© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 5/12/2014, Spring 2014 Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 11: Regression Analysis 1

Understand the concepts related to the regression model Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 11.1

3 Allows researchers to quantify precisely the relative importance of any proposed factor or variable Closely related to correlation A mathematical equation is used to predict the value of the dependent variable (denoted Y ) on the basis of the independent variable (denoted X ) a = the Y-intercept (or the constant) –The expected level of Y when X = 0 b = the slope (or regression coefficient) –The amount that Y is expected to change (increase or decrease) for each increase of one unit in X e = The error (or disturbance term) The Regression Model

4 Find equation of the line that minimizes the sum of the square errors

11.1 Figure 11.2

The Regression Model Formulas: b – The Slope –For deviations –For raw scores a – The Y-Intercept

Requirements for Regression 11.1 A Straight-Line Relationship Interval Data Random Sampling Normally Distributed Characteristics

Understand the importance of prediction errors Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 11.2

9 Prediction Errors The difference between the points (Y) and the regression line (Ŷ) is the error or disturbance term ( e) The value of the regression equation is in its ability to reduce predictive error The ability of a regression line to make predictions can be expressed as the proportionate reduction in error (PRE) –The PRE statistic shows how much of the variance can be explained

Understand how regression and Pearson’s correlation are related Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 11.3

11 Regression and Pearson’s Correlation The larger the value of r, the smaller the value of SS error relative to SS total The PRE is the square of Pearson’s r –This is also called the coefficient of determination –Provides us with the amount of variation in Y explained by X The coefficient of nondetermination –Provides us with the amount of variation in Y left unexplained

Understand how regression and analysis of variance are related Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 11.4

13 Regression and Analysis of Variance Using the coefficient of determination and non- determination as the proportions of explained and unexplained variation Regression sum of squares: df =1 Error sum of squares: df = N – 2

Regression and Analysis of Variance Next, calculate the MS reg and MS error by dividing the sums of squares by their respective degrees of freedom Calculate the F ratio for testing the significance of the regression and compare to Table D in Appendix C

15 Exercise Exercises 7 and 10

16 Homework Exercises 9 and 13