FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Regression Coefficient given Correlation Formula

GoRegression Coefficient Formula

Fx Copy

LaTeX Copy

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 = r \cdot (\frac{σ Y}{σ X})

b₁ - Regression Coefficient?r - Correlation between X and Y?σ_Y - Standard Deviation of Y?σ_X - Standard Deviation of X?

Regression Coefficient given Correlation Example

With values

With units

Only example

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

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

Here is how the Regression Coefficient given Correlation equation looks like.

5 = 2 \cdot (\frac{150}{60})

5 = 2 \cdot (\frac{150}{60})

5 = 2 \cdot (\frac{150}{60})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Statistics » Category

Coefficients, Proportion and Regression » fx Regression Coefficient given Correlation

Regression Coefficient given Correlation Solution

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

FIRST Step Consider the formula

b 1 = r \cdot (\frac{σ Y}{σ X})

Next Step Substitute values of Variables

∴

b 1 = 2 \cdot (\frac{150}{60})

Next Step Prepare to Evaluate

∴

b 1 = 2 \cdot (\frac{150}{60})

LAST Step Evaluate

∴

b 1 = 5

Regression Coefficient given Correlation 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

Correlation between X and Y

Correlation between X and Y is the measure of the strength and direction of the linear relationship between two variables X and Y. It ranges from -1 to 1.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Correlation between X and Y

Standard Deviation of Y

Standard Deviation of Y is the measure of the amount of variation or dispersion of values in the variable Y.

Symbol: σ_Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation of Y

Standard Deviation of X

Standard Deviation of X is the measure of the amount of variation or dispersion of values in the variable X.

Symbol: σ_X

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation of X

Other Formulas to find Regression Coefficient

Go Regression Coefficient

b 1 = \frac{ȳ - b 0}{x̅}

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 given Correlation?

Regression Coefficient given Correlation evaluator uses Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X) to evaluate the Regression Coefficient, Regression Coefficient given Correlation 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 calculated using the correlation between X and Y. Regression Coefficient is denoted by b₁ symbol.

How to evaluate Regression Coefficient given Correlation using this online evaluator? To use this online evaluator for Regression Coefficient given Correlation, enter Correlation between X and Y (r), Standard Deviation of Y (σ_Y) & Standard Deviation of X (σ_X) and hit the calculate button.

FAQs on Regression Coefficient given Correlation

What is the formula to find Regression Coefficient given Correlation?

The formula of Regression Coefficient given Correlation is expressed as Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X). Here is an example- 0.2 = 2*(150/60).

How to calculate Regression Coefficient given Correlation?

With Correlation between X and Y (r), Standard Deviation of Y (σ_Y) & Standard Deviation of X (σ_X) we can find Regression Coefficient given Correlation using the formula - Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X).

What are the other ways to Calculate Regression Coefficient?

Here are the different ways to Calculate Regression Coefficient-

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

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Regression Coefficient given Correlation Formula

​GoRegression Coefficient Formula

Regression Coefficient given Correlation Example

Regression Coefficient given Correlation Solution

Regression Coefficient given Correlation Formula Elements

Other Formulas to find Regression Coefficient

Other formulas in Regression category

How to Evaluate Regression Coefficient given Correlation?

FAQs on Regression Coefficient given Correlation

Variable Name

GoRegression Coefficient Formula