Start Date: 07/05/2020
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/linear-regression-r-public-health
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.Welcome to Linear Regression in R for Public Health! Public Health has been defined as “the art and science of preventing disease, prolonging life and promoting health through the organized efforts of society”. Knowing what causes disease and what makes it worse are clearly vital parts of this. This requires the development of statistical models that describe how patient and environmental factors affect our chances of getting ill. This course will show you how to create such models from scratch, beginning with introducing you to the concept of correlation and linear regression before walking you through importing and examining your data, and then showing you how to fit models. Using the example of respiratory disease, these models will describe how patient and other factors affect outcomes such as lung function. Linear regression is one of a family of regression models, and the other courses in this series will cover two further members. Regression models have many things in common with each other, though the mathematical details differ. This course will show you how to prepare the data, assess how well the model fits the data, and test its underlying assumptions – vital tasks with any type of regression. You will use the free and versatile software package R, used by statisticians and data scientists in academia, governments and industry worldwide.
INTRODUCTION TO LINEAR REGRESSION
Linear Regression in R
Multiple Regression and Interaction
MODEL BUILDING
Linear Regression in R for Public Health Regression in Public Health is a hands-on, data-driven course on linear regression in public health. Through this course you will learn how to construct linear models in R and how to use regression weights and measures. You will use R package to construct linear models and how to use regression weights and measures. In the course you will also learn about the basic methods used to construct linear models and how to use regression measures. You will also learn about regression error measures, standard errors, diagnostics, and how to construct diagnostic models. You will also learn about the basic methods used to construct diagnostic models.Linear Regression for Public Health Wrap Up Machine Learning Machine learning is the science and art of using computers to make things happen. Machine learning is the science of what computers can do if given enough resources, without too much effort. It is the science of how to use the computer science skills that one acquires in a relatively short period of time to realize real breakthroughs. The course also extends beyond the boundaries of computer science and is focused on the applications of machine learning, as the students apply the computer science knowledge gained to them. This course will cover the whole of the supervised learning and reinforcement learning processes of computer science, including the applications and challenges of supervised learning in public health, and the use of machine learning in biomedical and industrial predictive modeling. The course concepts and lectures are
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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". |
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. |
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. |
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. |
Bayesian multivariate linear regression | In statistics, Bayesian multivariate linear regression is a |
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. |
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. |
Logistic regression | Discrimination in linear regression models is generally measured using R. Since this has no direct analog in logistic regression, various methods including the following can be used instead. |
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 | 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. |
Bayesian linear regression | Consider a standard linear regression problem, in which for formula_1 we specify the conditional distribution of "formula_2" given a "formula_3" predictor vector "formula_4": |
Segmented regression | Segmented linear regression is segmented regression whereby the relations in the intervals are obtained by linear regression. |
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. |
Logistic regression | The basic setup of logistic regression is the same as for standard linear regression. |
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 | 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"). |