HomeDirectory of Statistical Analyses What is 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.
- 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:
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, Bivariate and Multivariate Analyses, Structural Equation Modeling, Path analysis, HLM, Cluster Analysis)
Clean and code dataset
Conduct descriptive statistics (i.e., mean, standard deviation, frequency and percent, as appropriate)
Conduct analyses to examine each of your research questions
Write-up results
Provide APA 6th edition tables and figures
Explain chapter 4 findings
Ongoing support for entire results chapter statistics
Please call 727-442-4290 to request a quote based on the specifics of your research, schedule using the calendar on this page, or email [emailprotected]
