Experiment: Logistic Regression Using a Built-in R Dataset

1. Experiment Title

Implementation of Binary Logistic Regression Using the Built-in mtcars Dataset in R

2. Aim

To perform Binary Logistic Regression using the built-in mtcars dataset in R and predict the transmission type of a car based on its characteristics.

3. Objectives

After completing this experiment, students should be able to:

Explore a built-in dataset in R.
Understand the concept of Binary Logistic Regression.
Identify dependent and independent variables.
Build a Logistic Regression model using glm().
Predict probabilities and class labels.
Create and interpret a confusion matrix.
Calculate classification accuracy.
Predict the class of a new observation.

4. Theory

4.1 Logistic Regression

Logistic Regression is used when the dependent variable is categorical.

When the dependent variable has two possible classes, it is called Binary Logistic Regression.

Examples include:

Yes / No
Pass / Fail
Disease / No Disease
Purchase / No Purchase
Automatic / Manual

Unlike linear regression, Logistic Regression predicts the probability of belonging to a particular class.

4.2 Logistic Regression Model

For Binary Logistic Regression, the dependent variable is represented as:

Y= \begin{cases} 0 & \text{Class 0}\\ 1 & \text{Class 1} \end{cases}

The logistic model is based on the logit function:

\log\left(\frac{p}{1-p}\right) = \beta_0+\beta_1X_1+\beta_2X_2+\cdots+\beta_nX_n

where:

$p$ = Probability of belonging to Class 1
$X_1,X_2,\ldots,X_n$ = Independent variables
$\beta_0$ = Intercept
$\beta_1,\beta_2,\ldots$ = Regression coefficients

The probability is obtained using the sigmoid function:

p= \frac{1}{1+e^{-(\beta_0+\beta_1X_1+\beta_2X_2)}}

The predicted probability always lies between 0 and 1.

5. Built-in Dataset: `mtcars`

The built-in R dataset:


mtcars

contains information about 32 automobiles.

Some important variables are:

Variable	Description
`mpg`	Miles per gallon
`cyl`	Number of cylinders
`hp`	Horsepower
`wt`	Weight
`am`	Transmission type

The variable am represents:

Value	Transmission
0	Automatic
1	Manual

6. Problem Statement

A car manufacturer wants to predict whether a car has a Manual or Automatic transmission based on its:

Horsepower (hp)
Weight (wt)

Using the built-in mtcars dataset:

Dependent Variable: am
Independent Variables: hp and wt

Perform Binary Logistic Regression and evaluate the model.

7. R Program


# -------------------------------------------------
# Binary Logistic Regression Using mtcars Dataset
# -------------------------------------------------

# Load the built-in dataset

data(mtcars)


# -------------------------------------------------
# Step 1: Explore the Dataset
# -------------------------------------------------

cat("First Few Records of mtcars Dataset:\n")

head(mtcars)


cat("\nStructure of Dataset:\n")

str(mtcars)


cat("\nSummary Statistics:\n")

summary(mtcars)


# -------------------------------------------------
# Step 2: Select Required Variables
# -------------------------------------------------

car_data <- mtcars[, c("am", "hp", "wt")]

cat("\nSelected Data:\n")

print(car_data)


# -------------------------------------------------
# Step 3: Convert Transmission into a Factor
# -------------------------------------------------

car_data$am <- factor(
  car_data$am,
  levels = c(0, 1),
  labels = c("Automatic", "Manual")
)


cat("\nTransmission Type:\n")

print(car_data$am)


# -------------------------------------------------
# Step 4: Build Logistic Regression Model
# -------------------------------------------------

model <- glm(
  am ~ hp + wt,
  data = car_data,
  family = binomial
)


# -------------------------------------------------
# Step 5: Display Model Summary
# -------------------------------------------------

cat("\nLogistic Regression Model Summary:\n")

summary(model)


# -------------------------------------------------
# Step 6: Predict Probabilities
# -------------------------------------------------

predicted_probability <- predict(
  model,
  type = "response"
)


cat("\nPredicted Probabilities:\n")

print(predicted_probability)


