By Xin Yan
ISBN-10: 9812834109
ISBN-13: 9789812834102
This booklet is sort of concise, yet there are various blunders or oversight. for example, phrases brought in proofs weren't given or mentioned past, making it tough to persist with the facts. one other instance is simply sheer sloppiness, resembling on p.45, the place the final line of the 1st paragraph is obviously wrong. at the similar web page, one other hassle-free mistakes appears to be like within the definition of orthonormal foundation (orthognality is missing). Readers could have little self belief within the proofs or formulation.
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Additional resources for Linear Regression Analysis: Theory and Computing
Sample text
Multiple regression allows researchers to examine the effect of more than one independent variables on response at the same time. For some research questions, regression can be used to examine how much a particular set of independent variables can explain sufficiently the outcome. In other cases, multiple regression is used to examine the effect of outcome while accounting for more than one factor that could influence the outcome. In this chapter we discuss multiple linear regression. To facilitate the discussion of the theory of the multiple regression model we start with a brief introduction of the linear space and the projection in the linear space.
Find the maximum likelihood estimates (MLE) of x0 using the ˆ 2 , βˆ1 , and βˆ2 . least squares estimators α ˆ1, α (c). Show that the distribution of Z, where ˆ 2 ) + x0 (βˆ1 − βˆ2 ), Z = (ˆ α1 − α is the normal distribution with mean 0 and variance A2 σ 2 , where x21j − 2x0 x1j + x20 n1 x22j − 2x0 x2j + x20 n2 + . A2 = 2 n1 (x1j − x¯1 ) n2 (x2j − x ¯2 )2 (d). Show that U = N σ ˆ 2 /σ 2 is distributed as χ2 (N ), where N = n1 + n2 − 4. (e). Show that U and Z are independent. ˆ 2 has the F distribution with degrees of (f).
The following classical data set contains the information of parent’s height and children’s height. 5 for parents. 69 parent height. The simple linear regression model is typically stated in the form y = β0 + β1 x + ε, where y is the dependent variable, β0 is the y intercept, β1 is the slope of the simple linear regression line, x is the independent variable, and ε is the 9 April 29, 2009 11:50 10 World Scientific Book - 9in x 6in Regression˙master Linear Regression Analysis: Theory and Computing random error.