Simple Linear Regression
As the name indicates, simple linear regression is the simplest regression model which involves only one predictor. This model assumes a linear relationship between the dependent variable and the predictor variable as shown in following figure.
Simple linear regression is a statistical method used to establish the relationship between two variables, where one variable is used to predict the other variable. The method assumes a linear relationship between the variables, meaning that a change in one variable will produce a proportional change in the other variable.
In simple linear regression, the variable that is being predicted (also known as the dependent variable) is referred to as Y, and the variable that is being used to predict the dependent variable (also known as the independent variable or predictor variable) is referred to as X.
The relationship between X and Y can be represented by the following equation:
Y = a + bX
where a is the intercept (the value of Y when X is zero) and b is the slope (the change in Y for every unit change in X).
The goal of simple linear regression is to estimate the values of a and b in the equation above using a set of data points. This can be done using the method of least squares, which involves finding the values of a and b that minimize the sum of the squared differences between the predicted values of Y and the actual values of Y.
Once the values of a and b have been estimated, the equation can be used to make predictions of Y for new values of X. Additionally, statistical tests can be performed to determine the significance of the relationship between X and Y and to assess the accuracy of the predicted values.