Week 6 - Regression Analysis

Week 6 - Regression Analysis - Engr9397 Week6...

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Engr 9397 – Week 6 Regression Analysis
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Regression Analysis Introduction So, far we have looked at statistical methods that have dealt with observations involving a single variable Many problems of quality improvement involve relations among several variables We are going to looks at statistical methods that apply to simultaneous observations made on multiple variables We will look at simple linear regression, correlation, multiple regression, analysis of residuals and their applications to quality management
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Regression Analysis Introduction A widely used method for studying relationships between multiple variables is regression analysis Examples of where this is used are everywhere in the product development and manufacturing environment The relationship between price and sales, weight and speed, geometry and drag are some examples of where regression analysis could be used to solve problems of interest to quality managers
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Why perform Regression? We use regression in order to: Learn something about the relationship between two variables, Remove a portion of the variation in one variable in order to gain a better understanding of the remaining variation Estimate or predict values of one variable based on another variable
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Variable Relationships Monotonic vs. Nonmonotonic Regression and correlation deal with describing/quantifying relationships between random variables Types of Relationships: Monotonic: variable relationships that have no reversals in slope (a linear relationship is a special case of a monotonic relationship where the slope is constant over x) Nonmonotonic: variable relationships where the slope reverses
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Variable Relationships: Linear vs. Non linear Linear functions satisfy the following properties: Additivity (aka superposition property) f ( x + y )= f ( x )+ f ( y ) (the net response by two or more factors is the sum of the responses caused by each factor) Homogeneity of degree 1 f (a x )=a f ( x ) for all a Nonlinear: a system which does not satisfy the above principles (often used to represent natural phenomena)
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Simple Linear Regression Simple linear regression: the use of statistical methods to find the ‘best fit’ linear relationship between two variables the value of a given random variable may depend upon the value of another (non random) variable In simple regression we are only dealing with a single relationship between two random variables In multiple regression, we are dealing with multiple relationships between variables
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Simple Linear Regression The non random variable, x , also called the independent variable or control variable, is fixed at certain known values without error by the experimenters in order to observe its effect on the values of the random variable The random variable, y , also called the response variable or the independent variable, is the variable we observe during the experiment we are interested in knowing how the value of y is affected by changes in the value of x
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Week 6 - Regression Analysis - Engr9397 Week6...

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