Line of Best Fit
What is the line of best fit?
The line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians generally use the method of least squares (sometimes known as ordinary least squares or OLS) to arrive at the geometric equation of the line, either by manual calculations or using software.
A straight line will result from a simple linear regression Analysis of two or more independent variables. A multiple regression involving multiple related variables may produce a curved line in some cases.
Key points to remember
- A line of best fit is a straight line that minimizes the distance between itself and some data.
- The line of best fit is used to express a relationship in a scatterplot of different data points.
- It is a regression analysis output and can be used as a forecasting tool for indicators and price movements.
- In finance, the line of best fit is used to identify trends or correlations in market returns between assets or over time.
Understanding the Line of Best Fit
The line of best fit estimates a straight line that minimizes the distance between itself and where observations lie in a data set. The line of best fit is used to show a trend or correlation between the dependent variable and the independent variable(s). It can be represented visually or as a mathematical expression.
The 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 useful to professionals in a wide range of fields ranging from science and public service to financial analysis.
Line of best fit.
Line of best fit and regression analysis
To perform regression analysis, a statistician collects a set of data points, each of which includes a complete set of dependent and independent variables. For example, the dependent variable could be a company’s stock price and the independent variables could be the Standard and Poor’s 500 the index and the national unemployment rate, assuming the stock is not in the S&P 500. The sample could be any of these three data sets for the past 20 years.
On a graph, these data points would appear as a scatter plot, a collection of points that may or may not appear to be arranged along a line. If a linear pattern is apparent, it may be possible to sketch a line of best fit that minimizes the distance of these points from that line. If no organization axis is visually apparent, regression analysis may generate a line based on the least squares method. This method constructs the line that minimizes the squared distance of each point from the line of best fit.
To determine the formula for this straight line, the statistician enters these three results from the last 20 years into regression software. 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 company’s future stock price based on these two independent variables.
How to Calculate the Line of Best Fit
A regression with two independent variables like 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 the second independent variable are b2 and x2, respectively. Using the example above, 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 to which y changes for each additional unit of that variable.
If the S&P 500 rises by one, the resulting y or stock price will rise 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, this coefficient is the slope of the line of best fit. In this example or in any regression with two independent variables, the slope is a mixture of the two coefficients. The constant c is the intercept of the line of best fit.
How do you find the line of best fit?
There are several approaches to estimate a line of best fit to certain data. The simplest and crudest is to visually estimate such a line on a scatter plot and draw it to the best of your ability.
The most accurate method involves the method of least squares. It is a statistical procedure for finding the best fit for a set of data points by minimizing the sum of the offsets or point residuals from the plotted curve. This is the main technique used in regression analysis.
Is a line of best fit always straight?
By definition, a line is always straight, so a line of best fit is linear. However, a curve can also be used to describe the best fit in a data set. Indeed, a curve of best fit can be squared (x2), cubic (x3), quadratic (x4), logarithmic (ln), a square root (√) or anything else that can be mathematically described with an equation. Note, however, that simpler explanations of fit are often preferred.
How is a line of best fit used in finance?
For financial analysts, the method of estimating a line of best fit can help quantify the relationship between two or more variables, such as a stock’s price and its earnings per share (EPS). When performing this type of analysis, investors often try to predict the future behavior of stock prices or other factors by extrapolating this line over time.