## Introduction to Least Squares Regression Line Calculator:

Least squares regression line calculator is a powerful tool that is used to **find the estimated point** values for data analysis in statistics. It helps you to evaluate the relationship between variables and the intercept line that passes through different points.

The least-squares regression line calculator is a helpful source for students, professionals, and research analysts to make a hypothesis about the given experiment data and it provides a complete understanding of the interpretation of a line in an easy way without going to any tutor.

## What is the Least Squares Regression Line?

The Least squares regression line is a straight line that best expresses the **data points on a graph**. This method gives information about the sum of the squared differences between the experiment values and the predicted values of a line.

The least square regression line is one of the processes used to find the slope of a line and intercept points for the linear equation.

## What is the Equation of the Least Squares Regression Line?

The Least squares regression line calculator **uses the equation** of the slope-intercept form is y = mx+b, least square regression for both the variables x and y becomes:

\begin{matrix} X \;\;on\;\; Y & Y\;\; on\;\; X \\ X \;=\; a + by & Y \;=\; a + bx \\ \end{matrix}

$$ a \;=\; \frac{n( \sum \; xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} $$

$$ b \;=\; \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2} $$

Whereas,

- y is the dependent variable when you use the rules Y on X.
- x is the independent variable when you follow X on Y.
- a is the slope of the line
- b is the y-intercept of the line
- n is the total number of points

## How to Calculate Least Squares Regression Line?

The least regression square method is a simple method that is used to find the nearest approximate line to intercept the slope line equation or in simple words for calculating the least squares regression line. For this, the least square regression line calculator **finds the slope of the equation** and intercept of the line with the help of the formula.

Let us understand how the calculator least squares regression line determines the least square regression with the help of example.

First, the linear regression least squares calculator finds the slope and then the intercept of a line. Suppose you have x and y values and you want to find the least square regression line.

x | 1 | 2 | 3 | 5 | 4 |
---|---|---|---|---|---|

y | 3 | 4 | 5 | 2 | 6 |

**Solution**:

First, we need to arrange the table in such a way as to find the value of x^{2}, y^{2}, and xy value for the formula of slope and intercept.

As to find the regression intercept line from X to Y and Y to X.

**X = a+by**, **Y = a+bx**

x | y | x^{2} |
y^{2} |
xy |
---|---|---|---|---|

1 | 3 | 1 | 9 | 3 |

2 | 4 | 4 | 16 | 8 |

3 | 5 | 9 | 25 | 15 |

5 | 2 | 25 | 4 | 10 |

4 | 6 | 16 | 36 | 24 |

∑x=15 | ∑y=20 | ∑x2=55 | ∑y2=90 | ∑xy=60 |

Put these values in the slope and intercept formula to get the values of a and b.

**For slope a**:

$$ a \;=\; \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} $$

$$ a \;=\; \frac{60 - 15 (20)}{55 - (15)^2} $$

$$ a \;=\; \frac{-240}{170} $$

$$ a \;=\; 1.141 $$

**For Intercept (b)**:

$$ b \;=\; \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2} $$

$$ b \;=\; (20)(55) - \frac{(15)(60)}{ 55 -(15)^2} $$

$$ b \;=\; \frac{200}{170} $$

$$ b \;=\; 1.176 $$

Put **a and b values** in the above equation to find the estimated line along with x and y variables.

\begin{matrix} X \;=\; a + by & Y \;=\; a + bx \\ X \;=\; 1.14 + 1.17y & Y \;=\; 1.14 + 1.17x \\ \end{matrix}

## How to Use Least Squares Regression Line Calculator?

The least-squares regression line calculator has a simple layout so that everyone can use it to solve regression line problems.

You just need to put your regression line variables problem in the least square regression line calculator by following some steps. These steps are:

**Enter the data**in which x and y value are present, in the input field.- Check the input number values of x and y that you provided before clicking the calculate button to get the estimated points.
- Click the “Calculate” button for the solution for the regression line problem.
- If you want to check the working process behind our linear regression least squares calculator, use the load example question to get an idea about its working method.
- Recalculate button provides you an opportunity to evaluate more examples of regression line questions to find the approximate line near the original line.

## Final Result of Least-Squares Regression Line Calculator:

Least squares regression line calculator provides you a solution regression line as per your input number problem when you click on the calculate button. It may include:

- When you click on the result button of calculator least squares regression line, you get the
**solution of the least square of the regression line**problem. - Steps option tells you to get the solution of estimated points that make an imaginary line near the original one questions in a step-by-step method.

## Benefits of Least Square Regression Line Calculator:

The linear least squares regression calculator has different benefits whenever you use it to solve regression line problems and get its solution. These benefits are:

- Least squares regression line equation calculator is a
**speedy tool**that determine least squares regression line problems with solutions in a couple of minutes without any type of external effort. - It is an educational tool that helps children to learn the concept of the least square method for finding the regression line easily just by sitting at home.
- The linear regression least squares calculator is a handy tool that quickly solves regression line problems with the help of the least square method.
- It is a free tool that allows you to use it for calculating the least squares regression line without any fee to get its solution.
- The least-squares regression line calculator has a simple interface you do not need to become expert for square line regression problem.
- Our Least squares regression line calculator only receives the input value and provides a solution without requiring a sign-up.