Linear regression is an approach to modeling the relationship between a scalar variable y and one or more variables denoted X. In linear regression, models of the unknown parameters are estimated from the data using linear functions. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis,it focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, 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.
Linear regression has many practical uses. Most applications of linear regression fall into one of the following two broad categories:
- If the goal is prediction, or forecasting, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y.
- Given a variable y and a number of variables X1, ..., Xp that may be related to y, then linear regression analysis can be applied to quantify the strength of the relationship between yXj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y, thus once one of them is known, the others are no longer informative and the
QUADRATIC REGRESSION
Quadratic regression models are often used in economics areas such as utility function , forecasting, cost-befit analysis, etc. This JavaScript provides parabola regression model. This site also presents useful information about the characteristics of the fitted quadratic function.
Quadratic regression models are often used in economics areas such as utility function , forecasting, cost-befit analysis, etc. This JavaScript provides parabola regression model. This site also presents useful information about the characteristics of the fitted quadratic function.
Prior to using this JavaScript it is necessary to construct the scatter-diagram for your data.
If by visual inspection of the scatter-diagram, you cannot reject a "parabola shape", then you may use this JavaScript. Otherwise, visual inspection of the scatter-diagram enables you to determine what degree of polynomial regression models is the most appropriate for fitting to your data.
In order to solve problems involving quadratic regression, it is necessary to:
- know how to enter data into your graphing calculator for completing modeling problems
- know how to solve quadratic equations
- know how to calculate a quadratic equation that best fits a set of given data
- write and solve an equation for the problem
BEER'S LAW AND LINEAR REGRESSION
TITRATION CURVE
LINE BEST FIT
QUADRATIC REGRESSION
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