# Regression Analysis

### Homoscedasticity

The assumption of homoscedasticity (literally, same variance) is central to linear regression models.  Homoscedasticity describes a situation in which the error term (that is, the “noise” or random disturbance in the relationship between the independent variables and the dependent variable) is the same across all values of the independent variables.  Heteroscedasticity (the violation of homoscedasticity)

### Using Logistic Regression in Research

Binary Logistic Regression is a statistical analysis that determines how much variance, if at all, is explained on a dichotomous dependent variable by a set of independent variables. Questions Answered: How does the probability of getting lung cancer change for every additional pound of overweight and for every X cigarettes smoked per day? Do body

### Conduct and Interpret a Logistic Regression

What is Logistic Regression? 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 continuous-level (interval or ratio

### What is Multiple Linear Regression?

Multiple linear regression is the most common form of linear regression analysis.  As a predictive analysis, the multiple linear regression is used to explain the relationship between one continuous dependent variable from two or more independent variables.  The independent variables can be continuous or categorical (dummy coded as appropriate). Click to Start Using Intellectus Statistics

### Validity

Validity implies precise and exact results acquired from the data collected.  In technical terms, a measure can lead to a proper and correct conclusions to be drawn from the sample that are generalizable to the entire population. Four Major Types: 1.Internal validity: When the relationship between variables is causal.  This type refers to the relationship

### Two-Stage Least Squares (2SLS) Regression Analysis

Two-Stage least squares (2SLS) regression analysis is a statistical technique that is used in the analysis of structural equations.  This technique is the extension of the OLS method.  It is used when the dependent variable’s error terms are correlated with the independent variables. Additionally, it is useful when there are feedback loops in the model.

### The Multiple Linear Regression Analysis in SPSS

This example is based on the FBI’s 2006 crime statistics. Particularly we are interested in the relationship between size of the state, various property crime rates and the number of murders in the city. It is our hypothesis that less violent crimes open the door to violent crimes and also that even we account for

### The Logistic Regression Analysis in SPSS

Our example is a research study on 107 pupils. These pupils have been measured with 5 different aptitude tests one for each important category (reading, writing, understanding, summarizing etc.). The question now is – How do these aptitude tests predict if the pupils passes the year end exam? First we need to check that all

### The Linear Regression Analysis in SPSS

This example is based on the FBI’s 2006 crime statistics. Particularly we are interested in the relationship between size of the state and the number of murders in the city. First we need to check whether there is a linear relationship in the data. For that we check the scatterplot. The scatter plot indicates a

### Selection Process for Multiple Regression

The basis of a multiple linear regression is to assess whether one continuous dependent variable can be predicted from a set of independent (or predictor) variables.  Or in other words, how much variance in a continuous dependent variable is explained by a set of predictors.  Certain regression selection approaches are helpful in testing predictors, thereby

### Scatter plot: An Assumption of Regression Analysis

What is the value in examining a scatter plot for a regression analysis? Residual scatter plots provide a visual examination of the assumption homoscedasticity between the predicted dependent variable scores and the errors of prediction.  The primary benefit is that the assumption can be viewed and analyzed with one glance; therefore, any violation can be

### Regression

A regression assesses whether predictor variables account for variability in a dependent variable.  This page will describe regression analysis examples, regression assumptions, the evaluation of the R-square (coefficient of determination), the F-test, the interpretation of the beta coefficient(s), and the regression equation. Questions answered: Do age and gender impact attitudes on gun regulation? How do

### Questions the Multiple Linear Regression Answers

There are 3 major areas of questions that the multiple linear regression analysis answers – (1) causal analysis, (2) forecasting an effect, (3) trend forecasting. Click to Start Using Intellectus Statistics for Free   The first category establishes a causal relationship between three or more metric variables: one continuous dependent variable and two or more

### Questions the Linear Regression Answers

There are 3 major areas of questions that the regression analysis answers – (1) causal analysis, (2) forecasting an effect, (3) trend forecasting. The first category establishes a causal relationship between two variables, where the dependent variable is continuous and the predictors are either categorical (dummy coded), dichotomous, or continuous..  In contrast to correlation analysis

### Question the Logistic Regression Answers

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 independent variables and one binary dependent variable. Examples: Medicine: Do body weight calorie intake, fat intake, and age have an influence on

### Ordinal Regression

Ordinal regression is a statistical technique that is used to predict behavior of ordinal level dependent variables with a set of independent variables.  The dependent variable is the order response category variable and the independent variable may be categorical or continuous.  In SPSS, this test is available on the regression option analysis menu. Questions answered:

### Nonlinear Regression

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