Linear Regression

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

Naming the Variables.  There are many names for a regression’s dependent variable.  It may be called an outcome variable, criterion variable, endogenous variable, or regressand.  The independent variables can be called exogenous variables, predictor variables, or regressors.

Three major uses for regression analysis are (1) determining the strength of predictors, (2) forecasting an effect, and (3) trend forecasting.

Discover How We Assist to Edit Your Dissertation Chapters

Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.

Schedule Your FREE Consultation
with a Dissertation Expert Today
Bring dissertation editing expertise to chapters 1-5 in timely manner.
Track all changes, then work with you to bring about scholarly writing.
Ongoing support to address committee feedback, reducing revisions.

First, the regression might be used to identify the strength of the effect that the independent variable(s) have on a dependent variable.  Typical questions are what is the strength of relationship between dose and effect, sales and marketing spending, or age and income.

Second, it can be used to forecast effects or impact of changes.  That is, the regression analysis helps us to understand how much the dependent variable changes with a change in one or more independent variables.  A typical question is, “how much additional sales income do I get for each additional $1000 spent on marketing?”

Third, regression analysis predicts trends and future values.  The regression analysis can be used to get point estimates.  A typical question is, “what will the price of gold be in 6 months?”

Types of Linear Regression

Simple linear regression
1 dependent variable (interval or ratio), 1 independent variable (interval or ratio or dichotomous)

Multiple linear regression
1 dependent variable (interval or ratio) , 2+ independent variables (interval or ratio or dichotomous)

Logistic regression
1 dependent variable (dichotomous), 2+ independent variable(s) (interval or ratio or dichotomous)

Ordinal regression
1 dependent variable (ordinal), 1+ independent variable(s) (nominal or dichotomous)

Multinomial regression
1 dependent variable (nominal), 1+ independent variable(s) (interval or ratio or dichotomous)

Discriminant analysis
1 dependent variable (nominal), 1+ independent variable(s) (interval or ratio)

When selecting the model for the analysis, an important consideration is model fitting.  Adding independent variables to a linear regression model will always increase the explained variance of the model (typically expressed as R2).  However, overfitting can occur by adding too many variables to the model, which reduces model generalizability.  Occam’s razor describes the problem extremely well – a simple model is usually preferable to a more complex model.  Statistically, if a model includes a large number of variables, some of the variables will be statistically significant due to chance alone.

To Reference this Page: Statistics Solutions. (2013). What is Linear Regression . Retrieved from here.

Related Pages:

Assumptions of a Linear Regression

Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. The services that we offer include:

Data Analysis Plan

Edit your research questions and null/alternative hypotheses

Write your data analysis plan; specify specific statistics to address the research questions, the assumptions of the statistics, and justify why they are the appropriate statistics; provide references

Justify your sample size/power analysis, provide references

Explain your data analysis plan to you so you are comfortable and confident

Two hours of additional support with your statistician

Quantitative Results Section (Descriptive Statistics, Biva.

要查看或添加评论,请登录

Sejal Baweja的更多文章

  • Team Unity

    Team Unity

    One of the most basic and foundational aspects of team building is the concept of team cohesion. It’s the motivating…

  • Random Forest

    Random Forest

    Random forest is a commonly-used machine learning algorithm trademarked by Leo Breiman and Adele Cutler, which combines…

  • Decision Tree

    Decision Tree

    A decision tree is a non-parametric supervised learning algorithm, which is utilized for both classification and…

  • Hibernate

    Hibernate

    Hibernate is an open source?object relational mapping (ORM)?tool that provides a?framework?to…

  • YARN

    YARN

    YARN stands for “Yet Another Resource Negotiator“. It was introduced in Hadoop 2.

  • Medical Coding

    Medical Coding

    Medical coding is the transformation of healthcare diagnosis, procedures, medical services, and equipment into…

  • CCAR

    CCAR

    Comprehensive Capital Analysis and Review (CCAR)The Comprehensive Capital Analysis and Review is a stress-test regime…

  • Logistic Regression

    Logistic Regression

    Logistic regression is one of the most popular Machine Learning algorithms, which comes under the Supervised Learning…

  • Model Validation

    Model Validation

    Model validation?is the process that is carried out after?Model Training?where the trained model is evaluated with a…

  • Node.js

    Node.js

    Node.js is an open-source, cross-platform JavaScript runtime environment and library for running web applications…

社区洞察

其他会员也浏览了