Regression Coefficient Calculator

✖Mean of Y is the average value of all the data points in the variable Y.ⓘ Mean of Y [ȳ]			+10% -10%
✖Regression Constant is the intercept of the regression line on the Y-axis. It represents the expected value of Y when X is 0.ⓘ Regression Constant [b₀]			+10% -10%
✖Mean of X is the average value of all the data points in the variable X.ⓘ Mean of X [x̅]			+10% -10%

✖Regression Coefficient is the value that represents the change in the dependent variable Y for a unit change in the independent variable X.ⓘ Regression Coefficient [b₁]

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Formula

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Regression Coefficient

Formula

`"b"_{"1"} = ("ȳ"-"b"_{"0"})/"x̅"`

Example

`"5"=("200"-"50")/"30"`

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Regression Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X
b₁ = (ȳ-b₀)/x̅
This formula uses 4 Variables

Variables Used

Regression Coefficient - Regression Coefficient is the value that represents the change in the dependent variable Y for a unit change in the independent variable X.
Mean of Y - Mean of Y is the average value of all the data points in the variable Y.
Regression Constant - Regression Constant is the intercept of the regression line on the Y-axis. It represents the expected value of Y when X is 0.
Mean of X - Mean of X is the average value of all the data points in the variable X.

STEP 1: Convert Input(s) to Base Unit

Mean of Y: 200 --> No Conversion Required
Regression Constant: 50 --> No Conversion Required
Mean of X: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

b₁ = (ȳ-b₀)/x̅ --> (200-50)/30

Evaluating ... ...

b₁ = 5

STEP 3: Convert Result to Output's Unit

5 --> No Conversion Required

FINAL ANSWER

5 <-- Regression Coefficient

(Calculation completed in 00.004 seconds)

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< 4 Regression Calculators

Simple Linear Regression Line

Go Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X)

Regression Coefficient given Correlation

Go Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X)

Regression Coefficient

Go Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X

Regression Constant

Go Regression Constant = Mean of Y-(Regression Coefficient*Mean of X)

Regression Coefficient Formula

Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X
b₁ = (ȳ-b₀)/x̅

What is Linear Regression?

Linear Regression is a statistical method used to model the relationship between a dependent variable (also known as the response variable) and one or more independent variables (also known as predictor variables). The goal of Linear Regression is to find the best-fitting line through a set of data points, which can then be used to make predictions about the response variable for different values of the predictor variables.
Linear Regression models are represented by the equation y = mx + b, where y is the response variable, x is the predictor variable, m is the slope of the line, and b is the y-intercept. Simple Linear Regression is used to model the relationship between one predictor variable and one response variable.
Linear Regression is a widely used statistical technique and is often used in fields such as economics, engineering, and the natural sciences.

How to Calculate Regression Coefficient?

Regression Coefficient calculator uses Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X to calculate the Regression Coefficient, The Regression Coefficient formula is defined as the value that represents the change in the dependent variable Y for a unit change in the independent variable X. Regression Coefficient is denoted by b₁ symbol.

How to calculate Regression Coefficient using this online calculator? To use this online calculator for Regression Coefficient, enter Mean of Y (ȳ), Regression Constant (b₀) & Mean of X (x̅) and hit the calculate button. Here is how the Regression Coefficient calculation can be explained with given input values -> 5.333333 = (200-50)/30.

FAQ

What is Regression Coefficient?

The Regression Coefficient formula is defined as the value that represents the change in the dependent variable Y for a unit change in the independent variable X and is represented as b₁ = (ȳ-b₀)/x̅ or Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X. Mean of Y is the average value of all the data points in the variable Y, Regression Constant is the intercept of the regression line on the Y-axis. It represents the expected value of Y when X is 0 & Mean of X is the average value of all the data points in the variable X.

How to calculate Regression Coefficient?

The Regression Coefficient formula is defined as the value that represents the change in the dependent variable Y for a unit change in the independent variable X is calculated using Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X. To calculate Regression Coefficient, you need Mean of Y (ȳ), Regression Constant (b₀) & Mean of X (x̅). With our tool, you need to enter the respective value for Mean of Y, Regression Constant & Mean of X and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Regression Coefficient?

In this formula, Regression Coefficient uses Mean of Y, Regression Constant & Mean of X. We can use 1 other way(s) to calculate the same, which is/are as follows -

Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X)

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