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Regression Coefficient Formula

GoRegression Coefficient given Correlation Formula

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Regression Coefficient is the value that represents the change in the dependent variable Y for a unit change in the independent variable X. Check FAQs

b 1 = \frac{ȳ - b 0}{x̅}

b₁ - Regression Coefficient?ȳ - Mean of Y?b₀ - Regression Constant?x̅ - Mean of X?

Regression Coefficient Example

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Here is how the Regression Coefficient equation looks like with Values.

Here is how the Regression Coefficient equation looks like with Units.

Here is how the Regression Coefficient equation looks like.

5 = \frac{200 - 50}{30}

5 = \frac{200 - 50}{30}

5 = \frac{200 - 50}{30}

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Regression Coefficient Solution

Follow our step by step solution on how to calculate Regression Coefficient?

FIRST Step Consider the formula

b 1 = \frac{ȳ - b 0}{x̅}

Next Step Substitute values of Variables

∴

b 1 = \frac{200 - 50}{30}

Next Step Prepare to Evaluate

∴

b 1 = \frac{200 - 50}{30}

LAST Step Evaluate

∴

b 1 = 5

Regression Coefficient Formula Elements

Variables

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.

Symbol: b₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Regression Coefficient

Mean of Y

Mean of Y is the average value of all the data points in the variable Y.

Symbol: ȳ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean of 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.

Symbol: b₀

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Regression Constant

Mean of X

Mean of X is the average value of all the data points in the variable X.

Symbol: x̅

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean of X

Other Formulas to find Regression Coefficient

Go Regression Coefficient given Correlation

b 1 = r \cdot (\frac{σ Y}{σ X})

Other formulas in Regression category

Go Regression Constant

b 0 = ȳ - (b 1 \cdot x̅)

Go Simple Linear Regression Line

Y = b 0 + (b 1 \cdot X)

How to Evaluate Regression Coefficient?

Regression Coefficient evaluator uses Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X to evaluate 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 evaluate Regression Coefficient using this online evaluator? To use this online evaluator for Regression Coefficient, enter Mean of Y (ȳ), Regression Constant (b₀) & Mean of X (x̅) and hit the calculate button.

FAQs on Regression Coefficient

What is the formula to find Regression Coefficient?

The formula of Regression Coefficient is expressed as Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X. Here is an example- 5.333333 = (200-50)/30.

How to calculate Regression Coefficient?

With Mean of Y (ȳ), Regression Constant (b₀) & Mean of X (x̅) we can find Regression Coefficient using the formula - Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X.

What are the other ways to Calculate Regression Coefficient?

Here are the different ways to Calculate Regression Coefficient-

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

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: Value
: Unit

Regression Coefficient Formula

​GoRegression Coefficient given Correlation Formula

Regression Coefficient Example

Regression Coefficient Solution

Regression Coefficient Formula Elements

Other Formulas to find Regression Coefficient

Other formulas in Regression category

How to Evaluate Regression Coefficient?

FAQs on Regression Coefficient

Variable Name

GoRegression Coefficient given Correlation Formula