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\

R – Logistic Regression

The Logistic Regression is a regression model in which the response variable (dependent variable) has categorical values such as True/False or 0/1. It actually measures the probability of a binary response as the value of response variable based on the mathematical equation relating it with the predictor variables.
The general mathematical equation for logistic regression is −
y = 1/(1+e^-(a+b1x1+b2x2+b3x3+…))
Following is the description of the parameters used −
• y is the response variable.
• x is the predictor variable.
• a and b are the coefficients which are numeric constants.
The function used to create the regression model is the glm() function.
Syntax
The basic syntax for glm() function in logistic regression is −
glm(formula,data,family)
Following is the description of the parameters used −
• formula is the symbol presenting the relationship between the variables.
• data is the data set giving the values of these variables.
• family is R object to specify the details of the model. It’s value is binomial for logistic regression.
Example
The in-built data set “mtcars” describes different models of a car with their various engine specifications. In “mtcars” data set, the transmission mode (automatic or manual) is described by the column am which is a binary value (0 or 1). We can create a logistic regression model between the columns “am” and 3 other columns – hp, wt and cyl.

# Select some columns form mtcars.
input <- mtcars[,c("am","cyl","hp","wt")]

print(head(input))
When we execute the above code, it produces the following result −
am cyl hp wt
Mazda RX4 1 6 110 2.620
Mazda RX4 Wag 1 6 110 2.875
Datsun 710 1 4 93 2.320
Hornet 4 Drive 0 6 110 3.215
Hornet Sportabout 0 8 175 3.440
Valiant 0 6 105 3.460

Create Regression Model

We use the glm() function to create the regression model and get its summary for analysis.

input <- mtcars[,c("am","cyl","hp","wt")]
am.data = glm(formula = am ~ cyl + hp + wt, data = input, family = binomial)

print(summary(am.data))
When we execute the above code, it produces the following result −
Call:
glm(formula = am ~ cyl + hp + wt, family = binomial, data = input)

Deviance Residuals: 
Min 1Q Median 3Q Max 
-2.17272 -0.14907 -0.01464 0.14116 1.27641

Coefficients:
Estimate Std. Error z value Pr(>|z|) 
(Intercept) 19.70288 8.11637 2.428 0.0152 *
cyl 0.48760 1.07162 0.455 0.6491 
hp 0.03259 0.01886 1.728 0.0840 .
wt -9.14947 4.15332 -2.203 0.0276 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 43.2297 on 31 degrees of freedom
Residual deviance: 9.8415 on 28 degrees of freedom
AIC: 17.841

Number of Fisher Scoring iterations: 8

Conclusion

In the summary as the p-value in the last column is more than 0.05 for the variables “cyl” and “hp”, we consider them to be insignificant in contributing to the value of the variable “am”. Only weight (wt) impacts the “am” value in this regression model.
So, this brings us to the end of blog. This Tecklearn ‘Multiple and Logistic Regression in R’ blog helps you with commonly asked questions if you are looking out for a job in Data Science. If you wish to learn R Language and build a career in Data Science domain, then check out our interactive, Data Science using R Language Training, that comes with 24*7 support to guide you throughout your learning period. Please find the link for course details:

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