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Least Squares Calculator

The Least Squares calculator that helps to find the line of best fit of the form

What is Least Squares Calculator?

The Least Squares method is a statistical regression analysis method used to find the line of best fit of the form 'y = mx + b' for a given set of data. 'Least Squares calculator' is a free online tool that finds the line of best fit for a given data set within a few seconds.

Least squares calculator

How to Use the Least Squares Calculator?

Follow the steps mentioned below to find the line of best fit.

Step 1- Enter the data points in the respective input box.
Step 2- Click on "Calculate" to find the least square line for the given data.
Step 3- Click on "Reset" to clear the fields and enter a new set of values.

How to Calculate Least Squares?

The least-squares method is used to find a linear line of the form y = mx + b. Here, 'y' and 'x' are variables, 'm' is the slope of the line and 'b' is the y-intercept.

Here, the value of slope 'm' is given by the formula, m = (n ∑ (XY) - ∑ Y ∑ X) / (n ∑ (X²) - (∑ X)²) and 'b' is calculated using the formula b = (∑ Y - m∑ X) / n

Let us look at an example on how to find the least square line for a given data set.

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Solved Examples on Least squares calculator

Example 1:

Find the least square line for the data shown below and verify it using least squares calculator.

X	1	2	3	4	5
Y	2	5	3	8	7

Solution:

X	Y	XY	X²
1	2	2	1
2	5	10	4
3	3	9	9
4	8	32	16
5	7	35	25
∑ X = 15	∑ Y = 25	∑ XY = 88	∑ X²= 55

Find the value of m.

m = (n ∑ (XY) - ∑ Y ∑ X) / (n ∑ (X²) - (∑ X)²)

= ( 5(88) - (15 × 25) ) / ( 5(55) - (15)² )

= 13/10

= 1.3

Find the value of b.

b = (∑ Y - m∑ X) / n

= (25 - (1.3 × 15)) / 5

= 11/10

= 1.1

So, the required equation of least squares is y = (1.3)x + 1.1

Now, use our online least squares calculator and find the least squares Line for the given data points

X	1.7	2.3	3.1	4.5	5.9
Y	12	45	29	65	45

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