# Line of Best Fit Calculator

Line of best fit refers to a line that best expresses the relationship between a scatter plot of data points. Various types of best fit line are:

- Linear Best Fit Line: The line of best fit is a straight line when data points appear to be in a straight line.
- Polynomial Best Fit Line: A polynomial best fit line has many curves and bumps. In the real world, data usually follows a polynomial trend.
- Exponential Best Fit Line: An exponential best fit line shows exponential growth. Eg: rise in COVID-19 cases etc.

## What is a Line of Best Fit Calculator?

A 'Line of Best Fit Calculator' is a free online tool that calculates the equation of the best fit line for the given data points. In this calculator, you can enter the data points of the given distribution and the equation of the best fit line will be calculated within a few seconds.

NOTE: [Each pair should be enclosed in a bracket separated by a comma]

## How to Use Line of Best Fit Calculator?

Follow the steps given below to use the calculator:

**Step 1:**Enter the data points (x, y) in the space provided.**Step 2:**Click on the**"Calculate"**button to find the best fit.**Step 3:**Click on**"Reset"**to clear the field and enter new data points.

## How to Find a Line of Best Fit?

Statisticians generally use the least-squares method to find the equation of the best fit line. The least-square method is a more accurate way of finding the line of best fit. We use the following steps:

1. Calculate the mean of x values and y values (X and Y)

2. Find the slope of the best fit line using the formula:

**m = (Σ (xi - X) (yi - Y)) / (xi - X) ^{2}**

3. Find the y-intercept of the line using the formula:

**b = Y - mX**

So, the equation of the line of best fit for a given data is b = y - mx

Where Y and X are the mean of y and x data points respectively.

**Solved Example:**

What is the equation of the best fit line for the given data points?

(1.3), (3,4), (2,5) and (8,4)

**Solution:**

Mean of x data points X = (1+3+2+8)/4

= 3.5

Mean of y data points Y = (3+4+5+4)/4

= 4

Slope of the line m = (Σ (xi - X) (yi - Y)) / (xi - X)^{2}

m = 0.034

Now, intercept b = Y - mX

b = 4 - 3.5(0.034) = 3.879

Therefore, the equation of the best fit line will be y = 0.034x + 3.879

Similarly, you can try the calculator and find the best fit for the following:

- (2.3), (4,6), (6,9) and (8,2)
- (5.3), (1,4), (8,5) and (7,9)