Line Of Best Fit - Definition, Example, How To Calculate?

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Publication Date :

25 Oct, 2021

Blog Author :

Gabriel Machado Pureza

Edited by :

Collins Enosh

Reviewed by :

Dheeraj Vaidya, CFA, FRM

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Table Of Contents

Line of Best Fit Definition

The line of best fit is a mathematical concept that correlates points scattered across a graph. It is a form of linear regression that uses scatter data to determine the best way of defining the relationship between the dots.

The concept enables the visualization of collected data. In doing so, it makes data interpretation easier.

Key Takeaways

• The line of best fit demonstrates the correlation between the different points in a grid.
• It can be used to find trends by determining the relationship between different points on a graph. It’s widely used in the financial market and in the scientific world.
• For calculation, the following formula is used: Y = C +B¹(x¹) + B²(x²)

Understanding the Line of Best Fit

The line of best fit, also known as a regression line. It is essentially a line that shows trends followed by the dots on a grid. It is used to interpret the visual representation of data. This concept helps understand the correlation between one point and another. The line is not as important as the data used. It is only a tool that enables the visualization of collected data.

This method determines whether the collected data is linear or not. The more linear the data, the easier it will be to draw the line. Also, the line is straighter if the data is linear. In contrast, for correlated information involving several sources, the line is curved.

Why do Researches Use a Line of Best Fit?

This concept can be useful in several contexts. One of them is to establish a relationship between different variables. By establishing this relationship, one can identify trends that would be difficult without it. As a result, several distinctive fields like the financial market and science use this method.

In the financial market, it is used to analyze collected market data. One could, for example, take variables from the last ten years of Nasdaq or United States employment data. By correlating the data and using this concept, one can get a better grasp of how these topics correlate with each other. This concept is then used to predict future trends involving both variables.

Consider another example from science. In geoscience, the regression line is used to find relationships between several variables related to the Earth. In doing so, scientists better understand the history of the planet and predict natural issues.

However, it’s essential to note that this concept does not automatically give a correlation between data. If given data has no relationship at all, one can still calculate the line, but it won’t be very useful. To get better results, researchers need to analyze the data independently and see if it makes sense.

How to Calculate the Line of Best Fit ?

The easiest way to calculate the line of best fit is by using regressive analysis software. However, it’s essential to figure out the logic behind the process to understand what the computer is doing. After learning the method, anyone can calculate it using just a piece of paper and a pencil.

First, chart the collected data on a scatter graph. This is essential because it sets and organizes the values needed for the formula. The following formula is used to calculate the line of best fit:

Y = C +B¹(x¹) + B²(x²)

Here, Y is the dependent variable of the equation.

• C is constant.
• B¹ and B² are first and second regression coefficients.
• X¹ and X² are the first and second independent variables.

Before calculating the formula, researchers need to understand the corresponding values on the graph. Consider the financial example cited before: Nasdaq’s correlation with ten years of US employment. If researchers can pick samples from four data sets during each year, they would have 40 different points.

In this case, the stock price would be constant, while the Nasdaq prices and employment rates would be the other independent variables. By finding the results, researchers will be able to draw the line.

Line of Best Fit Examples

Consider the following examples to better understand how the line should be positioned and what it means.

In the first example, it is easy to determine the line because the results are relatively linear. Generally, it shows the continuity of whatever the researcher is looking for.

However, in the second example, it’s possible to understand how the graph changes when one of the dots gets plotted slightly below the regression. Even a single dot can pull the whole line down. Despite the one data point lying outside the line, the overall result is still fairly linear.

The third example clearly demonstrates that it is still possible to draw a straight regressive line even if the results are less linear. This is when this mathematical concept is really useful because it shows a perfect line among data that is not completely linear. Without using this method, it would be difficult to interpret given data.

In the fourth example, a line was drawn based on calculation, but it does not really represent anything. This happens when the data is not really correlated. When there is no relation between points of data, this method cannot find a new relationship.

Frequently Asked Questions (FAQs)

Line of Best Fit FAQs1

What is meant by a line of best fit?

2

What is a line of good fit used for?

3

Is the regression line a line of good fit?

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