# Linear Regression

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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 3 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 4 Questions How many unknown parameters are there? Can you name them? How many populations will be sampled? What are conceptual populations? 5 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. 24 Variance Inflation Factor (VIF) Example 25 Collinearity Diagnostics – Not Adjusted 26 Collinearity Diagnostics – Adjusted 27 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| 30 continued... What Is Being Tested by Pr >|t| 31 Partial F-Tests H o : 3  0 | all other  's are in the model 32 Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 33 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 34 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 35 ... Graphs Predicted versus Y Residual versus Independents Student versus Independents Cook’s D versus Weight Leverage versus Weight 36 Moral of the Story  Removing more than one variable at a time is a