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Topic 03

# Topic 03 - Topic 3 Multiple Regression Analysis Regression...

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1 Topic 3 – Multiple Regression Analysis Regression on Several Predictor Variables (Chapter 8)

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2 Topic Overview Systolic Blood Pressure Example Multiple Regression Models SAS Output for Regression Multicollinearity
3 Systolic Blood Pressure Data In this topic we will fully analyze the SBP dataset described in Problem #5.2 in the text. This dataset illustrates some excellent points regarding multiple regression. The file 03SBP.sas provides the data and all of the code that has been utilized to produce output shown in the CLG handout and lecture notes.

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4 Dataset Overview ( n = 32) Response Variable : systolic blood pressure for an individual Note: SBP is the maximum pressure exerted when the heart contracts (top number). Predictor Variables Age (measured in years) Body Size (measured using the quetelet index) Smoking Status (0 = nonsmoker, 1 = smoker)
5 Multiple Regression Analysis For the SBP data, our goal is to determine whether SBP may be reasonably well predicted by some combination of age, body size, and smoking status. Additionally we may want to try to describe relationships and answer questions such as: Does the SBP increase (on average) with an increase in size?

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6 Multiple Regression Analysis (2) The first step in a multiple regression analysis is to consider the individual variables and their pairwise (SLR) relationships. Identify potential problems (e.g. outliers) Identify and assess the form, direction, and strength of pairwise relationships.
7 CLG Activity #1 Please discuss questions 3.1-3.6 from the handout. Additional slides will be made available on the website after we have done the activities in class.

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8 Multiple Regression Analysis (3) The next step in multiple regression analysis is to consider using more than one predictor variable in the same model. You can think of adding variables to the model in a certain order. Each variable takes up a portion of the total sums of squares.
9 Graphical View of MLR Rectangle represents total SS; Ovals represent variables; Note OVERLAP! X1 X2 X3 Total SSY

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10 Some Key Points Must take into account relationships (correlation) among the potential predictor variables – these relationships are responsible for the overlap in explained SS. Interaction between predictors may also become a consideration. Interaction means that the effect of one predictor changes depending on the value of the other. More on this later...
11 Some Additional Concerns Dealing with multiple predictors is much more difficult than SLR: More difficult to choose the “best” model (we now have many more choices). Calculation of estimates can be problematic – generally we always employ a computer. Interpretation of the parameter estimates is usually less clear, and can in fact be meaningless if highly correlated variables are used in the same model.

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Topic 03 - Topic 3 Multiple Regression Analysis Regression...

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