Chapter 1 Spring 2017.pdf - Stats331 Introduction to...

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Stats331 Introduction to Regression Models Chapter 1
Chapter objectives Model Building. Data Collection. Uses of Regression. 2 Chapter 1 -Introduction to Regression Models 30/04/2017
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. 30/04/2017 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. 30/04/2017 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. 30/04/2017 Chapter 1 -Introduction to Regression Models 5
6 What is Regression Modeling? Chapter 1 -Introduction to Regression Models 6 30/04/2017
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). 30/04/2017 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. 30/04/2017 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. 30/04/2017 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. 30/04/2017 10 Chapter 1 -Introduction to Regression Models
Mathematical Models A deterministic model. Statistical or probabilistic model. 30/04/2017 Chapter 1 -Introduction to Regression Models 11
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 12 30/04/2017 Chapter 1 -Introduction to Regression Models
Example (1) Chapter 1 -Introduction to Regression Models 13 y = temperature in Fahrenheit y = 32 + 1.8 x x = temperature in Celsius 30/04/2017 This is an example of deterministic relationship (theory-based models).
Example

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