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Words 1277

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Multiple Linear Regression

Section 4.1

The Model and Assumptions

Objectives

Participants will: understand the elements of the model understand the major assumptions of doing a regression analysis learn how to verify the assumptions understand a median split

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The Model y o 1x1 ... p x p or in Matrix Notation

Dependent Variable nx1 Unknown Parameters (p+1) x 1

Y X e

Independent Variables – n x(p+1)

Error – nx1

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Questions

How many unknown parameters are there? Can you name them? How many populations will be sampled? What are conceptual populations?

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Major Requirements for Doing a Regression Analysis

The errors are normally distributed (not Y). Constant variance – What is the null hypothesis? Linear in the parameters Errors are independent. Some people call these assumptions.

EY () X

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Example

We have observed y = response (change in blood pressure) and x = dosage level of a drug. We assume a linear relationship between E(y) and x. The two graphs are the same, but they have been rotated to give additional views.

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continued...

Example

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continued...

Example

Sketch E(y). Based on the graphs, make comments about the assumptions. Do they appear to be satisfied or violated? How many populations are represented by the graphs? List all of the parameters. Write the model down.

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Checking Assumptions

Testing the residuals for normality PROC CAPABILITY

Testing for constant variance Use the test for Heteroscedasticity in PROC REG

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y versus x1

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Residual versus x1 after Fitting x1 and x1*x1

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Heteroscedasticity

Conclusion?

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Demonstration

Car1

This demonstration illustrates the model and parameters testing the assumptions virtual populations.

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Tasks to Do

Write down the…...

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