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Chapter 11--Regression and Correlation Methods

Chapter 11--Regression and Correlation Methods -...

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Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Stat 491: Biostatistics Chapter 11: Regression and Correlation Methods Solomon W. Harrar The University of Montana Fall 2012 Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics
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Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression What is Regression? A method by which a quantitative variable is predicted or its variation is explained by means of other quantitative variables. The variable being predicted or whose variation being explained is called the dependent, outcome or response variable. The variables that are used to make the perdition or explain the variation of the dependent variable are called independent or explanatory variables. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics
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Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Types of Regression Linear Regression: quantitative (interval or ratio scale) dependent variable Simple: one independent variable Multiple: two or more independent variables Logistic Regression: qualitative ( binary ) dependent variable (yes or no, absent or present, ...) Simple or Multiple Many others types of univariate regressions exist. Multivariate Regression: More than one dependent variable. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics
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Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Model for Simple Linear Regression For a given value of the independent variable x , y = β 0 + β 1 x + ε where ε is random variation assumed to be normally distributed with mean 0 and variance σ 2 ε . The random variations for different observations are assumed to be independent. The expected response for a given value of x is μ y | x = β 0 + β 1 x . β 0 is the intercept and β 1 is the slope of the regression line. The unknown quantities β 0 , β 1 and σ 2 ε are parameters to be estimated from the data. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics
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Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Model for Simple Linear Regression Cont’d... 0 2 4 6 8 10 12 8 10 12 14 16 FERTILIZER (cwt. per acre) YIELD OF POTATOES (tons per acre) μ y x = 8.4 + 0.5x Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics
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Introduction Least Square Estimates of the Parameters
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