Regression In R | R Multiple Regression - r - learn r - r programming
- 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
- 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