how to find the estimated simple linear regression equation

To be able to get reliable estimators for the coefficients and to be able to interpret the results from a random sample of data, we need to make model assumptions. In simple linear regression, we essentially predict the value of the dependent variable yi using the score of the independent variable xi, for observation i. β0 is the intercept (a constant term) and β1 is the gradient. Here, β0 and β1 are the coefficients (or parameters) that need to be estimated from the data. Where the subscript i refers to a particular observation (there are n data points in total). In this way, the linear regression model takes the following form: To capture all the other factors, not included as independent variable, that affect the dependent variable, the disturbance term is added to the linear regression model. The disturbance is primarily important because we are not able to capture every possible influential factor on the dependent variable of the model. The relationship is modeled through a random disturbance term (or, error variable) ε. The linearity of the relationship between the dependent and independent variables is an assumption of the model.

Linear regression is used to study the linear relationship between a dependent variable (y) and one or more independent variables ( X). As the name suggests, this type of regression is a linear approach to modeling the relationship between the variables of interest.

In this article, I am going to introduce the most common form of regression analysis, which is the linear regression. By applying regression analysis, we are able to examine the relationship between a dependent variable and one or more independent variables. Regression analysis is an important statistical method for the analysis of data. Introduction to the core concepts of simple linear regression and OLS estimation Background

How to find the estimated simple linear regression equation