9.4.21 Regression Analysis

Interprets the Results from Regression Analysis: Simple Linear, Multiple and Logistic

Regression analysis is a statistical method that helps to investigate the relationship between a dependent variable and one or more independent variables. There are different types of regression analyses, including simple linear regression, multiple regression, and logistic regression. Each type of regression analysis has a different purpose, but they all aim to find an equation that best fits the data and can be used to make predictions.

Simple linear regression:

Multiple regression analysis:

Multiple regression analysis, on the other hand, is used when we want to determine the relationship between a dependent variable and multiple independent variables. For example, we may want to determine the relationship between a patient’s blood pressure and age, gender, weight, and smoking status.

Logistic regression:

Logistic regression is a type of regression analysis used when the dependent variable is binary, i.e., it has only two possible outcomes. It is used to determine the relationship between one or more independent variables and a binary outcome. For example, we may want to determine the relationship between a patient’s age, gender, and smoking status with the likelihood of developing lung cancer.

Type of Regression	Description	Example
Simple Linear Regression	Examines the relationship between two continuous variables	Examining the relationship between age and blood pressure
Multiple Regression	Examines the relationship between one continuous dependent variable and multiple independent variables	Examining the relationship between a patient’s age, BMI, and cholesterol level on their risk for heart disease
Logistic Regression	Examines the relationship between a binary dependent variable and one or more independent variables	Examining the relationship between smoking status (binary dependent variable) and age, gender, and BMI (independent variables) on the likelihood of developing lung cancer

When interpreting the results from regression analysis, it is important to look at several key statistics. These include the coefficient of determination (R-squared), the regression coefficients, the standard error of the estimate, and the p-values. The coefficient of determination (R-squared) provides a measure of the proportion of variation in the dependent variable that can be explained by the independent variables. The regression coefficients show the direction and strength of the relationship between the dependent variable and each independent variable. The standard error of the estimate provides a measure of the precision of the regression coefficients, and the p-values indicate whether the regression coefficients are statistically significant.

In summary, regression analysis is a powerful tool that can be used to investigate the relationship between a dependent variable and one or more independent variables. It is important to choose the appropriate type of regression analysis based on the research question and data. When interpreting the results, it is important to consider several key statistics to determine the strength and significance of the relationships.

References:

1. Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models (5th ed.). McGraw-Hill/Irwin.
2. Hosmer Jr, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). John Wiley & Sons.