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Linear Model in R

Priya Pedamkar
Article byPriya Pedamkar

Updated March 24, 2023

Linear Model in R

Introduction to Linear Model in R

A statistical or mathematical model that is used to formulate a relationship between a dependent variable and single or multiple independent variables called as, linear model in R. The criteria is that the variables involved in the formation of model meet certain assumptions as necessary prerequisites prior model building and that the model has certain important elements as its parts, which are formula, data, subset, weights, method, model, offset etc. It is not necessary that all have to be used every time, but only those that are sufficient and essential in the given context.

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Advantages of Linear Model:

  • Helps us to understand the type and nature of the data.
  • Helps us to predict the data.
  • Helps us to make statistical inferences from data.

Now we will learn about linear regression basically it is a statistical method used to create these models. The main objective of this model is to explain the relationship between the dependent variable and the independent variable.

Syntax of Linear Model in R

Here is the syntax of the linear model in R which is given below.

Syntax:

lm(formula, data, subset, weights, na.action,
method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE,
singular.ok = TRUE,offset, ...)

Here are the parameters of the linear model which are explained below:

  • Formula: Here we have to enter the variables of our dataset, basically, those variables where we are planning to trace out whether any relationship exists between them or not. The format should be fixed like (Dependent variable ~ Independent variables). Eg (Distance ~ Speed), (Demand~Price), etc.
  • Data: It is used when we have to pass an optional list of data, data frame or environment.
  • Subset: It helps us to define the data when we have to use a subset of the observations.
  • Weights: It accepts only numeric vector or “NULL” command. If it is not null, “WLS (Weighted least squares)” is used with weights or if Null then OLS (ordinary least squares) is used.
  • Na.action: It will give the instruction of what should be done when the data points have NA values, like na.fail, na.omit, na.exclude, etc.
  • Method: It is used for fitting.
  • Model: It is a logical vector if it is TRUE the corresponding components of the fit are returned.
  • X: It is a logical vector if it is TRUE the corresponding components of the fit are returned.
  • Y: It is a logical vector if it is TRUE the corresponding components of the fit are returned.
  • qr: It is a logical vector if it is TRUE the corresponding components of the fit are returned.
  • ok: It is also a logical vector if it is FALSE then singular fits are the error.
  • Offset: It can be NULL, numerical vector or matrix. This is used to specify an a priori known component to be included in the linear predictor during fitting.

Types of Linear Model in R

Let’s now discuss different types of linear models which are as follows:

Types of Linear Models in R

1. Simple Linear Regression

This model helps us to explain a relationship between one dependent variable and one independent variable. With the help of it, we can also predict the data, by providing the input values. In general, the dependent variable is also known as the response variable, regressand, observed variable, responding variable, measured variable, explained variable, experimental variable, outcome variable, and/or output variable). And independent variable known as a controlled variable, regressors, explanatory variable, manipulated variable, exposure variable, and/or input variable. The equation for the simple linear regression model is:

Y = β1 + β2X + ϵ

Where β1 is an intercept, β2 is a slope and ϵ is an error term. We will use the “USArrest” data set.

