Line of Best Fit: Definition, How It Works, and Calculation

What Is the Line of Best Fit?

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least squares method (sometimes known as ordinary least squares, or OLS) to arrive at the geometric equation for the line, either through manual calculations or by using software.

A straight line will result from a simple linear regression analysis of two or more independent variables. A multiple regression involving several related variables can produce a curved line in some cases.

Understanding the Line of Best Fit

The line of best fit estimates a straight line that minimizes the distance between itself and where observations fall in some data set. 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 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 and Regression Analysis

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 500 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 data sets 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. This method builds the line which 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 between 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.

How to Calculate the Line of Best Fit

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 x_2, 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.

The Bottom Line

A line of best fit estimates the one line that minimizes the distance between it and observed data. Estimating a line of best fit is a key component of regression analysis in statistics in order to infer the relationships between some dependent variable and one or more explanatory variables. In finance, the line of best fit is utilized in this way to conduct econometric studies and in certain tools used in technical analysis.