LectureOct27

# LectureOct27 - Linear Regression I Idea II Estimating...

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Linear Regression I. Idea II. Estimating Trends from a Sample A. Regression Line (Least Squares) B. Variability About the Regression Line C. Standard Error of Regression Line Glantz p 253-278

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200 Martians ( population ) Height (cm) (x) ~ N(40, 5) Weight (g) (y) ~ N(12, 2.5) Mean weight of Martians at each height increases as height increases. I Idea
The line of means for the population of Martians X – independent variable Y – dependent variable x x y β α μ + = ( ) x cm g g x y 5 . 0 8 + = yx 1 σ = 2 given ~ ( , ) xyN μσ Variability about line of means

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Assumptions for the population The mean of the population of the dependent variable at a given value of the independent variable increases (or decreases) linearly as the independent variable increases. For any given value of the independent variable, the possible values of the dependent variable are distributed normally The standard deviation of population of the dependent variable about its mean at any given value of the independent variable is the same for all values of the independent variable.
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LectureOct27 - Linear Regression I Idea II Estimating...

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