Author: Mehmet Niyazi Cankaya
Date: 2025-12-09

# Introduction to cosCorr Package

#### Mehmet Niyazi Cankaya

#### 2025-12-09

# Introduction to cosCorr Package

## Overview

The cosCorr package implements the cosine-correlation coefficient for measuring the degree of linear dependence among variables in multidimensional contexts.

## The Cosine-Correlation Theorem

The cosine-correlation coefficient rho is defined as:

rho = [(p-1) * prod(|t_i|)] / sum(|t_i|^(p-1))

where t_1 = 0 and t_2, …, t_p are the variables in the system.

## Basic Usage

    library(cosCorr)

    # Simple example with 4 variables (p=4)
    x <- c(0, 2, 3, 4)
    rho <- cosCorr(x)
    print(rho)
    #> [1] 0.7272727

## More Examples

    # Example with 5 variables
    x2 <- c(0, 1, 2, 3, 4)
    rho2 <- cosCorr(x2)
    print(rho2)
    #> [1] 0.2711864

    # Example with NA values removed
    x3 <- c(0, 2, NA, 4, 5)
    rho3 <- cosCorr(x3, na.rm = TRUE)
    print(rho3)
    #> [1] 0.6091371

## Properties of the Coefficient

- Range: The coefficient always lies in [0, 1]
- Interpretation: Higher values indicate stronger linear dependence
- Generalization: Extends naturally to p-dimensional spaces
- Applications: Useful in experimental design, time series analysis, and geometric analysis

## Mathematical Background

The coefficient is derived from dimensional exploration principles in time scale calculus. It quantifies angular relationships between variables in a p-dimensional space.

## References

Cankaya, M. N. (2025). Derivatives through Probes in Regular Geometric Objects: A Dimensional Exploration for qqq-Sets in Time Scale Calculus. Fractals, in printing progress.