## (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.

### Syntax

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.

## Example

### 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")] print(head(input))

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. print(model) # Get the Intercept and coefficients as vector elements. cat("# # # # The Coefficient Values # # # ","n") a <- coef(model)[1] print(a) Xdisp <- coef(model)[2] Xhp <- coef(model)[3] Xwt <- coef(model)[4] print(Xdisp) print(Xhp) print(Xwt)

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

Call: lm(formula = mpg ~ disp + hp + wt, data = input) Coefficients: (Intercept) disp hp wt 37.105505 -0.000937 -0.031157 -3.800891 # # # # The Coefficient Values # # # (Intercept) 37.10551 disp -0.0009370091 hp -0.03115655 wt -3.800891

### 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 or 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

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.

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