Multiple Regression Analysis

Multiple regression analysis is a statistical technique used to examine the relationship between a dependent variable and two or more independent variables. It allows researchers to identify which independent variables have a significant impact on the dependent variable, while controlling for the effects of other variables.

The basic model for multiple regression is:

y = b0 + b1x1 + b2x2 + … + bnxn + e

where y is the dependent variable, x1, x2, …, xn are the independent variables, b0 is the intercept (the value of y when all independent variables are 0), and b1, b2, …, bn are the regression coefficients (the amount by which y changes when x1, x2, …, xn change by one unit), and e is the error term.

To perform multiple regression analysis in SPSS, you can use the Regression procedure. This procedure allows you to select the dependent and independent variables, specify the type of regression model you want to use (e.g., linear, quadratic), and examine the significance and strength of the relationships between the variables. The output of the Regression procedure includes regression coefficients, R-squared, and other statistics.

Multiple regression analysis can be useful in a variety of fields, such as psychology, economics, and medicine. For example, in psychology, multiple regression can be used to examine the relationship between personality traits, demographic variables, and mental health outcomes. In economics, multiple regression can be used to analyze the impact of government policies, consumer behavior, and other factors on economic growth. In medicine, multiple regression can be used to examine the relationship between medical treatments, patient characteristics, and health outcomes.

Multiple Regression Analysis Theories

Multiple regression analysis is a widely used statistical method that allows researchers to examine the relationship between a dependent variable and two or more independent variables. Here are some important theories related to multiple regression analysis:

General Linear Model: The general linear model is a framework that underlies many statistical analyses, including multiple regression. It assumes that the relationship between the dependent variable and the independent variables is linear, meaning that a unit increase in an independent variable corresponds to a fixed increase or decrease in the dependent variable.

Ordinary Least Squares: Ordinary least squares (OLS) is a method used to estimate the parameters in multiple regression analysis. It involves finding the values of the regression coefficients that minimize the sum of the squared differences between the observed values of the dependent variable and the predicted values based on the independent variables.

Assumptions of Multiple Regression: Multiple regression analysis relies on several assumptions, including that the relationship between the independent variables and the dependent variable is linear, that the residuals (i.e., the difference between the observed values and predicted values) are normally distributed, and that there is no multicollinearity (i.e., high correlation) between the independent variables.

R-squared: R-squared is a statistic that measures the proportion of variance in the dependent variable that is explained by the independent variables in the model. It ranges from 0 to 1, with higher values indicating a better fit between the model and the data.

Multicollinearity: Multicollinearity occurs when two or more independent variables in a multiple regression model are highly correlated with each other. This can cause problems in estimating the regression coefficients and can make it difficult to interpret the results of the analysis.