,
  where values appear most often, and so on

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Graphic Analysis of Data

• Histograms are used to graphically display
  Relative Frequency data.
• From the Frequency Distribution spreadsheet on
  page 141, we get
• Relative Frequency - calculated by "number of
  observations" in a class, divided by the total
  number of observations.

.400
.300
.200
.100
.50
15.15- 15.65
14.35- 14.75
13.95- 14.35
12.75- 13.15
12.35- 12.75
15.65- 16.05
14.75- 15.15
13.55- 13.95
13.15- 13.55
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Graphic Analysis of Data

• Cumulative Frequency is used with a process of
  graphing called "Ogive" (Oh-jive)
• Estimate on the future or trend - using
  historical
• When plotted using the variables (normally two) a
  Scatter Diagram is created.

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Graphic Analysis of Data

• Data on a Scatter Diagram takes many forms

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Graphic Analysis of Data

• Steps to generate a Scatter Diagram
• 1) Collect data
• 2) Draw horizontal axis Independent ("cause")
  variable goes on "X".
• 3) Draw vertical axis Dependent ("effect")
  variable goes on "Y".
• 4) Plot data. Circle repeat points
• 5) Analyze

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Graphic Analysis of Data

• "see" where the data is going
• Mathematical methods (Algorithms)
• Linear Least Squares Regression
• Curvilinear Least Squares Regression

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Least Squares and Regression

• Generate a mathematical equation for line of best
  fit to the data
• The first method we will examine is the Linear
  Least Squares Regression

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Least Squares and Regression

• Linear Least Squares Regression
• Best fit through the historical points
• Assumptions
• 1) Data are normally distributed
• 2) y is the depend variable and x is the
  independent variable
• 3) Data appears to be linear, not curvilinear

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Least Squares and Regression

• The linear equation is
• Y a bx, where
• a is a constant value and is equal to the Y
  value at the point where x0.
• b is the slope of the line
• x is the independent variable
• Y is the dependent variable
• The two equations necessary are

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Linear (Data) Example
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Linear Example
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Handout Problem (1)
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Least Squares and Regression

• Curvilinear Least Squares Regression
• Logarithmic functions - Log and Antilog
• Same assumptions as Linear, except data is
  curvilinear
• Power Equation. (Eq. 5.25)(pg. 201)
• Y axb
• a is a constant value equal to the Y value
  at the point where x0
• b is the slope of the line
• x is the independent variable
• Y is the dependent variable
• from eq. 5.29 5.30 (pg. 202)

a antilog of log a
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Curvilinear Example
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Handout Problem (2)
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Caution!

• There is a axiom in statistics that says,
  "Correlation does not imply causality." In other
  words, your scatter plot may show that a
  relationship exists, but it does not and cannot
  prove that one variable is causing the other.
  There could be a third factor involved which is
  causing both, some other systemic cause, or the
  apparent relationship could just be a fluke.
  Nevertheless, the scatter plot can give you a
  clue that two things might be related, and if so,
  how they move together.

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Standard Error of Estimate

• Standard Error of Estimate (not in book, but
  important). To measure the reliability of the
  estimating equation, statisticians have developed
  the standard error of estimate. This is
  symbolized by Se and it is a measure of
  dispersion, or the variability (scatter) around
  the regression line.
• The equation is

VS
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Standard Error of Estimate
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Handout Problem 1-Standard Error
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Interpretation of Standard Error

• If Se 0, the equation would be perfect. All
  points would lie on the line instead of around it
• 68 of all points lie within the 1st standard
  deviation
• 95.5 of all points lie within the 2nd standard
  deviation
• 99.73 of all points lie within the 3rd standard
  deviation

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Interpretation of Standard Error

• Problem 1 6,515,346 Kilowatts. The first
  standard deviation is ? 120, 2nd is ? 240, 3rd is
  ? 360 Kilowatts
• This means
• 68 data points are between 6,515,226 and
  6,515,466 (? 120)
• 95.5 data points are between 6,515,106 and
  6,515,586 (? 240)
• 99.7 data points are between 6,514,986 and
  6,515,706 (? 360)
• This also shows the (probability) of where new
  data will fall in relation to the regression line.

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Interpretation of Standard Error Graphically
3rd
2nd
1st
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
Standard Deviations
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Correlation

• A correlation coefficient is a number between -1
  and 1 which measures the degree to which two
  variables are linearly related.

