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Simple Linear Regression Line Formula

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Dependent Random Variable Y is the variable whose value depends on other variables in a statistical analysis. Check FAQs

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

Y - Dependent Random Variable Y?b₀ - Regression Constant?b₁ - Regression Coefficient?X - Independent Random Variable X?

Simple Linear Regression Line Example

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Here is how the Simple Linear Regression Line equation looks like with Values.

Here is how the Simple Linear Regression Line equation looks like with Units.

Here is how the Simple Linear Regression Line equation looks like.

100 = 50 + (5 \cdot 10)

100 = 50 + (5 \cdot 10)

100 = 50 + (5 \cdot 10)

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Simple Linear Regression Line Solution

Follow our step by step solution on how to calculate Simple Linear Regression Line?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Y = 50 + (5 \cdot 10)

Next Step Prepare to Evaluate

∴

Y = 50 + (5 \cdot 10)

LAST Step Evaluate

∴

Y = 100

Simple Linear Regression Line Formula Elements

Variables

Dependent Random Variable Y

Dependent Random Variable Y is the variable whose value depends on other variables in a statistical analysis.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Dependent Random 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.

Symbol: b₀

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Regression Constant

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

Independent Random Variable X

Independent Random Variable X is the variable that is not influenced by other variables in a statistical analysis. It is used to predict or explain the behavior of the dependent variable Y.

Symbol: X

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Independent Random Variable X

Other formulas in Regression category

Go Regression Constant

b 0 = ȳ - (b 1 \cdot x̅)

Go Regression Coefficient given Correlation

b 1 = r \cdot (\frac{σ Y}{σ X})

Go Regression Coefficient

b 1 = \frac{ȳ - b 0}{x̅}

How to Evaluate Simple Linear Regression Line?

Simple Linear Regression Line evaluator uses Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X) to evaluate the Dependent Random Variable Y, Simple Linear Regression Line formula is defined as the value of the dependent random variable Y corresponds to the given value of the independent random variable X determined using the simple linear regression line. Dependent Random Variable Y is denoted by Y symbol.

How to evaluate Simple Linear Regression Line using this online evaluator? To use this online evaluator for Simple Linear Regression Line, enter Regression Constant (b₀), Regression Coefficient (b₁) & Independent Random Variable X (X) and hit the calculate button.

FAQs on Simple Linear Regression Line

What is the formula to find Simple Linear Regression Line?

The formula of Simple Linear Regression Line is expressed as Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X). Here is an example- 90 = 50+(5*10).

How to calculate Simple Linear Regression Line?

With Regression Constant (b₀), Regression Coefficient (b₁) & Independent Random Variable X (X) we can find Simple Linear Regression Line using the formula - Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X).

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Simple Linear Regression Line Formula

Simple Linear Regression Line Example

Simple Linear Regression Line Solution

Simple Linear Regression Line Formula Elements

Other formulas in Regression category

How to Evaluate Simple Linear Regression Line?

FAQs on Simple Linear Regression Line

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