Regression analysis is a statistical method used to examine the relationship between one or more independent variables (predictors) and a dependent variable (outcome). It aims to understand how changes in the independent variables are associated with changes in the dependent variable. One common form of regression analysis is simple linear regression.

Simple linear regression is a basic form of regression analysis that models the relationship between two variables: one independent variable (X) and one dependent variable (Y). It assumes that there is a linear relationship between X and Y, meaning that as X changes, Y changes proportionally. The goal of simple linear regression is to find the best-fitting straight line that describes the relationship between X and Y.

The equation for a simple linear regression model is typically expressed as:

**y**Â is the predicted value of the dependent variable (**y**) for any given value of the independent variable (**x**).**B0**Â is theÂ**intercept**, the predicted value ofÂ**y**Â when theÂ**x**Â is 0.**B1**Â is the regression coefficient â€“ how much we expectÂ**y**Â to change asÂ**x**Â increases.**x**Â is the independent variable ( the variable we expect is influencingÂ**y**).**e**Â is theÂ**error**Â of the estimate, or how much variation there is in our estimate of the regression coefficient.

The regression model estimates the values of **B0** and **B1**Â that minimize the sum of the squared differences between the observed values of Y and the values predicted by the model. This is typically done using the method of least squares.

Once the model is fitted, it can be used to make predictions about the dependent variableY based on values of the independent variable X .Â Additionally, the model can provide insights into the strength and direction of the relationship between the two variables, as well as the variability of the data around the regression line.

[…] d) What is regression? What is simple linear regression? […]