Help Analyze Data Using Regression Model
What is the Regression Model of Analysis?
Are you looking for expert help on how to analyze data using the regression model? Then our statisticians will be glad to provide the best data analysis services. Regression is a statistical method that is used to determine the relationship between a dependent variable, denoted by y and one or more independent variables, denoted by x. Regression analysis is used to model a relationship between the dependent and independent variables to predict what will happen in the future.
A regression model focuses on the direction and the strength between two or more variables. The model assumes a relationship between the dependent and the independent variable or variables. The independent variable is the variable that is not affected by the other variables being measured in a study. The dependent variables are affected by the independent variable or variables. Regression models have many assumptions such as linearity, autocorrelation, multicollinearity, and multiple variances.
Types of Regression Models
There are six types of regression models: Linear models, logistic models, polynomial regression, ridge regression, lasso regression, and Bayesian linear regression. The major regression models are linear regression models and logistic regression models. The major models are discussed below.
Linear Regression Model
A linear regression model determines the relationship between variables by fitting a straight line to the data. The strength of the relationship between the dependent and the independent variables is determined before fitting a linear model to the data. A scatter plot can be used to determine the strength of the linear relationship.
a. Simple linear regression model
The simple linear model determines the relationship between two continuous variables; one dependent variable and one independent variable. The formula for the simple linear regression model is y = α + βx. Y is the dependent variable, x is the independent variable, α is the y-intercept on the graph, and β is the slope of the graph.
b. Multiple linear regression model
In multiple regression, one dependent variable is affected by multiple independent variables. For example, the price of a house can depend on the location of the house, the number of bedrooms, and the square feet of the house. The price of the house is the dependent variable, while the independent variables are the number of bedrooms, the square feet, and the location of the house. The model is represented by the following equation: y = β0 + β1x1 + β2x2 + …+ βkxk + ε, where y is the dependent variable, x1, x2…xk are the independent variables up to k variables, β0 is the y-intercept, β1, β2,…, βk are the parameters of the regression line, and ε is the residual.
Logistic Regression
Logistic regression is a statistical model that estimates conditional probabilities. The model is often used when the dependent variable is binary in nature. For the logistic regression to be applied, a linear relationship between the variables is not a requirement. In logistic regression, logit transformation is applied to the data to obtain a linear model of the log odds of success. The logistic regression model is as shown below:
ln () = y = β0 + β1x1 + β2x2
Where y is the binary dependent variable, p(y=1) is the probability that the binary dependent variable takes the value 1, q(y=1) is the probability that the y variable does not take the value 1. In case the dependent variable is non-binary, the polynomial logistic regression is applied.
Applications of Regression
There are three major uses of regression; causality, forecasting, and prediction. Causality, which refers to the attribution of effects and relationships between variables. Regression is also used in forecasting, for example, emergency departments use regression to forecast the number of patients who will seek emergency services. The last application is prediction, for example, the logistic model is used to predict the risk factors of cancer.
The regression model determines the relationship between the dependent variable and one or more independent variables. Before fitting regression models on the data, it is best if a scatter plot of the data is plotted to determine if a relationship exists between the variables. The scatter plot is best used when using the linear regression models. Assumptions made in the regression analysis are linearity, autocorrelation, multicollinearity, and multiple variances. There are two main types of regression models: linear regression models and logistic regression models.