In linear regression, the best-fit line is the straight line that most accurately represents the relationship between the independent variable (input) and the dependent variable (output). It is the line that minimizes the difference between the actual data points and the predicted values from the model.
1. Goal of the Best-Fit Line
The goal of linear regression is to find a straight line that minimizes the error (the difference) between the observed data points and the predicted values. This line helps us predict the dependent variable for new, unseen data.
Here Y is called a dependent or target variable and X is called an independent variable also known as the predictor of Y.
- θ1 represents the intercept, which is the value of Y when X = 0
- θ2 represents the slope, which shows how much Y changes for a unit change in X
There are many types of functions or modules that can be used for regression. A linear function is the simplest type of function. Here, X may be a single feature or multiple features representing the problem.
2. Equation of the Best-Fit Line
For simple linear regression (with one independent variable), the best-fit line is represented by the equation
y=mx+b
