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    Linear Regression

    Linear regression is an approach to model the relationship between a scalar dependent variable y and one or more explanatory variable denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, it is called multiple linear regressions. In linear regression, data is modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models.

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

    Standard linear regression models with standard estimation techniques make a number of assumptions about the predictor variables, the response variables and their relationships. Numerous extensions have been developed that allow each of these assumptions to be relaxed and sometimes entirely eliminated. Numerous extensions of linear regression have been developed, which allow some or all of the assumptions underlying the basic model to be relaxed.  

    A large number of procedures have been developed for parameter estimation and inference in linear regression. These methods differ in computational simplicity of algorithms, presence of a closed-form solution, robustness with respect to heavy-tailed distributions, and theoretical assumptions needed to validate desirable statistical properties such as consistency and asymptotic efficiency.

    Linear regression has many application including biological, behavioral and social sciences. It is used to describe possible relationships between variables. Its ranked as one of the most important tools used in these disciplines. 

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    BrainMass Categories within Linear Regression

    Simple Linear Regression

    Solutions: 30

    Simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable.

    Ordinary Least Squares

    Solutions: 13

    Ordinary least squares is a method for estimating the unknown parameters in a linear regression model.

    General Linear Model

    Solutions: 25

    The generalized linear model is a flexible generalization of ordinary linear regression that allows for response variables that have other than a normal distribution.

    Bayesian Regression

    Solutions: 0

    Bayesian linear regression is an approach in which the statistical analysis is undertaken within the context of Bayesian inference.

    BrainMass Solutions Available for Instant Download

    Linear Regression Analysis Prediction

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    Multiple Regression Analysis

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    Run a Multiple Linear Regression

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    linear regression and chi sq

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    steps on performing simple regression

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    Regression Analysis: Songs

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    Linear and Exponential Relation

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    Correlation and Simple Linear Regression Using SPSS

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    Regression Model Vs. Computerized Regression Routine

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    Regression Model for The Undrained Strength of Some Thawed Permafrost Soils

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    Hypothesis Testing and Linear Regression Analysis

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    Statistics Problem Set: Regression and Linear Programming

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    Linear Regression and Square Residuals

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    Solve: Line of Best Fit

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    Simple Linear Regression Test

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    Conducting a linear regression analysis

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    Forecasting: Develop a Linear Regression Model

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    Application of Linear Regression

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    Cost Accounting: Favata, Trustme Vehicle, Konrade's Engine, Merriamn Company

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    Adriana Corporation Method of estimating costs: Simple Regression

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    Discuss: Statistical Variation and Regression Methods

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    Linear Regression of Monthly Electrical Usage

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    Data Analysis on Soft Drink Study

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    Linear Programming Problem for Print Media Advertising (PMA)

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