multiregress3 - Regression Analysis III Model buliding...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Regression Analysis III Model buliding Variable selection Residual Analysis
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 pp 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).
Background image of page 2
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 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 .
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 27

multiregress3 - Regression Analysis III Model buliding...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online