Univariate regressio n 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. Building a regression model involves collecting predictor and response values for common samples, and then fitting a predefined mathematical relationship to the collected data.
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.
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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:.
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MLR is a method for relating the variations in a response variable Y-variable to the variations of several predictors X-variables , with explanatory or predictive purposes. An important assumption for the method is that the X-variables are linearly independent, i. When the X-variables carry common information, problems can arise due to exact or approximate collinearity. Multiple Linear Regression MLR is a well-known statistical method based on ordinary least squares regression.
This operation involves a matrix inversion, which leads to collinearity problems if the variables are not linearly independent.
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Incidentally, this is the reason why the predictors are called independent variables in MLR; the ability to vary independently of each other is a crucial requirement to variables used as predictors with this method. MLR also requires more samples than predictors or the matrix cannot be inverted. No missing values are accepted. Interpretation of the relationship between X-data and Y-data is then simplified as this relationship is concentrated on the smallest possible number of components. By plotting the first PLS components one can view main associations between X-variables and Y-variables, and also interrelationships within X-data and within Y-data.
Multivariate statistical analysis
A PLS 2 Regression overview. A method for relating the variations in one or several response variables Y-variables arranged in a 2-D table to the variations of several predictors arranged in a 3-D table Primary and Secondary X-variables , with explanatory or predictive purposes. PCR is a method for relating the variations in a response variable Y-variable to the variations of several predictors X-variables , with explanatory or predictive purposes.
This method performs particularly well when the various X-variables express common information, i. Principal Component Regression is a two-step method.
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First, a Principal Component Analysis is carried out on the X-variables. The principal components are then used as predictors in a Multiple Linear Regression.
Contrary to regression, which predicts the values of one or several quantitative variables, classification is useful when the response is, a category variable that can be interpreted in terms of several classes to which a sample may belong. The main goal of classification is to reliably assign new samples to existing classes in a given population.
Heavy metal soil contamination is associated with potential toxicity to humans or ecotoxicity. Scholars have increasingly used a combination of geographical information science GIS with geostatistical and multivariate statistical analysis techniques to examine the spatial distribution of heavy metals in soils at a regional scale.
A review of such studies showed that most soil sampling programs were based on grid patterns and composite sampling methodologies. Many programs intended to characterize various soil types and land use types. Once a network component is infected by viruses, worms, or became a target of network attacks, its operational state shifts from normal to abnormal state. Online monitoring mechanism can collect important aspects of network traffic and host data CPU utilization, memory usage, etc.
Aspects of Multivariate Statistical Analysis in Geology
In this paper, we develop an online multivariate analysis algorithm to analyze the behaviors of system resources and network protocols in order to proactively detect network attacks. We have validated an algorithm and showed how it can proactively detect accurately well-known attacks such as distributed denial of service, SQL slammer worm, and email spam attacks.
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