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Chapter 10

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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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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