# ALRLec7 - 1 Chapter 4 Drawing Conclusions 4.1 Understanding...

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Unformatted text preview: 1 Chapter 4 Drawing Conclusions 4.1 Understanding parameter estimates E (Y | X) = β +β 1 x 1 + β 2 x 2 +…+β p x p β i : rate of change increase x i by one unit, all other x being hold constant, how much y changes. Least square regression does not mean x cause y. From the data, we only observe association between x and y. The value of a parameter estimate not only depends on the other terms in a mean function but it can also change if the other terms are replaced by linear combination of the terms. Example E (Y | X) = β +β 1 x 1 + β 2 x 2 z = 5x 1- 4x 2 E (Y | X 1 z 1 ) = β * +β 1 x 1 * + β 2 z * 2 Rank deficient and over-parameterization Aliased: a term is a linear combination of the terms already in the mean function. The coefficient for it is not estimable. Linearly dependent : a term can be expressed as a linear combination of other terms. Linear independent Making inference Experiment: some treatment applied to experimental unit....
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ALRLec7 - 1 Chapter 4 Drawing Conclusions 4.1 Understanding...

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