511_Chap7 - 1 Simple Linear Regression: A Model for the...

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Unformatted text preview: 1 Simple Linear Regression: A Model for the Mean Chapter 7 2 An Intermediate Model (if the groups are defined by values of a numeric variable) Separate Means Model Equal Means Model Means fall on a straight line function of the group values 3 Meaning of the Word Regression statistical meaning not related to the usual English definition of regression misnomer, but there s a historical reason refers to finding the best fitting (straight line) relationship between the mean of Y and values of the variable defining the groups (X) 4 Galton s data 75 70 65 60 75 70 65 60 height of father height of son 5 Case Study 1 Hubble data (from 1920 s) observational data each point represents a nebula Y distance of the nebula X recession velocity of the nebula 6 Case Study 1 don t worry about the geometry, but Big Bang theory implies that Y = const. * X (i.e. a straight line relationship between Y and X, with intercept 0) furthermore, const. should be an estimate of the age of the universe 7 Case Study 1 0.5 1 1.5 2 DISTANCE-250 250 500 750 1000 1250 VELOCITY 8 Case Study 1 Regression methods can help answer big cosmological questions: Is the Big Bang theory correct? is the intercept of the straight-line relationship 0? How old is the universe? what is the slope of the straight-line relationship? 9 Case Study 2 designed experiment response variable (Y) pH of steer carcass explanatory variable (X) log time (hours) after slaughter what is the approximate pH of a particular steer carcass 3 hours after slaughter? about how long do you have to wait after slaughter for the pH to reach 6.0? 10 Case Study 2-0.20-0.10 0.00 0.10 0.20 Residual 1 2 3 4 5 6 7 8 9 TIME 5.5 6 6.5 7 PH 1 2 3 4 5 6 7 8 9 TIME 11 Case Study 2 5.5 6 6.5 7 PH 0.5 1 1.5 2 logtime-0.10-0.05 0.00 0.05 0.10 Residual 0.5 1 1.5 2 logtime 12 Regression Analysis statistical methods based on describing the distribution of values of one variable (Y the response variable ) as a function of the other variable (X the explanatory variable ) simple linear regression: the function is a straight line function 13 Regression Analysis specifically, the mean of Y is a straight line function of X {Y|X} = + 1 X where is the intercept and 1 is the slope...
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511_Chap7 - 1 Simple Linear Regression: A Model for the...

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