Ordinary Regression Farrokh Alemi Ph D HEALTH INFORMATICS

Ordinary Regression Farrokh Alemi, Ph. D. HEALTH INFORMATICS PROGRAM HI. GMU. EDU

Purpose of Regression

Regress Y on one or more independent variables X 1 … Xn HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Parameter Estimation HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Regression Is Everywhere HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Multiple Regression HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Multiple Regression HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Multiple Regression HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Multiple Regression HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Parameter Estimation HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Sum of Squared Residuals HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Sum of Squared Residuals Y 10 12 14 HEALTH INFORMATICS PROGRAM X 1 2 3 4 5 Predicted Squared Y Residuals 10. 00 10. 80 1. 20 1. 44 11. 60 -1. 60 2. 56 12. 40 -0. 40 0. 16 13. 20 0. 80 0. 64 GEORGE MASON UNIVERSITY

Residuals HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Minimize SSR HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Why Minimize SSR? HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Why Minimize SSR? Because it is easy. HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Preparing Variables for Regression

Preparing Independent Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Dependent Variable: Continuous Interval Scale HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Independent Binary Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Independent Categorical Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Categorical Variable Race X 1 X 2 X 3 X 4 White=1, Otherwise = 0 Black=1, Otherwise = 0 Asian=1, Otherwise = 0 Other=1, Otherwise = 0 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Categorical Variable Race X 1 X 2 X 3 X 4 White=1, Otherwise = 0 Black=1, Otherwise = 0 Asian=1, Otherwise = 0 Other=1, Otherwise = 0 HEALTH INFORMATICS PROGRAM Dropped & Reference GEORGE MASON UNIVERSITY

Independent Continuous Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Independent Interaction Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Interaction Variables HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

How to Regress in R And Excel?

Regression: Using Excel HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

First Add-in Analysis Tool Pack 5 6 1 2 add in the analysis tool pack 4 3 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Regression Menu in Excel 7 8 8 9 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Regression: Using R HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Using R 1. Download R https: //cran. r-project. org/bin/windows/base/old/3. 3. 1/ HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Using R 2. Set Working Directory HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Using R 3. Read Data HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Using R: 4 Regression HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Meaning of Regression Output Fit Statistics Coefficients

Meaning of Regression Coefficients HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Increase in Y for 1 unit of X 30 25 Dependent Y 20 Rise 15 10 Run 5 0 0 HEALTH INFORMATICS PROGRAM 5 10 Independent X 15 20 25 GEORGE MASON UNIVERSITY

Interaction Variables Warning: Changes Meaning HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Interaction Variables Not how much Y changes for 1 unit of X HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Meaning of Probability of Observing Coefficients HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Meaning of the Probabilities HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Hypothesis Testing HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Hypothesis Testing : g n i n r a W text t n n e o d C n e p e D HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Meaning of Fit Statistics HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Goodness of Fit, 2 R Total SS = Explained SS + Unexplained SSR HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Goodness of Fit, 2 R : s g e l n i b n a r i r a a W re V 2 o M er R h g i H Total SS = Explained SS + Unexplained SS HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Goodness of Fit, 2 R : g n a i t n a r D a W sive 2 s a M er R w Lo Total SS = Explained SS + Unexplained SS HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Models that are predictive & parsimonious HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Hierarchical Regression: Add & Re-Test HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Forward Selection: Add & Re-Test HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Backward Selection: Remove & Re-Test HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Cross Validation: 2 Report R in New Data HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Co-linearity: Can Change Significance HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

Co-linearity: Sex Age Cost HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

ORDINARY REGRESSION ASSUMPTIONS MUST BE VERIFIED AND OUTPUT CORRECTLY INTERPRETED