Chapter_12_Guide Fall 10

Chapter_12_Guide Fall 10 - AMS 315 Data Analysis Chapter...

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AMS 315 Data Analysis Chapter Twelve Study Guide Multiple Regression and the General Linear Model Fall 2010 Context The statement of the theory of multiple linear regression in matrix terms is given in Section 12.9. Understanding the results of this chapter is much easier if you invest in learning how to use these tools. I will present the theory in matrix form in this chapter’s study guide. We assume that , Z X Y σ β + = where Y is an 1 × n vector of observations, X is an p n × matrix of known constants, is a 1 × p vector of unknown but constant parameters, , 0 and Z is an 1 × n vector of ) 1 , 0 ( NID random variables. The sum of squares function is given by . 2 ) ( ) ( ) ( Xb X b Y X b Y Y Xb Y Xb Y b SS T T T T T T + - = - - = The OLS estimate ˆ is any solution of the system of normal equations: Y X X X T T = ˆ ) ( . If 1 ) ( - X X T exists, then the OLS estimate is unique and Y X X X T T 1 ) ( ˆ - = . The procedures in this chapter provide tools to deal with the association of one continuous dependent variable and an arbitrary number of independent variables. 12.1. Introduction and Abstract of Research Study This section contains a statement of the multiple linear regression model and key definitions. It is an important section with key definitions. 12.2 The General Linear Model This section contains the statement of the multiple linear regression model without using matrix notation. You should work on Section 12.9. 12.3 Estimating Multiple Regression Coefficients Ordinary Least Squares (OLS) estimates are the ones most commonly used. If 1 ) ( - X X T exists, then the OLS estimate is unique and Y X X X T T 1 ) ( ˆ - = . 12.4 Inferences in Multiple Regression Definition 12.2 is important. The overall F test statistic and the coefficient of determination (multiple correlation coefficient squared) 2 . 1 k x x y R are important statistics. The supplemental material contains an example examination problem worked out in detail.

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12.5 Testing a Subset of Regression Coefficients This is a common procedure. The most common example is to test the contribution of variables sequentially. 12.6. Forecasting Using Multiple Regression
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Chapter_12_Guide Fall 10 - AMS 315 Data Analysis Chapter...

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