Unit 14-1

Unit 14-1 - Regression Regression y = + x t hg e W i What...

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Regression Regression
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60 62 64 66 68 Height W e i g h t How much would an adult female weigh if she were 5 feet tall? She could weigh varying amounts – in other words, there is a distribution of weights for adult females who are 5 feet tall. This distribution is normally distributed. (we hope) What would you expect for other heights? Where would you expect the TRUE LSRL to be? What about the standard deviations of all these normal distributions? x y β α μ + = We want the standard deviations of all these normal distributions to be the same.
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Regression Model Regression Model • The mean response μ y has a straight-line relationship with x : Where: slope β and intercept α are unknown parameters For any fixed value of x , the response y varies according to a normal distribution . Repeated responses of y are independent of each other. • The standard deviation of y ( σ y ) is the same for all values of x . ( σ y is also an unknown parameter) x y β α μ + =
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The slope b of the LSRL is an unbiased estimator of the true slope β . The intercept a of the LSRL is an unbiased estimator of the true intercept α . The standard error s is an unbiased estimator of the true standard deviation of y ( σ y ). bx
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This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.

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Unit 14-1 - Regression Regression y = + x t hg e W i What...

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