Statistics with R for Business Analysts – Multiple Regression

(R Tutorials for Citizen Data Scientist)

Statistics with R for Business Analysts – Multiple Regression

Multiple regression is an extension of linear regression into relationship between more than two variables. In simple linear relation we have one predictor and one response variable, but in multiple regression we have more than one predictor variable and one response variable.

The general mathematical equation for multiple regression is −

y = a + b1x1 + b2x2 +...bnxn

Following is the description of the parameters used −

  • y is the response variable.
  • a, b1, b2…bn are the coefficients.
  • x1, x2, …xn are the predictor variables.


We create the regression model using the lm() function in R. The model determines the value of the coefficients using the input data. Next we can predict the value of the response variable for a given set of predictor variables using these coefficients.

lm() Function

This function creates the relationship model between the predictor and the response variable.


The basic syntax for lm() function in multiple regression is −

lm(y ~ x1+x2+x3...,data)

Following is the description of the parameters used −

  • formula is a symbol presenting the relation between the response variable and predictor variables.
  • data is the vector on which the formula will be applied.



Input Data

Consider the data set “mtcars” available in the R environment. It gives a comparison between different car models in terms of mileage per gallon (mpg), cylinder displacement(“disp”), horse power(“hp”), weight of the car(“wt”) and some more parameters.

The goal of the model is to establish the relationship between “mpg” as a response variable with “disp”,”hp” and “wt” as predictor variables. We create a subset of these variables from the mtcars data set for this purpose.

input <- mtcars[,c("mpg","disp","hp","wt")]

When we execute the above code, it produces the following result −

                   mpg   disp   hp    wt
Mazda RX4          21.0  160    110   2.620
Mazda RX4 Wag      21.0  160    110   2.875
Datsun 710         22.8  108     93   2.320
Hornet 4 Drive     21.4  258    110   3.215
Hornet Sportabout  18.7  360    175   3.440
Valiant            18.1  225    105   3.460

Create Relationship Model & get the Coefficients

input <- mtcars[,c("mpg","disp","hp","wt")]

# Create the relationship model.
model <- lm(mpg~disp+hp+wt, data = input)

# Show the model.

# Get the Intercept and coefficients as vector elements.
cat("# # # # The Coefficient Values # # # ","n")

a <- coef(model)[1]

Xdisp <- coef(model)[2]
Xhp <- coef(model)[3]
Xwt <- coef(model)[4]


When we execute the above code, it produces the following result −

lm(formula = mpg ~ disp + hp + wt, data = input)

(Intercept)         disp           hp           wt  
  37.105505      -0.000937        -0.031157    -3.800891  

# # # # The Coefficient Values # # # 

Create Equation for Regression Model

Based on the above intercept and coefficient values, we create the mathematical equation.

Y = a+Xdisp.x1+Xhp.x2+Xwt.x3
Y = 37.15+(-0.000937)*x1+(-0.0311)*x2+(-3.8008)*x3

Apply Equation for predicting New Values

We can use the regression equation created above to predict the mileage when a new set of values for displacement, horse power and weight is provided.

For a car with disp = 221, hp = 102 and wt = 2.91 the predicted mileage is −

Y = 37.15+(-0.000937)*221+(-0.0311)*102+(-3.8008)*2.91 = 22.7104


How to summarize correlation coefficients in R | Jupyter Notebook | R Data Science for beginners


Statistics with R for Business Analysts – Multiple Regression

Personal Career & Learning Guide for Data Analyst, Data Engineer and Data Scientist

Applied Machine Learning & Data Science Projects and Coding Recipes for Beginners

A list of FREE programming examples together with eTutorials & eBooks @ SETScholars

95% Discount on “Projects & Recipes, tutorials, ebooks”

Projects and Coding Recipes, eTutorials and eBooks: The best All-in-One resources for Data Analyst, Data Scientist, Machine Learning Engineer and Software Developer

Topics included: Classification, Clustering, Regression, Forecasting, Algorithms, Data Structures, Data Analytics & Data Science, Deep Learning, Machine Learning, Programming Languages and Software Tools & Packages.
(Discount is valid for limited time only)

Disclaimer: The information and code presented within this recipe/tutorial is only for educational and coaching purposes for beginners and developers. Anyone can practice and apply the recipe/tutorial presented here, but the reader is taking full responsibility for his/her actions. The author (content curator) of this recipe (code / program) has made every effort to ensure the accuracy of the information was correct at time of publication. The author (content curator) does not assume and hereby disclaims any liability to any party for any loss, damage, or disruption caused by errors or omissions, whether such errors or omissions result from accident, negligence, or any other cause. The information presented here could also be found in public knowledge domains.

Learn by Coding: v-Tutorials on Applied Machine Learning and Data Science for Beginners

Please do not waste your valuable time by watching videos, rather use end-to-end (Python and R) recipes from Professional Data Scientists to practice coding, and land the most demandable jobs in the fields of Predictive analytics & AI (Machine Learning and Data Science).

The objective is to guide the developers & analysts to “Learn how to Code” for Applied AI using end-to-end coding solutions, and unlock the world of opportunities!