Murder arrests (per 100,000) Assault arrests (per 100,000) Percent urban population Rape arrests (per 100,000)
Alabama 13.2 236 58 21.2
Alaska 10 263 48 44.5
Arizona 8.1 294 80 31
Arkansas 8.8 190 50 19.5
California 9 276 91 40.6
Colorado 7.9 204 78 38.7
Connecticut 3.3 110 77 11.1
Delaware 5.9 238 72 15.8
Florida 15.4 335 80 31.9
Georgia 17.4 211 60 25.8
Hawaii 5.3 46 83 20.2
Idaho 2.6 120 54 14.2
Illinois 10.4 249 83 24
Indiana 7.2 113 65 21
Iowa 2.2 56 57 11.3
Kansas 6 115 66 18
Kentucky 9.7 109 52 16.3
Louisiana 15.4 249 66 22.2
Maine 2.1 83 51 7.8
Maryland 11.3 300 67 27.8
Massachusetts 4.4 149 85 16.3
Michigan 12.1 255 74 35.1
Minnesota 2.7 72 66 14.9
Mississippi 16.1 259 44 17.1
Missouri 9 178 70 28.2
Montana 6 109 53 16.4
Nebraska 4.3 102 62 16.5
Nevada 12.2 252 81 46
New Hampshire 2.1 57 56 9.5
New Jersey 7.4 159 89 18.8
New Mexico 11.4 285 70 32.1
New York 11.1 254 86 26.1
North Carolina 13 337 45 16.1
North Dakota 0.8 45 44 7.3
Ohio 7.3 120 75 21.4
Oklahoma 6.6 151 68 20
Oregon 4.9 159 67 29.3
Pennsylvania 6.3 106 72 14.9
Rhode Island 3.4 174 87 8.3
South Carolina 14.4 279 48 22.5
South Dakota 3.8 86 45 12.8
Tennessee 13.2 188 59 26.9
Texas 12.7 201 80 25.5
Utah 3.2 120 80 22.9
Vermont 2.2 48 32 11.2
Virginia 8.5 156 63 20.7
Washington 4 145 73 26.2
West Virginia 5.7 81 39 9.3
Wisconsin 2.6 53 66 10.8
Wyoming 6.8 161 60 15.6

Now we will find the relationship between the Assault variable and the Urban population.

>dataset = USArrests
>Linear_relationship1 = lm(Assault~ UrbanPop, data=dataset)
> Linear_relationship

Simple Regression - Ex 1

Equation looks like:

Assault = β1 + β2(UrbanPop)

Now we have intercept and slope also, Assault = 73.08 + 1.49(UrbanPop). Here we have a linear model equation, we have to supply the inputs in the form of “UrbanPop”, and the model equation will automatically predict the value of “Assualt” for us. Let’s take another example of this model, now we will run this model on Murder variable and Urban Population variable.

>View(USArrests)
>Linear_relationship2= lm(Murder~ UrbanPop, data=dataset)

Linear Model in R - Ex 2

Equation looks like:

Murder = β1 + β2(UrbanPop)

Now we have intercept and slope also, Murder= 6.41594 + 0.02093(UrbanPop). Here we have a linear model equation, we have to supply the inputs in the form of “UrbanPop”, and the model equation will automatically predict the value of “Murder” for us.

2. Multiple Linear Regression

In this model, we will have one dependent variable and multiple independent variables. Multiple independent variables are used in this model to predict one dependent variable. Let’s take an example of this model. Here also we will use the “USArrests” dataset.

Dependent variable = Urban Population
Independent variable = Assault, Rape, and Murder

>Multiple_Linear_Relationship = lm(UrbanPop~ Assault+Rape+Murder , data=dataset)
>Multiple_Linear_Relationship

Multiple Regression - Ex 3

The equation looks like:

UrbanPop = β1 + β2(Assault) + β3(Rape) + β4(Murder)

Now we have intercept and slope also, UrbanPop= 52.8419 + 0.0519(Assault) + 0.6984(Rape) – 1.4115(Murder)

Conclusion

The linear model generally works around two parameters: one is slope which is often known as the rate of change and the other one is intercept which is basically an initial value. These models are very common in use when we are dealing with numeric data. Outcomes of these models can easily break down to reach over final results. Therefore, researchers, academicians, economists prefer these models.

Recommended Articles

This is a guide to Linear Model in R. Here we discuss the types, syntax, and parameters of the Linear Model in R along with its advantages. You can also go through our other suggested articles to learn more –

  1. What is Regression Analysis? | Working | Benefits
  2. An Introduction to Factors in R
  3. Poisson Regression in R
  4. Linear Regression Modeling
  5. Complete Guide to Multiple Linear Regression
  6. Guide to Multiple Linear Regression in R
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