Regression analysis is a modeling technique used to analyze the relationship between a continuous dependent variable Y and one or more independent variables X1, X2, X3…… Multiple regression has the word “multiple” in it because it evaluates many independent variables as against the simple linear regression that evaluates only one variable X1.

We have seen what simple linear regression is in detail earlier. In essence, we defined simple linear regression as a way of analyzing and defining the relationship between variables using the Least Squares Method with two constraints: 1) only two variables are considered at a time and 2) the relationship is assumed to be a linear relationship. We have also seen how to interpret regression output earlier. We now turn our attention to multiple regression.

Multiple regression is essentially simple regression without the constraint that only two variables are considered at a time! Multiple regression considers the impact more than one variable (independent variable) has on the variable of interest or the dependent variable.

Multiple regression is a modeling technique with a wide range of applications. It is one of the most widely used modeling techniques in the business world. The insights that multiple regression analysis can provide in almost any business situation and the availability of relevant tools such as spreadsheets and other specialized software that provide regression output make it a very valuable technique to master. The application of regression analysis can be classified generally into analysis of data and prediction of variables. Other regression analysis techniques *include but are not limited to **simple linear regression modeling, curvilinear regression models, polynomial regression models, discriminant analysis models……….(a really long list!). *

Graduate Tutor’s Statistics Tutor Group is well equipped to tutor you in the various multiple regression analysis models and techniques. Work with our tutors online and learn the concepts underlying the multiple regression analysis techniques. Apply the multiple regression analysis technique on sample data from a wide variety of industries to consolidate and reinforce what you learn. Use commonly available multiple regression analysis tools including Microsoft Excel or R.

A sample of the multiple regression analysis topics, methods and tools you can learn with Graduate Tutor’s Statistics Tutor Group is outlined below. Please email us if you do not find the multiple regression analysis topic you are looking for below and we will be happy to assist you in finding what you need.

### Multiple Regression Analysis Topics

- Introduction to Multiple Regression Analysis
- Examples of Multiple Regression Applications in Business
- Types of Regression Models
- Defining “Best Fit” of a Multiple Regression Analysis Model
- Solving the Multiple Regression Analysis Model Using Solver
- Solving the Regression Model Using the Regression Tool in Microsoft Excel
- Evaluating the Fit of the Multiple Regression Analysis Model
- Interpreting the R Statistic in a Multiple Regression Model Output
- Making Predictions using the Multiple Regression Model
- Interpreting the Standard Error in the Multiple Regression Model Output
- Prediction Intervals for New Values of Y using the Multiple Regression Model
- Confidence Intervals for Mean Values of Y in the Multiple Regression Model
- Extrapolation
- Statistical Tests for Population Parameters
- Assumptions for the Statistical Tests
- Polynomial Regression Models

Other operations research and statistics topics that Graduate Tutor’s Statistics Tutor Group tutor in include:

Simulation using Crystal Ball Software

Financial Modeling using Microsoft Excel

## Multiple Regression code in R

If you are looking for R code to run a multiple regression analysis with all the variables, lm(y~., data) is what you need. Contrast it with the R code required for simple linear regression: lm(y∼x, data) . For easier use, define it as a variable. For example:

RegMod <- lm(y∼., data=”file”)

And to see the summary, run the following code in R:

summary(RegMod)

This will make it easier for you to look at the output. The above code works if you are looking to use all the variables you have. If you are looking to use only a few of those variables, you can select the variables of interest using their column heading and ‘+’ to add more. The R code for a data based where you would like to use Revenues as the dependent variable and Ad_spend, Inflation and Price as independent variables would look as follows.

RegMod2<-lm(Revenues~Ad_spend+Inflation+Price, data=’file’)

And to see the summary, run the following code in R:

summary(RegMod2)

## What after Multiple Regression Analysis?

Now that you have the regression output in R, you can learn more about interpreting the regression output here. Enjoy multiple linear regression using R!