# Line of Best Fit in Regression Analysis: Definition & Calculation

> **Definition**
>
> A line of best fit estimates the line that minimizes the distance between it and observed data.

## What Is the Line of Best Fit?

A line of best fit is a form of regression analysis that shows the relationship between two variables. It helps illustrate trends and patterns in data and is often used to predict outcomes in fields like finance. The line is usually determined using the least squares method, which minimizes the distance between the line and the actual data points. By showing the overall trend, the line of best fit is an important tool for decision-making and financial analysis.

### Key Takeaways

*   The line of best fit minimizes the distance between itself and the data points in a scatter plot.  
    
*   It is a fundamental output of regression analysis, used to show trends or correlations between variables.  
    
*   Financial analysts use it to predict stock prices or other financial indicators by extrapolating data.  
    
*   The least squares method is commonly used to calculate the line of best fit, ensuring the smallest deviation from data points.  
    
*   Although a line of best fit is usually straight, complex data may require a best-fit curve.

![Line of Best Fit: A line through a scatter plot of data points that best expresses the relationship between those points.](https://www.investopedia.com/thmb/U0vCJoyO7HDkx4lOsWeTYwxniDg=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/line-of-best-fit.asp-final-ed50f47f6cf34662846b3b89bf13ceda.jpg)

*Lines of best fit are used in economics, finance, science, and marketing. — Eliana Rodgers / Investopedia*

## Grasping Line of Best Fit Concepts in Data Analysis

The line of best fit estimates a straight line that minimizes the distance between itself and where observations fall in some dataset. The line of best fit is used to show a trend or correlation between the dependent variable and independent variable(s). It can be depicted visually, or as a mathematical expression.

Line of best fit is one of the most important concepts in [regression](https://www.investopedia.com/terms/r/regression.asp) analysis. Regression refers to a quantitative measure of the relationship between one or more independent variables and a resulting dependent variable. Regression is of use to professionals in a wide range of fields, from science and public service to financial analysis.

![Line of Best Fit](https://www.investopedia.com/thmb/N3OMxXSXRzzPVPqG84sBtMzkjgA=/1217x0/filters:no_upscale():max_bytes(150000):strip_icc()/Linalg_line_of_best_fit_running-15836f5df0894bdb987794cea87ee5f7.png)

*Line of Best Fit.*

## Integrating Line of Best Fit with Regression Analysis Techniques

To perform a regression analysis, a statistician collects a set of data points, each including a complete set of dependent and independent variables. For example, the dependent variable could be a firm’s stock price and the independent variables could be the [Standard and Poor’s (S&P) 500](https://www.investopedia.com/terms/s/sp500.asp) Index and the national unemployment rate, assuming that the stock is not listed in the S&P 500. The sample set could be each of these three datasets for the past 20 years.

On a chart, these data points would appear as a scatter plot, a set of points that may or may not appear to be organized along any line. If a linear pattern is apparent, it may be possible to sketch a line of best fit that minimizes the distance of those points from that line. If no organizing axis is visually apparent, regression analysis can generate a line based on the [least squares method](https://www.investopedia.com/terms/l/least-squares-method.asp). This method builds the line that minimizes the squared distance of each point from the line of best fit.

To determine the formula for this line, the statistician enters these three results for the past 20 years into a regression software application. The software produces a linear formula that expresses the causal relationship among the S&P 500, the unemployment rate, and the stock price of the company in question. This equation is the formula for the line of best fit. It is a predictive tool, providing analysts and traders with a mechanism to project the firm’s future stock price based on those two independent variables.

## Calculating the Line of Best Fit: Methods and Formulas

A regression with two independent variables such as the example discussed above will produce a formula with this basic structure:

> y= c + b1(x1) + b2(x2)

In this equation, y is the dependent variable, c is a constant, b1 is the first regression coefficient, and x1 is the first independent variable. The second coefficient and second independent variable are b2 and x2, respectively. Drawing from the above example, the stock price would be y, the S&P 500 would be x1, and the unemployment rate would be x2. The coefficient of each independent variable represents the degree of change in y for each additional unit in that variable.

If the S&P 500 increases by one, the resulting y or share price will go up by the amount of the coefficient. The same is true for the second independent variable, the unemployment rate. In a simple regression with one independent variable, that coefficient is the slope of the line of best fit. In this example or any regression with two independent variables, the slope is a mix of the two coefficients. The constant c is the y-intercept of the line of best fit.

## How Do You Find the Line of Best Fit?

There are several approaches to estimating a line of best fit to some data. The simplest, and crudest, involves visually estimating such a line on a scatter plot and drawing it in to your best ability.

The more precise method involves the least squares method. This is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve. This is the primary technique used in regression analysis.

## Is a Line of Best Fit Always Straight?

By definition, a line is always straight, so a best-fit line is linear. However, a curve may also be used to describe the best fit in a set of data. Indeed, a best-fit curve may be squared (x), cubic (x), quadratic (x), logarithmic (ln), a square root (√), or anything else that can be described mathematically with an equation. Note, however, that simpler explanations of fit are often preferred.

## How Is a Line of Best Fit Used in Finance?

Financial analysts use the line of best fit to quantify relationships between variables, like stock price and [earnings per share (EPS)](https://www.investopedia.com/terms/e/eps.asp). By performing this type of analysis, investors often try to predict the future behavior of stock prices or other factors by extrapolating that line out in time.

## The Bottom Line

The line of best fit visually and mathematically shows the relationship between variables in a dataset. It is derived using the least squares method, which minimizes the sum of squared differences between observed and predicted values. This line can serve as a predictive tool in many areas, where it helps identify trends or correlations. It is applied in econometric studies and in technical analysis to forecast future market trends based on past data. The line of best fit is a key part of regression analysis and is essential for understanding relationships between variables across different fields.