Simple Linear Regression Tool (Proof of Concept)

This tool implements a simple linear regression algorithm as a proof of concept. It is designed to perform linear regression given a dataset and a target value, returning the predicted value, slope, and intercept.

Formula Explanation

The linear regression formula predicts the value of a dependent variable based on the value of an independent variable. It assumes a linear relationship between the variables and is represented by the equation:

$ȳ = (1/n) Σ yi$

$x̄ = (1/n) Σ xi$

$m = Σ((xi - x̄) * (yi - ȳ)) / Σ((xi - x̄)^2)$

$b = ȳ - m * x̄$

$y = mx + b$

Variables Explanation:

• Dependent Variable $( y )$:

  • Represents the variable we aim to predict based on the independent variable $x$. It is often referred to as the predicted value.

• Independent Variable $( x )$:

  • Denotes the variable used to make predictions about the dependent variable $y$. It serves as the input to our model or predictor variable.

• Slope $( m )$:

  • Indicates the rate of change of the dependent variable $y$ concerning the independent variable $x$. It shows how much $y$ changes for a unit change in $x$.
  • A positive slope $m$ suggests a positive relationship between $x$ and $y$, while a negative slope suggests a negative relationship.

• Intercept $( b )$:

  • Represents the point where the regression line intersects the y-axis when $x = 0$. It indicates the value of $y$ when $x$ is zero and signifies the baseline value of $y$ when all other factors are zero.

Demo

The tool takes a dataset consisting of pairs of $[ x, y ]$ values and a target value $x$. It performs simple linear regression on the dataset and returns the predicted value, slope, and intercept.

Input

• dataset: A vector of $[x, y]$ pairs representing the dataset.
• target: The target value for which the prediction is to be made.

Output

• Predicted value: The predicted value of the dependent variable $y$ for the given target value $x$.
• Slope: The slope of the regression line.
• Intercept: The intercept of the regression line.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Feel free to contribute, report issues, or suggest improvements.