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STATS 2B03 (25)
Chapter 10

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McMaster University
Aaron Childs

Stats 2B03: Statistical Methods for Science Chapter 10: Multiple Regression and Correlation 10.2 The Multiple Linear Regression Model - Assumptions:  The X are non-random (fixed) variables. This assumptions i distinguishes the multiple regression model from the multiple correlation model. This condition indicates that any inferences that are drawn from sample data apply only to the set of X values observed and not to some larger collection of X’s. Under the regression model, correlation analysis is not meaningful.  For each set of Xivalues there is a subpopulation of Y values. To construct certain confidence intervals and test hypotheses, it must be known, or the researcher must be willing to assume, that these subpopulations of Y values are normally distributed. Since we will want to demonstrate these inferential procedures, the assumption of normality will be made.  The variances of the subpopulation of Y are all equal  The Y values are independent. That is, the values of Y selected for one set of X values do not depend on the values of Y selected at another set of X values - The model equation:  10.3 Obtaining the Multiple Regression Equation - sum of squares of deviations: ∑ ∑ 10.4 Evaluating the Multiple Regression Equation - The coefficient of multiple determination:  ∑ ∑ ∑ , SST = SSR + SSE  ∑ ∑ - Testing the regression hypothesis:  Data: the research situation and the data generated by the research are examined to determine if multiple regression is an appropriate technique for analysis  Assumptions: we assume that the multiple regression model and its underlying assumptions are applicable  Hypotheses: in general, the null hypothesis is H0: 1 = β2= β3= …= β =k 0 and the alternative is HA: not alliβ = 0. In words, the null hypothesis states that all the independent variables are of no value in explaining
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