0508P - REGRESSION ANALYSIS

By Professor Omar Hasan Kasule Sr.

Learning Objectives:

·        Concepts of dependent and independent variables in a scatter-gram

·        Difference between correlation and regression

·        The linear regression line and the linear regression equation (Y=a + bx)

·        Interpreting the intercept, a (+ve and -ve)

·        Interpreting the regression coefficient, b (+ve, -ve, range -infinity to +infinity)

·        Use of the regression line/equation for  testing of association

·        Use of regression for  prediction (interpolation and extrapolation)

·        Definition and use of multiple linear regression

·        Use of multivariate methods in controlling confounding and prediction

Key Words and Terms:

·        Prediction, linear extrapolation

·        Prediction, linear interpolation

·        Regression Analysis

·        Regression Coefficient, partial

·        Regression coefficient, total

·        Regression Equation/Line

·        Regression, multiple linear

·        Regression, multiple logistic

·        Regression, non-linear

·        Regression, simple linear

·        Regression. Logistic

·        Variable, dependent

·        Variable, independent

UNIT OUTLINE

LINEAR REGRESSION

A. Overview or Regression

B. Simple Linear Regression

C. Multiple Linear Regression

D. Prediction in Regression

LOGISTIC REGRESSION

A. Definition

E. Multiple Logistic Regression

UNIT SYNOPSIS

LINEAR REGRESSION

Regression to the mean, first described by Francis Galton (1822-1911) is one of the basic laws of nature, sunan al llah fi al kawn. The simple linear regression equation is y=a + bx where y is the dependent/response variable, a is the intercept, b is the slope/regression coefficient, and x is the dependent/predictor variable.

Multiple linear regression, a form of multivariate analysis, is defined by y=a+b₁x₁ + b₂x₂ + …b_nx_n.

Linear regression is used for prediction (intrapolation and extrapolation) and for analysis of variance.

LOGISTIC REGRESSION

Logistic regression is non-linear regression with y dichotomous/binary Logistic regression is used in epidemiology because of a dichotomized outcome variable. Multiple logistic regressions are used for prediction and other purposes.