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multiregress3

multiregress3 - Regression Analysis III Model buliding...

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Regression Analysis III Model buliding Variable selection Residual Analysis

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Models in which the parameters ( 0 , 1 , . . . , p ) all have exponents of one are called linear models . General Linear Model A general linear model involving p independent variables is 0 1 1 2 2 p p y z z z Each of the independent variables z is a function of x 1 , x 2 ,..., x k (the variables for which data have been collected).
General Linear Model y x 0 1 1 y x 0 1 1 The simplest case is when z 1 = x 1 . This is the simple first-order model with one predictor variable. This model is called a second-order model with one predictor variable . y x x 0 1 1 2 1 2 y x x 0 1 1 2 1 2 To account for a curvilinear relationship, we might set z 1 = x 1 and z 2 = x 1 2 .

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Interaction y x x x x x x 0 1 1 2 2 3 1 2 4 2 2 5 1 2 y x x x x x x 0 1 1 2 2 3 1 2 4 2 2 5 1 2 This type of effect is called interaction . In this model, the variable z 5 = x 1 x 2 is added to account for the potential effects of the two variables acting together. If the original data set consists of observations for y and two independent variables x 1 and x 2 we might develop a second-order model with two predictor variables .
Interaction See example 11.6, where we have the associated t- statistics for the interaction term being 6.11, thus we keep this term in our model. In this model, the variable x 1 x 2 is added to account for the potential effects of the two variables acting together. Suppose the collector of grandfather clocks believes that the rate of the increase in the auction price with age will be driven up by a large number of bidders. So there are two variables: number of bidders, and the age of the clock. 2 1 3 2 2 1 1 0 x x x x y

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Interaction Once interaction is deemed important in the model, the first order terms should be kept regardless of the associated p-values shown on the output.
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