# -------------------------------------------------
# Step 7: Convert Probabilities into Classes
# -------------------------------------------------

predicted_class <- ifelse(
  predicted_probability >= 0.5,
  "Manual",
  "Automatic"
)


cat("\nPredicted Transmission Type:\n")

print(predicted_class)


# -------------------------------------------------
# Step 8: Add Predictions to Dataset
# -------------------------------------------------

car_data$Predicted_Probability <- predicted_probability

car_data$Predicted_Class <- predicted_class


cat("\nActual and Predicted Results:\n")

print(car_data)


# -------------------------------------------------
# Step 9: Create Confusion Matrix
# -------------------------------------------------

confusion_matrix <- table(
  Actual = car_data$am,
  Predicted = predicted_class
)


cat("\nConfusion Matrix:\n")

print(confusion_matrix)


# -------------------------------------------------
# Step 10: Calculate Accuracy
# -------------------------------------------------

accuracy <- sum(diag(confusion_matrix)) /
            sum(confusion_matrix)


cat(
  "\nAccuracy =",
  round(accuracy * 100, 2),
  "%\n"
)


# -------------------------------------------------
# Step 11: Predict Transmission for a New Car
# -------------------------------------------------

new_car <- data.frame(
  hp = 120,
  wt = 3.0
)


# Predict probability

new_probability <- predict(
  model,
  newdata = new_car,
  type = "response"
)


# Convert probability to class

new_class <- ifelse(
  new_probability >= 0.5,
  "Manual",
  "Automatic"
)


cat("\nPrediction for New Car\n")

cat("Horsepower =", 120, "\n")

cat("Weight =", 3.0, "\n")

cat(
  "Probability of Manual Transmission =",
  round(new_probability, 4),
  "\n"
)

cat(
  "Predicted Transmission =",
  new_class,
  "\n"
)
Output
First Few Records of mtcars Dataset:

Structure of Dataset:
'data.frame':	32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
 $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

Summary Statistics:

Selected Data:
                    am  hp    wt
Mazda RX4            1 110 2.620
Mazda RX4 Wag        1 110 2.875
Datsun 710           1  93 2.320
Hornet 4 Drive       0 110 3.215
Hornet Sportabout    0 175 3.440
Valiant              0 105 3.460
Duster 360           0 245 3.570
Merc 240D            0  62 3.190
Merc 230             0  95 3.150
Merc 280             0 123 3.440
Merc 280C            0 123 3.440
Merc 450SE           0 180 4.070
Merc 450SL           0 180 3.730
Merc 450SLC          0 180 3.780
Cadillac Fleetwood   0 205 5.250
Lincoln Continental  0 215 5.424
Chrysler Imperial    0 230 5.345
Fiat 128             1  66 2.200
Honda Civic          1  52 1.615
Toyota Corolla       1  65 1.835
Toyota Corona        0  97 2.465
Dodge Challenger     0 150 3.520
AMC Javelin          0 150 3.435
Camaro Z28           0 245 3.840
Pontiac Firebird     0 175 3.845
Fiat X1-9            1  66 1.935
Porsche 914-2        1  91 2.140
Lotus Europa         1 113 1.513
Ford Pantera L       1 264 3.170
Ferrari Dino         1 175 2.770
Maserati Bora        1 335 3.570
Volvo 142E           1 109 2.780

Transmission Type:
 [1] Manual    Manual    Manual    Automatic Automatic Automatic
 [7] Automatic Automatic Automatic Automatic Automatic Automatic
[13] Automatic Automatic Automatic Automatic Automatic Manual   
[19] Manual    Manual    Automatic Automatic Automatic Automatic
[25] Automatic Manual    Manual    Manual    Manual    Manual   
[31] Manual    Manual   
Levels: Automatic Manual

Logistic Regression Model Summary:

Predicted Probabilities:
          Mazda RX4       Mazda RX4 Wag          Datsun 710 
       8.423355e-01        4.047825e-01        9.702408e-01 
     Hornet 4 Drive   Hornet Sportabout             Valiant 
       4.172803e-02        6.938812e-02        4.988159e-03 
         Duster 360           Merc 240D            Merc 230 
       2.480412e-01        9.265579e-03        4.099813e-02 
           Merc 280           Merc 280C          Merc 450SE 
       1.119071e-02        1.119071e-02        5.486846e-04 
         Merc 450SL         Merc 450SLC  Cadillac Fleetwood 
       8.500812e-03        5.690614e-03        9.787752e-08 
Lincoln Continental   Chrysler Imperial            Fiat 128 
       3.445824e-08        1.124127e-07        9.699832e-01 
        Honda Civic      Toyota Corolla       Toyota Corona 
       9.995459e-01        9.983241e-01        9.210955e-01 
   Dodge Challenger         AMC Javelin          Camaro Z28 
       1.553207e-02        3.041008e-02        3.585962e-02 
   Pontiac Firebird           Fiat X1-9       Porsche 914-2 
       2.815112e-03        9.963800e-01        9.923618e-01 
       Lotus Europa      Ford Pantera L        Ferrari Dino 
       9.999782e-01        9.433828e-01        9.437365e-01 
      Maserati Bora          Volvo 142E 
       8.960342e-01        5.856710e-01 

Predicted Transmission Type:
          Mazda RX4       Mazda RX4 Wag          Datsun 710 
           "Manual"         "Automatic"            "Manual" 
     Hornet 4 Drive   Hornet Sportabout             Valiant 
        "Automatic"         "Automatic"         "Automatic" 
         Duster 360           Merc 240D            Merc 230 
        "Automatic"         "Automatic"         "Automatic" 
           Merc 280           Merc 280C          Merc 450SE 
        "Automatic"         "Automatic"         "Automatic" 
         Merc 450SL         Merc 450SLC  Cadillac Fleetwood 
        "Automatic"         "Automatic"         "Automatic" 
Lincoln Continental   Chrysler Imperial            Fiat 128 
        "Automatic"         "Automatic"            "Manual" 
        Honda Civic      Toyota Corolla       Toyota Corona 
           "Manual"            "Manual"            "Manual" 
   Dodge Challenger         AMC Javelin          Camaro Z28 
        "Automatic"         "Automatic"         "Automatic" 
   Pontiac Firebird           Fiat X1-9       Porsche 914-2 
        "Automatic"            "Manual"            "Manual" 
       Lotus Europa      Ford Pantera L        Ferrari Dino 
           "Manual"            "Manual"            "Manual" 
      Maserati Bora          Volvo 142E 
           "Manual"            "Manual" 

