Statistical Regression Analysis

Regression is a generic term for all methods attempting to fit a model to observed data in order to quantify the relationship between two groups of variables. The fitted model may then be used either to merely describe the relationship between the two groups of variables, or to predict new values.

General Notation and Definitions

The two data matrices involved in regression are usually denoted X and Y, and the purpose of regression is to build a model Y = f(X). Such a model tries to explain, or predict, the variations in the Y-variable(s) from the variations in the X-variable(s). The link between X and Y is achieved through a common set of samples for which both X- and Y-values have been collected.

Names for X and Y

The X- and Y-variables can be denoted with a variety of terms, according to the particular context (or culture). The most common ones are listed in the table below:

Usual names for X- and Y-variables

 Context X Y General Predictors Responses Multiple Linear Regression (MLR) Independent Variables Dependent Variables Designed Data Factors, Design Variables Responses Spectroscopy Spectra Constituents

Univariate vs. Multivariate Regression

Univariate regression uses a single predictor, which is often not sufficient to model a property precisely. Multivariate regression takes into account several predictive variables simultaneously, thus modeling the property of interest with more accuracy.

How and why to use a Statistical Regression Model?

Building a regression model involves collecting predictor and response values for common samples,
and then fitting a predefined mathematical relationship to the collected data.

Statistical Regression Analysis

For example, in analytical chemistry, spectroscopic measurements are made on solutions with known concentrations of a given compound. Regression is then used to relate concentration to spectrum. Once you have built a regression model, you can predict the unknown concentration for new samples, using the spectroscopic measurements as predictors. The advantage is obvious if the concentration is difficult or expensive to measure directly.

More generally, classical indications for regression as a predictive tool could be the following:

1. Every time you wish to use cheap, easy-to-perform measurements as a substitute for more expensive or time-consuming ones;
2. When you want to build a response surface model from the results of some experimental design, i.e. describe precisely the response levels according to the values of a few controlled factors.
 All-In-One Multivariate Data Analysis (MVA) and Design of Experiments (DoE) Package with Statistical Regression Analysis

Verticals in Statistical Regression Analysis

A Snapshot of Industry Applications of The Unscrambler® Suite of Software Products
The Unscrambler® Suite of Software Products (The Unscrambler® X, Unscrambler Predictor & Unscrambler Classifier and Unscrambler Optimizer) are industry leading standards used in a variety of industries. Select an industry from below to read more on how the software products are useful to each industry, with actual case studies included.

Tailor-made for advanced multivariate statistical modeling, prediction, and classification, The Unscrambler® X Software’s wizard-driven design of experiments functionality completes this all-in-one, powerhouse analytical package, enabling users to delve deep into the value embedded within their data and derive models and results that add tremendous value in R&D efficiency, time and cost savings to a wide array of growing client installations.

 Food and Beverage Agriculture Oil and Gas Chemical Manufacturing Polymer and Paper Pharmaceutical and Biotechnology

Related Training

CAMO Software provides professional training in multivariate data analysis, sensometrics, statistical regression analysis, simple linear regression, Linear Regression, K-Means Clustering and chemometrics across United States & Canada, Europe, South America, Africa, Australia and Asia through our panel of chemometric experts, spectroscopy professionals, sensometrics instructors and Multivariate Data Analysis Trainers.