Logistic regression is a class of regression where the independent variable is used to predict the dependent variable. The dependent variable is dichotomous.  When the dependent variable has two categories, then it is binary logistic regression.  When the dependent variable has more than two categories, then it is multinomial logistic regression.  When the dependent variable category is to be ranked, then it is ordinal logistic regression (OLS)….

Multiple regression generally explains the relationship between multiple independent or multiple predictor variables and one dependent or criterion variable.  A dependent variable is modeled as a function of several independent variables with corresponding coefficients, along with the constant term.  Multiple regression requires two or more predictor variables, and this is why it is called multiple regression. The multiple regression equation ex…

What kinds of research questions can logistic regression address? A team of researchers at the Health Department is interested in the demographic characteristics of those who get tested for HIV in the US. Using the 2006 National Health Interview Survey, they use logistic regression to explore the effect of sex and age on the likelihood of having ever been tested for HIV. How does logistic regression work? Binary logistic regression is a powerful…

Nonlinear regression is a regression in which the dependent or criterion variables are modeled as a non-linear function of model parameters and one or more independent variables.  There are several common models, such as Asymptotic Regression/Growth Model, which is given by: b1 + b2 * exp(b3 * x) Logistic Population Growth Model, which is given by: b1 / (1 + exp(b2 + b3 * x)), and Asymptotic Regression/Decay Model, which is given by: b1 – …

Multiple linear regression is the most common form of the regression analysis.  As a predictive analysis multiple linear regression is used to describe data and to explain the relationship between one dependent variable and two or more independent variables. At the center of the multiple linear regression analysis is the task of fitting a single line through a scatter plot.  More specifically the multiple linear regression fits a line through a …

Multiple linear regression analysis makes several key assumptions: Linear relationship Multivariate normality No or little multicollinearity No auto-correlation Homoscedasticity Multiple linear regression needs at least 3 variables of metric (ratio or interval) scale.  A rule of thumb for the sample size is that regression analysis requires at least 20 cases per independent variable in the analysis, in the simplest case of having just two inde…

Logistic regression is the linear regression analysis to conduct when the dependent variable is dichotomous (binary).  Like all linear regressions the logistic regression is a predictive analysis.  Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more metric (interval or ratio scale) independent variables. Standard linear regression requires the dependent variable to be…

There are 3 major areas of questions that the multiple linear regression analysis answers – (1) causal analysis, (2) forecasting an effect, (3) trend forecasting. The first category establishes a causal relationship between three or more metric variables.  In contrast to correlation analysis, which does not indicate directionality of effects, the multiple linear regression analysis assumes that the independent variables have an effect on the dep…

Ordinal regression is a statistical technique that is used to predict behavior of dependent variables with a set of independent variables.  The dependent variable is the order response category variable and the independent variable may be categorical, interval or a ratio scale variable.  In SPSS, this test is available on the regression option analysis menu. Key terms and concepts: Dependent variable: The dependent variable is ordinal.  The firs…

There are 3 major questions that the logistic regression analysis answers – (1) causal analysis, (2) forecasting an outcome, (3) trend forecasting. The first category establishes a causal relationship between one or more ordinal (or better) independent variables and one binary dependent variable.  In contrast to Point-Biserial correlation analysis, which does not indicate directionality of effects, the logistic regression analysis assumes that t…