Development of prediction model through linear multiple regression for the prediction and analysis of the GSM of embroidered fabric
Authors: Dutta Anirban , Chatterjee Biswapati 
Published: January 2020

Purpose
The purpose of this paper is to establish the regression equation based upon a set of samples prepared through structured design of experiment and form a prediction model for prediction of the areal density gram per square meter (GSM) of the embroidered fabrics and study the influence of basic input parameters.

Design/methodology/approach
Embroidery samples are prepared taking input parameters as GSM of the base fabric, linear density of the embroidery thread and stitch density of the embroidery design. Three levels of values are identified for each of the input parameters. Taguchi and Box-Behnken experiment design principles are used to prepare two sets of samples. Linear multiple regression is used to determine the prediction equations based upon each of the two sets and the combined set as well. Prediction equations are statistically verified for the prediction accuracy. Also, surface curves are prepared to study the influence of embroidery parameters on the GSM.

Findings
It is found that all the three prediction models developed in this study can predict with a very satisfactory level of accuracy. However, the regression equation based upon the data set prepared according to Taguchi experiment design is emerged as the prediction model with highest level of prediction accuracy. Corresponding equation coefficients and several three-dimensional surface curves are used to study the influence of embroidery parameters and it is found that the stitch density is the most influential input parameter followed by stitch length and the GSM of base fabric.

Research limitations/implications
This can be used to assess the GSM of embroidered fabrics before starting the actual embroidery process. So, this model can help the embroidery designers significantly to pre-estimate the GSM of the embroidered fabrics and select the design parameters accordingly. Also, this model can be a useful tool for estimation of thread consumption and thread cost in embroidery.

Practical implications
The input parameters used here are very basic parameters related to design and materials, which can be easily available. And also, a simple linear multiple regression is used to make the prediction equation simple and easy to use. So, this model can help the embroidery designers or garment designers to select/adjust the embroidery parameters and thread parameters accordingly in the planning and designing stage itself to ensure that the GSM of embroidered fabrics remains within desirable range. Also, this prediction model developed hereby may be a very useful tool for estimation of the consumption and cost of embroidery threads.

Originality/value
This paper presents a very fundamental study to reveal the effect of embroidery parameters on the GSM, through development of regression equations. It can help future researchers in optimizations of input parameters and forming a technical guideline for the embroidery designers for selection of the design parameters for a desired GSM of embroidered fabric.