Formula for Regression Coefficients
The formula for regression coefficients lies at the heart of linear regression analysis, a powerful statistical technique used to model the relationship between variables. At its core, linear regression seeks to find the best-fitting straight line that describes the relationship between a predictor variable (often denoted as X) and a response variable (often denoted as Y).
In the formula for regression coefficients:
[Tex]a = \frac{n(\sum xy) – (\sum x)(\sum y)}{n(\sum x^2) – (\sum x)^2}[/Tex]
[Tex]b = \frac{(\sum y)(\sum x^2) – (\sum x)(\sum xy)}{n(\sum x^2) – (\sum x)^2}[/Tex]
Each term plays a crucial role in determining the slope (a) and intercept (b) of the best-fitted line:
n: Represents the number of data points in the dataset. It ensures that the calculations are representative of the entire dataset.
By computing a and b using these formulas, analysts can derive the equation of the best-fitted line: Y = aX + b. This equation enables predictions and insights into the relationship between the variables, empowering decision-making processes across various domains.
Regression Coefficients
Regression coefficients in linear regression are the amounts by which variables in a regression equation are multiplied. Linear regression is the most commonly used form of regression analysis. Linear regression aims to determine the regression coefficients that result in the best-fitting line. These coefficients are helpful when estimating the value of an unknown variable using a known variable. This article explains regression coefficients and their formulas and provides related examples.
Table of Content
- What are Regression Coefficients?
- Regression Line
- Formula for Regression Coefficients
- Regression Coefficients Interpretation
- Steps to Calculate the Regression Coefficient
- Regression Coefficients in Different Types of Regression Models
- Solved Examples on Regression Coefficients
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