# Chapter 1 S18.pdf - STATS 331 Introduction to Regression...

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STATS 331 Introduction to Regression Models Chapter 1 By Nagham Mohammad
Chapter objectives Model Building. Data Collection. Uses of Regression. 2 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 3
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 4
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 5
6 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). Chapter 1 -Introduction to Regression Models 7
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. Chapter 1 -Introduction to Regression Models 8
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. Chapter 1 -Introduction to Regression Models 9
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. 10 Chapter 1 -Introduction to Regression Models
Mathematical Models Types of Relationships A deterministic model (relationship). Statistical or probabilistic model (relationship). Chapter 1 -Introduction to Regression Models 11
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) 12 Chapter 1 -Introduction to Regression Models 12
Example Chapter 1 -Introduction to Regression Models 13 y = temperature in Fahrenheit y = 32 + 1.8 x x = temperature in Celsius This is an example of deterministic relationship (theory-based models).