Stats331
Introduction to Regression Models
Chapter 1
Chapter objectives
•
Model Building.
•
Data Collection.
•
Uses of Regression.
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Chapter 1 Introduction to
Regression Models
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Model Building
•
Medical researchers use mouse physiology
as a model for human physiology.
The hope is the response of mouse to a specific drug will suggest
what response to expect in human.
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Chapter 1 Introduction to
Regression Models
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An engineer constructs a scale model of a proposed building.
The scale model may be used to help route the plumbing, but
may give no information about the acoustics of rooms inside the
building.
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A good model captures enough important features of the object
that it represents to be useful for a specific purpose.
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Chapter 1 Introduction to
Regression Models
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What is Regression Modeling?
Chapter 1 Introduction to
Regression Models
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Regression modeling is an activity(a collection of statistical
techniques) that leads to a
mathematical description
( model or
law) of a process in terms of a set of associated variables.
•
The values of one variable frequently depend on the levels of
several others.
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Regression Models
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Example
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The yield of a certain production process may depend on
temperature, pressure, catalyst, and the rate of throughput.
•
The number of defective seals on toothpaste tubes may depend
on the temperature and the pressure of the sealing process.
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Chapter 1 Introduction to
Regression Models
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The term regression was originally used in 1885 by Sir Francis
Galton in his analysis of the relationship between the heights
of children and parents.
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Regression Models
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Sir Galton was the first to apply the word regression to
biological and psychological data. Specifically, Galton
observed the heights of children versus the heights of their
parents.
He discovered that taller than average parents
tended to have children who were also taller than average,
but not as tall as their parents.
Galton characterized this as
regression toward mediocrity.
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Chapter 1 Introduction to
Regression Models
Mathematical Models
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A deterministic model.
•
Statistical or probabilistic model.
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Regression Models
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Deterministic Model
Makes no allowance for statistical or measurement error, has no
variance nor uncertainty.
If we know the value of one variable, we can determine the value
of the other
exactly
.

Unit conversions (E.g., miles to kilometers, meter to cm)

Known scientific formulas (E.g. water volume and weight)
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Chapter 1 Introduction to
Regression Models
Example (1)
Chapter 1 Introduction to
Regression Models
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y = temperature in
Fahrenheit
y =
32
+
1.8
x
x = temperature in Celsius
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This is an example of
deterministic relationship
(theorybased models).
Example
•
Starting from rest above the earth’s surface, a rock falls for a
period of times.