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Linear Regression

Satisfactory Essays

Chapter 4
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 …show more content…

Problems if VIF > 10. Some people use the condition index. In order to avoid false positives, use the COLLINOINT option.

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Variance Inflation Factor (VIF) Example

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Collinearity Diagnostics – Not Adjusted

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Collinearity Diagnostics – Adjusted

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Body Fat Example
Variables
              28

Percent body fat from Siri’s (1956) equation – dependent Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference (cm Knee circumference (cm) Ankle circumference (cm) Biceps (extended) circumference (cm) Forearm circumference (cm) Wrist circumference (cm)

What Is Being Tested by |t|

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continued...

What Is Being Tested by Pr >|t|

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Partial F-Tests

H o : 3  0 | all other  's are in the model

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Interpretation – The Stable Table

Do I need this leg to have a stable table?

Nope!

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...

Interpretation – The Stable Table

Do I need this leg to have a stable table?

Nope!

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...

Interpretation – The Stable Table

Do I need this leg to have a stable table?

Nope!

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...

Graphs
Predicted versus Y Residual versus Independents Student versus Independents Cook’s D versus Weight Leverage versus Weight

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Moral of the Story


Removing more than one variable at a time is a

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