Start Date: 09/15/2019
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/linear-regression-model
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.This short module introduces basics about Coursera specializations and courses in general, this specialization: Statistics with R, and this course: Linear Regression and Modeling. Please take several minutes to browse them through. Thanks for joining us in this course!
This course introduces simple and multiple linear regression models. These models allow you to asses
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Linear regression | In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable "y" and one or more explanatory variables (or independent variables) denoted "X". 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.) |
Linear regression | The very simplest case of a single scalar predictor variable "x" and a single scalar response variable "y" is known as "simple linear regression". The extension to multiple and/or vector-valued predictor variables (denoted with a capital "X") is known as "multiple linear regression", also known as "multivariable linear regression". Nearly all real-world regression models involve multiple predictors, and basic descriptions of linear regression are often phrased in terms of the multiple regression model. Note, however, that in these cases the response variable "y" is still a scalar. Another term "multivariate linear regression" refers to cases where "y" is a vector, i.e., the same as "general linear regression". |
Regression analysis | In linear regression, the model specification is that the dependent variable, formula_2 is a linear combination of the "parameters" (but need not be linear in the "independent variables"). For example, in simple linear regression for modeling formula_3 data points there is one independent variable: formula_4, and two parameters, formula_5 and formula_6: |
Linear regression | 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 "y" given the value of "X" is assumed to be an affine function of "X"; less commonly, 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, linear regression 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 | Some of the more common estimation techniques for linear regression are summarized below. |
Linear regression | The capital asset pricing model uses linear regression as well as the concept of beta for analyzing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets. |
Linear regression | Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the "lack of fit" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression ("L"-norm penalty) and lasso ("L"-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms "least squares" and "linear model" are closely linked, they are not synonymous. |
Logistic regression | The basic idea of logistic regression is to use the mechanism already developed for linear regression by modeling the probability "p" using a linear predictor function, i.e. a linear combination of the explanatory variables and a set of regression coefficients that are specific to the model at hand but the same for all trials. The linear predictor function formula_97 for a particular data point "i" is written as: |
Linear regression | The following are the major assumptions made by standard linear regression models with standard estimation techniques (e.g. ordinary least squares): |
Linear regression | Linear regression has many practical uses. Most applications fall into one of the following two broad categories: |
Bayesian linear regression | In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of prior distribution is assumed, explicit results are available for the posterior probability distributions of the model's parameters. |
Bayesian multivariate linear regression | In statistics, Bayesian multivariate linear regression is a |
Linear regression | The general linear model considers the situation when the response variable "Y" is not a scalar but a vector. Conditional linearity of "E"("y"|"x") = "Bx" is still assumed, with a matrix "B" replacing the vector "β" of the classical linear regression model. Multivariate analogues of Ordinary Least-Squares (OLS) and Generalized Least-Squares (GLS) have been developed. "General linear models" are also called "multivariate linear models". These are not the same as multivariable linear models (also called "multiple linear models"). |
Linear regression | 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 | In statistics and numerical analysis, the problem of numerical methods for linear least squares is an important one because linear regression models are one of the most important types of model, both as formal statistical models and for exploration of data sets. The majority of statistical computer packages contain facilities for regression analysis that make use of linear least squares computations. Hence it is appropriate that considerable effort has been devoted to the task of ensuring that these computations are undertaken efficiently and with due regard to numerical precision. |
Linear regression | Numerous extensions of linear regression have been developed, which allow some or all of the assumptions underlying the basic model to be relaxed. |
Linear regression | Linear regression is widely used in biological, behavioral and social sciences to describe possible relationships between variables. It ranks as one of the most important tools used in these disciplines. |
Linear regression | where "β" determines the initial velocity of the ball, "β" is proportional to the standard gravity, and "ε" is due to measurement errors. Linear regression can be used to estimate the values of "β" and "β" from the measured data. This model is non-linear in the time variable, but it is linear in the parameters "β" and "β"; if we take regressors x = ("x", "x") = ("t", "t"), the model takes on the standard form |
Bayesian linear regression | A similar analysis can be performed for the general case of the multivariate regression and part of this provides for Bayesian estimation of covariance matrices: see Bayesian multivariate linear regression. |
Simple linear regression | In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the "x" and "y" coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variables. |