Statistical Models

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Statistical Models
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Typical Statistical Regression Models
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One Problem Area

• Many people have forgotten what the intercept is
  and what the slope is.
• Assignment look up and be able to explain what
  the intercept is and what the slope is.
• Give me an example in your field give y x1 x2
  hypothetical betas and interpret everything

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Examples
Suppose, for example, that the director of a
county highway department wants to predict the
cost of a resurfacing contract that is up for
bids. We could reasonably predict the costs to be
a function of the road miles to be resurfaced. A
reasonable first attempt is to use a linear
production function. Let y total cost of a
project in thousands of dollars, x number of
miles to be resurfaced
Write down the statistical model. What are the
parameters? What are the hypotheses? How many
populations are sampled?
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Examples

• A mail-order retailer spends considerable
  effort in picking ordersselecting the
  ordered items and assembling them for shipment. A
  small study took a sample of 100 orders. An
  experienced picker carried out the entire
  process. The time in minutes needed was recorded
  for each order.

Write down the statistical model. What are the
parameters? What are the hypotheses? How many
populations are sampled?
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Examples

• A laundry detergent manufacturer wished to
  test a new product prior to market release. One
  area of concern was the relationship between the
  height of the detergent suds in a washing machine
  as a function of the amount of detergent added
  and the degree of agitation in the wash cycle.
  For a standard size washing machine tub filled to
  the full level, random assignments of different
  agitation levels (measured in minutes) and
  amounts of detergent were made and tested on the
  washing machine.

Write down the statistical model. What are the
parameters? What are the hypotheses? How many
populations are sampled?
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Typical ANOVA ModelsPopulation Means Model
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Typical ANOVA ModelsPopulation Means Model
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Examples

• Researchers conducted an experiment to
  compare the starch content of tomato plants grown
  in sandy soil supplemented by one of three
  different nutrients, A, B, or C. The researchers
  selected 18 tomato seedlings of one particular
  variety for the study, with six assigned to each
  of the nutrient groups. They planted all
  seedlings in a sand culture and maintained them
  in a controlled environment. Those seedlings
  assigned to nutrient A served as the control
  group (receiving distilled water only). Plants
  assigned to nutrient B were fed a weak
  concentration of Hoagland nutrient, while those
  assigned to nutrient C received the Hoagland
  nutrient at full strength. The researchers
  determined the stem starch contents 25 days after
  planting the contents are recorded here, in
  micrograms per milligram.

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Questions

• Write down the statistical model both ways.
• What are the parameters?
• What are the hypotheses?
• How many populations are sampled?

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For SAS SPSS

• Do an example

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Example 2 by 3 Factorial
B 1
B 2
B 3
A 1
A 2
Assumptions?
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ANOVA 2 - Factors
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Example

• An experiment was conducted to determine the
  effects of four different pesticides on the yield
  of fruit from three different varieties (B1, B2,
  B3) of a citrus tree. Eight trees from each
  variety were randomly selected from an orchard.
  The four pesticides were then randomly assigned
  to two trees of each variety and applications
  were made according to recommended levels. Yields
  of fruit (in bushels per tree) were obtained
  after the test period.

Write down the statistical model. What are the
parameters? What are the hypotheses? How many
populations are sampled?
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The Other Model
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Meaning

• The meaning of the parameters depends upon the
  computer package. SAS and SPSS have the same
  meaning
• Other programs may have different meaning

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What is being tested
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Questions

• Write down the statistical model.
• What are the parameters?
• What are the hypotheses?
• How many populations are sampled?

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What is being estimated / tested?
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Parameters - 2 by 3
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Example

• An experiment was conducted to determine the
  effects of four different pesticides on the yield
  of fruit from three different varieties (B1, B2,
  B3) of a citrus tree. Eight trees from each
  variety were randomly selected from an orchard.
  The four pesticides were then randomly assigned
  to two trees of each variety and applications
  were made according to recommended levels. Yields
  of fruit (in bushels per tree) were obtained
  after the test period.

Write down the statistical model. What are the
parameters? What are the hypotheses? How many
populations are sampled?