STATS 331
Introduction to Regression Models
Chapter 1
By
Nagham Mohammad
Chapter objectives
•
Model Building.
•
Data Collection.
•
Uses of Regression.
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Chapter 1 Introduction to Regression Models
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.
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.
Chapter 1 Introduction to Regression Models
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•
A good model captures enough important features of the object
that it represents to be useful for a specific purpose.
Chapter 1 Introduction to Regression Models
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What is Regression Modeling?
Chapter 1 Introduction to Regression Models
•
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 (response variable) frequently
depend on the levels of several others (explanatory variables).
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Example
•
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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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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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
Types of Relationships
•
A deterministic model (relationship).
•
Statistical or probabilistic model (relationship).
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Deterministic (or Functional) Relationships
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
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Example
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y = temperature in
Fahrenheit
y =
32
+
1.8
x
x = temperature in Celsius
This is an example of
deterministic relationship
(theorybased models).