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Correlation
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Correlation

• 1) If there is perfect linear relationship with
  positive slope between the two variables, we have
  a correlation coefficient of 1. If there is
  positive correlation, Y (dependent variable)
  increases as X (independent variable) increases.

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Correlation

• 2) If there is a perfect linear relationship with
  negative slope between the two variables, we have
  a correlation coefficient of -1. If there is
  negative correlation, Y (dependent variable)
  decreases as X (independent variable) increases.

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Correlation
Positive Correlation (as X increases, Y
increases)
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Handout Problem 1- Correlation
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Cost Indexes

• An index is a dimensionless number used to
  indicate how a cost has changed over time
  relative to a base year. The creator of the
  index publishes a table showing the value of the
  index for the years of interest.

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Cost Index Example Graph
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Cost Indexes

• For example, the Bureau of Labor Statistics
  tracks the Consumer Price Index (CPI) which "is a
  measure of the average change over time in the
  prices paid by urban consumers for a market
  basket of consumer goods and services. It
  includes a number of goods and services in
  categories such as Food and Beverages, Housing,
  Apparel, and Transportation. Selected index
  values are shown below.
• Source Bureau of Labor Statistics

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Cost Indexes

• Using the indexes, if we know the cost of goods
  in one year, we can estimate the cost of the same
  goods in another year by using a simple ratio.
• Where IA and IB are the indexes in years A and B
  respectively and CA and CB are the cost in years
  A and B respectively.

which simplifies to
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Index Examples

• Example 1
• A family spent 160 per month on groceries in
  1987, how much can they expect to spend in 1994?
• Solution
• To find the cost in 1994 we need the cost of
  groceries in 1987 (C1987160), and the index
  values for the years 1987 and 1994 (I1987 118.2
  and I1994 156.5). Then,
• C1994 C1987 ( I1994 / I1987 )
• C1994 160 ( 156.5 / 118.2 )
• C1994 160 (1.3240)
• C1994 212
• Since the index value for 1994 is higher than the
  index value for 1987, we should expect the cost
  of groceries to increase, and it does.

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Index Examples

• Example 2
• When Anna graduated as an engineer in 1992, her
  starting salary was 33,000. What would her first
  employer have to offer a 2000 graduate to start
  in her job? Given (I1992 147.3 and I2000
  182.3)
• Solution
• Simply taking into account the change in the cost
  of living reflected in the CPI, her employer
  would have to offer
• C2000 C1992 ( I2000 / I1992 )
• C2000 33,000 ( 182.3 / 147.3 )
• C2000 33,000 (1.2376)
• C2000 40,841

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Cost Indexes

• Cost Indexes A cost index expresses a change or
  the relationship in price levels between two
  points in time. All that is needed to generate
  an index is a base period. The relationship
  between the base period and each of the other
  periods is an index value. See the example below
  where period four is selected as the base period.
• Year Period Price Index
• 1981 1 43.75 43.75/46.10 .949 or 94.9
• 1982 2 44.25 44.25/46.10 .960 or 96.0
• 1983 3 45.00 45.00/46.10 .976 or 97.6
• 1984 4 46.10 46.10/46.10 1.000 or 100.0 lt
  Base
• 1985 5 47.15 47.15/46.10 1.023 or 102.3
• 1986 6 49.25 49.25/46.10 1.068 or 106.8

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Cost Indexes

• The base period can be shifted or changed by
  dividing by the dollar amounts as above or by
  simply dividing the current indexes by the index
  value of the new base period. For example, if we
  select period 5 as the new base, then our
  indexes would appear as follows
• New
• Year Period Price
  Index
• 1981 1 43.75 .949/1.023 .928 or 92.8
• 1982 2 44.25 .960/1.023 .938 or 93.8
• 1983 3 45.00 .976/1.023 .954 or 95.4
• 1984 4 46.10 1.000/1.023 .977 or 97.7
• 1985 5 47.15 1.023/1.023 1.000 or 100.0 lt
  New Base
• 1986 6 49.25 1.068/1.023 1.044 or 104.4

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Cost Indexes

• Instead of trying to work with dollars throughout
  all computations, it is often easier to use an
  index to convert a prior cost into an estimate of
  future cost.