Linear Regression Calculator

Calculate the least squares regression line for a set of data points.

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About Linear Regression Calculator

The Linear Regression Calculator computes the least squares regression line for a set of data points, allowing you to understand the relationship between two variables and make predictions.

What is Linear Regression?

Linear regression is a statistical method used to model the relationship between a dependent variable (Y) and one independent variable (X) by fitting a linear equation to observed data.

The regression line equation is represented as:

\( Y = b_0 + b_1 X \)

Where:
\( Y \) = Dependent variable
\( X \) = Independent variable
\( b_0 \) = Intercept of the regression line
\( b_1 \) = Slope of the regression line

How to Calculate Linear Regression

The slope (\( b_1 \)) and intercept (\( b_0 \)) are calculated using the following formulas:

\( b_1 = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sum (X_i - \bar{X})^2} \)

\( b_0 = \bar{Y} - b_1 \bar{X} \)

Where:
\( X_i, Y_i \) = Individual data points
\( \bar{X}, \bar{Y} \) = Means of X and Y

What is the Slope of the Regression Line?

The slope (\( b_1 \)) of the regression line indicates the change in the dependent variable (Y) for a one-unit change in the independent variable (X). It represents the strength and direction of the relationship.

Least Squares Regression Line

The least squares regression line minimizes the sum of the squares of the vertical distances of the points from the line. It provides the best fit for the data.

Multiple Linear Regression Calculator

While this calculator focuses on simple linear regression with one independent variable, multiple linear regression involves two or more independent variables. For multiple regression analysis, specialized statistical software or calculators are recommended.

Use Cases of Linear Regression

Linear regression is widely used in various fields:

Finance: Predicting stock prices based on historical data.
Economics: Modeling the relationship between consumption and income.
Marketing: Forecasting sales based on advertising spend.
Engineering: Estimating material strength based on stress tests.

References:

Linear Regression - Wikipedia

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"Linear Regression Calculator" at https://MiniWebtool.com/linear-regression-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Nov 04, 2024

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About Linear Regression Calculator

What is Linear Regression?

How to Calculate Linear Regression

What is the Slope of the Regression Line?

Least Squares Regression Line

Multiple Linear Regression Calculator

Use Cases of Linear Regression

References:

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