Question

What are differences between in precision analysis for a calibration fit in comparison to a standard scatter analysis?

Describe the theory behind linear regression analysis.

Answer 1

Linear Regression

Linear regression is a basic and commonly used type of predictive analysis. The overall idea of regression is to examine two things(1) does a set of predictor variables do a good job in predicting an outcome (dependent) variable?
(2) Which variables in particular are significant predictors of the outcome variable and in what way do they–indicated by the magnitude and sign of the beta estimates–impact the outcome variable? These regression estimates are used to explain the relationship between one dependent variable and one or more independent variables. The simplest form of the regression equation with one dependent and one independent variable is defined by the formula y = c + b*x, where y = estimated dependent variable score, c = constant, b = regression coefficient, and x = score on the independent variable.

In statistics linear regression is a linear approach to modeling the relationship between a scalar response and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression.This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models.[ Most commonly, the conditional mean of the response given the values of the explanatory variables is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.

Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.