A best fit line is also known as a trend line or regression line, and it is an essential component of linear regression analysis. This line represents the linear relationship between two variables, typically an independent variable (x) and a dependent variable (y).

- A best fit line is a straight line that best represents the trendline of a scatter plot or data series.
- It is used to show the relationship between two variables, allowing for predictions based on this relationship.
- The line is determined by finding the slope and y-intercept that minimizes the overall distance between the line and the data points.
- This distance is measured using a technique called ordinary least squares.
- A best fit line can be utilized to estimate future values of the dependent variable based on the independent variable’s value.

There are different types of best fit lines, depending on the nature of the relationship between the variables. These include:

- Linear best fit line, for a linear relationship between variables;
- Quadratic best fit line, for a relationship that may be modeled by a quadratic equation;
- Exponential best fit line, for a relationship that may be modeled by an exponential equation.

A best fit line is a useful tool in data analysis and is often used in a variety of fields, including science, finance, and engineering. It is used to model the relationship between two variables and can be used to make predictions and inform decisions based on this information.

## Example problem for best fit line

What is a best fit line?

- A best fit line is a straight line that represents the relationship between two variables on a scatter plot.
- It is called a “best fit” line because it is drawn to pass through as many data points as possible while still minimizing the distance between the line and the points.

How is a best fit line calculated?

- A best fit line is calculated using a mathematical formula that takes into account the coordinates of all the data points on a scatter plot.
- The formula finds the values of the slope and y-intercept that minimize the distance between the line and the points.

Why is a best fit line important?

- A best fit line helps to show the relationship between two variables on a scatter plot.
- It can be used to make predictions about future data points based on the trend of the existing data.
- It can also be used to identify outliers or data points that do not fit the trend of the rest of the data.

What are the limitations of a best fit line?

- A best fit line assumes a linear relationship between the two variables on a scatter plot.
- If the relationship is non-linear, a best fit line may not accurately represent the trend of the data.
- A best fit line is also affected by outliers or data points that do not fit the trend of the rest of the data.