# Coordinating Qualitative Predictor Variables in an Applied Linear Model: Analysis and Application for Applied Sciences

## TL;DR

This paper introduces a new method to include qualitative variables in linear models using dummy variables, fuzzy regression, and neural networks, improving prediction accuracy.

## Contribution

The novel contribution is combining dummy variables, fuzzy regression, and MLFFNN to enhance qualitative predictor integration in linear models.

## Key findings

- The multiple linear regression model achieved an R-squared of 0.95 and MSE of 9.97, indicating a strong fit.
- Fuzzy regression outperformed linear regression in predictability when comparing actual and predicted values.
- MLFFNN reduced the MSE to 0.362, showing improved prediction precision.

## Abstract

Background

In applied sciences, statistical models are pivotal for uncovering relationships in complex datasets. The applied linear model establishes associative links between variables. While qualitative predictors are essential, their integration into linear models poses challenges. The dummy variable approach transforms qualitative variables into binary ones for regression analysis. Multilayer Feedforward Neural Networks (MLFFNN) offer validation of regression models, and fuzzy regression offers alternative methods to address the ambiguity of qualitative predictors. This study aims to enhance the integration of qualitative predictors in applied linear models through statistical methodologies.

Material and methods

This study design involves the transformation of qualitative predictors into dummy variables, the bootstrapping technique to improve the parameter estimates, the Multilayer Feedforward Neural Network, and fuzzy regression. This study uses the programming language R as an analysis tool.

Results

The multiple linear regression model demonstrates precision and a significant fit (p<0.05), with an R-squared value of 0.95 and mean square error (MSE) of 9.97. Comparing actual and predicted values, fuzzy regression exhibits superior predictability over linear regression. The MLFFNN yields a reduced MSE net of 0.362, indicating enhanced prediction precision for derived models.

Conclusion

This study presents a precise methodology for integrating qualitative variables into linear regression, supported by the combination of specific statistical methodologies to enhance predictive modeling. By integrating fuzzy linear regression, MLFF neural networks, and bootstrapping, the proposed technique emerges as the most effective approach for modeling and prediction. These findings underscore the efficacy of this method in seamlessly integrating qualitative variables into linear models, ultimately enhancing accuracy and prediction capabilities.