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Lecture21standard

# Lecture21standard - Statistics 511 Statistical Methods Dr...

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Lecture : Simple linear regression: Model and its estimation Devore: Section 12.1-12.2 Dec, 2011 Page 1

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 A simple linear regression investigates the relationship between the two variables that is not deterministic. The variable whose value is fixed by the experimenter is called the independent, predictor or explanatory variable. For fixed x , the second variable is random; it is referred to as the dependent or response variable. The data is usually given as n pairs ( x 1 , y 1 ) , . . . , ( x n , y n ) . A scatter plot gives a good indication of the nature of the relationship between the two variables. Arsenic removed ( y ) vs. x = pH scatter plot example Dec, 2011 Page 2
Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 A Linear Model The usual linear regression model is Y = β 0 + β 1 x + where ε N (0 , σ 2 ) ε is the random error term or the random deviation while the line

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