Simple Linear Regression Line Calculator

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Regression Coefficients Proportion

✖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%
✖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]			+10% -10%
✖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.ⓘ Independent Random Variable X [X]			+10% -10%

✖Dependent Random Variable Y is the variable whose value depends on other variables in a statistical analysis.ⓘ Simple Linear Regression Line [Y]

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Simple Linear Regression Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X)
Y = b₀+(b₁*X)
This formula uses 4 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Regression Constant: 50 --> No Conversion Required
Regression Coefficient: 5 --> No Conversion Required
Independent Random Variable X: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Y = b₀+(b₁*X) --> 50+(5*10)

Evaluating ... ...

Y = 100

STEP 3: Convert Result to Output's Unit

100 --> No Conversion Required

FINAL ANSWER

100 <-- Dependent Random Variable Y

(Calculation completed in 00.020 seconds)

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Simple Linear Regression Line

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

Regression Coefficient given Correlation

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

Regression Coefficient

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

Regression Constant

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

Simple Linear Regression Line Formula

LaTeX Go

Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X)
Y = b₀+(b₁*X)

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 Simple Linear Regression Line?

Simple Linear Regression Line calculator uses Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X) to calculate 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 calculate Simple Linear Regression Line using this online calculator? To use this online calculator for Simple Linear Regression Line, enter Regression Constant (b₀), Regression Coefficient (b₁) & Independent Random Variable X (X) and hit the calculate button. Here is how the Simple Linear Regression Line calculation can be explained with given input values -> 90 = 50+(5*10).

FAQ

What is Simple Linear Regression Line?

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 and is represented as Y = b₀+(b₁*X) or Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X). 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 Coefficient is the value that represents the change in the dependent variable Y for a unit change in the independent 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.

How to calculate Simple Linear Regression Line?

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 is calculated using Dependent Random Variable Y = Regression Constant+(Regression Coefficient*Independent Random Variable X). To calculate Simple Linear Regression Line, you need Regression Constant (b₀), Regression Coefficient (b₁) & Independent Random Variable X (X). With our tool, you need to enter the respective value for Regression Constant, Regression Coefficient & Independent Random Variable X and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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