Regression Coefficient given Correlation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X)
b1 = r*(σY/σX)
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.
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.
Standard Deviation of Y - Standard Deviation of Y is the measure of the amount of variation or dispersion of values in the variable 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.
STEP 1: Convert Input(s) to Base Unit
Correlation between X and Y: 2 --> No Conversion Required
Standard Deviation of Y: 150 --> No Conversion Required
Standard Deviation of X: 60 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
b1 = r*(σYX) --> 2*(150/60)
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 given Correlation Formula

Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X)
b1 = r*(σY/σX)

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 given Correlation?

Regression Coefficient given Correlation calculator uses Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X) to calculate 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 calculate Regression Coefficient given Correlation using this online calculator? To use this online calculator for Regression Coefficient given Correlation, enter Correlation between X and Y (r), Standard Deviation of Y Y) & Standard Deviation of X X) and hit the calculate button. Here is how the Regression Coefficient given Correlation calculation can be explained with given input values -> 0.2 = 2*(150/60).

FAQ

What is Regression Coefficient given Correlation?
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 and is represented as b1 = r*(σYX) or Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X). 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, Standard Deviation of Y is the measure of the amount of variation or dispersion of values in the variable Y & Standard Deviation of X is the measure of the amount of variation or dispersion of values in the variable X.
How to calculate Regression Coefficient given Correlation?
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 is calculated using Regression Coefficient = Correlation between X and Y*(Standard Deviation of Y/Standard Deviation of X). To calculate Regression Coefficient given Correlation, you need Correlation between X and Y (r), Standard Deviation of Y Y) & Standard Deviation of X X). With our tool, you need to enter the respective value for Correlation between X and Y, Standard Deviation of Y & Standard Deviation 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 Correlation between X and Y, Standard Deviation of Y & Standard Deviation of X. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Regression Coefficient = (Mean of Y-Regression Constant)/Mean of X
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