Actual and Predicted Results:
                           am  hp    wt Predicted_Probability
Mazda RX4              Manual 110 2.620          8.423355e-01
Mazda RX4 Wag          Manual 110 2.875          4.047825e-01
Datsun 710             Manual  93 2.320          9.702408e-01
Hornet 4 Drive      Automatic 110 3.215          4.172803e-02
Hornet Sportabout   Automatic 175 3.440          6.938812e-02
Valiant             Automatic 105 3.460          4.988159e-03
Duster 360          Automatic 245 3.570          2.480412e-01
Merc 240D           Automatic  62 3.190          9.265579e-03
Merc 230            Automatic  95 3.150          4.099813e-02
Merc 280            Automatic 123 3.440          1.119071e-02
Merc 280C           Automatic 123 3.440          1.119071e-02
Merc 450SE          Automatic 180 4.070          5.486846e-04
Merc 450SL          Automatic 180 3.730          8.500812e-03
Merc 450SLC         Automatic 180 3.780          5.690614e-03
Cadillac Fleetwood  Automatic 205 5.250          9.787752e-08
Lincoln Continental Automatic 215 5.424          3.445824e-08
Chrysler Imperial   Automatic 230 5.345          1.124127e-07
Fiat 128               Manual  66 2.200          9.699832e-01
Honda Civic            Manual  52 1.615          9.995459e-01
Toyota Corolla         Manual  65 1.835          9.983241e-01
Toyota Corona       Automatic  97 2.465          9.210955e-01
Dodge Challenger    Automatic 150 3.520          1.553207e-02
AMC Javelin         Automatic 150 3.435          3.041008e-02
Camaro Z28          Automatic 245 3.840          3.585962e-02
Pontiac Firebird    Automatic 175 3.845          2.815112e-03
Fiat X1-9              Manual  66 1.935          9.963800e-01
Porsche 914-2          Manual  91 2.140          9.923618e-01
Lotus Europa           Manual 113 1.513          9.999782e-01
Ford Pantera L         Manual 264 3.170          9.433828e-01
Ferrari Dino           Manual 175 2.770          9.437365e-01
Maserati Bora          Manual 335 3.570          8.960342e-01
Volvo 142E             Manual 109 2.780          5.856710e-01
                    Predicted_Class
Mazda RX4                    Manual
Mazda RX4 Wag             Automatic
Datsun 710                   Manual
Hornet 4 Drive            Automatic
Hornet Sportabout         Automatic
Valiant                   Automatic
Duster 360                Automatic
Merc 240D                 Automatic
Merc 230                  Automatic
Merc 280                  Automatic
Merc 280C                 Automatic
Merc 450SE                Automatic
Merc 450SL                Automatic
Merc 450SLC               Automatic
Cadillac Fleetwood        Automatic
Lincoln Continental       Automatic
Chrysler Imperial         Automatic
Fiat 128                     Manual
Honda Civic                  Manual
Toyota Corolla               Manual
Toyota Corona                Manual
Dodge Challenger          Automatic
AMC Javelin               Automatic
Camaro Z28                Automatic
Pontiac Firebird          Automatic
Fiat X1-9                    Manual
Porsche 914-2                Manual
Lotus Europa                 Manual
Ford Pantera L               Manual
Ferrari Dino                 Manual
Maserati Bora                Manual
Volvo 142E                   Manual

Confusion Matrix:
           Predicted
Actual      Automatic Manual
  Automatic        18      1
  Manual            1     12

Accuracy = 93.75 %

Prediction for New Car
Horsepower = 120 
Weight = 3 
Probability of Manual Transmission = 0.2624 
Predicted Transmission = Automatic

8. Explanation of the Program

Step 1: Loading the Dataset


data(mtcars)

The mtcars dataset is already available in R.

The first few records can be displayed using:


head(mtcars)

Step 2: Selecting Variables


car_data <- mtcars[, c("am", "hp", "wt")]

We select only the variables required for this experiment:

am → Transmission type
hp → Horsepower
wt → Vehicle weight

Step 3: Converting the Output Variable

The original am variable contains:


0 → Automatic
1 → Manual

It is converted into a factor for easier interpretation:


car_data$am <- factor(
  car_data$am,
  levels = c(0, 1),
  labels = c("Automatic", "Manual")
)

9. Building the Logistic Regression Model

The model is created using:


model <- glm(
  am ~ hp + wt,
  data = car_data,
  family = binomial
)

The function glm() means Generalized Linear Model.

The argument:


family = binomial

specifies that Binary Logistic Regression is being used.

The expression:


am ~ hp + wt

means:

Predict the transmission type using horsepower and vehicle weight.

10. Predicting Probabilities

The model predicts the probability that a car belongs to the positive class:


predicted_probability <- predict(
  model,
  type = "response"
)

Since the positive class is Manual, the values represent:

Probability that the car has a Manual transmission.

For example:


0.80

means approximately:

80% predicted probability of Manual transmission.

11. Converting Probability into a Class

A threshold of 0.5 is used.


predicted_class <- ifelse(
  predicted_probability >= 0.5,
  "Manual",
  "Automatic"
)

Probability	Prediction
≥ 0.5	Manual
< 0.5	Automatic

12. Confusion Matrix

The confusion matrix compares:

Actual transmission type
Predicted transmission type


confusion_matrix <- table(
  Actual = car_data$am,
  Predicted = predicted_class
)

A good model will have more observations along the main diagonal, representing correct predictions.

13. Accuracy

Accuracy is calculated as:

\text{Accuracy} = \frac{\text{Number of Correct Predictions}} {\text{Total Number of Predictions}} \times100

In R:


accuracy <- sum(diag(confusion_matrix)) /
            sum(confusion_matrix)

14. Predicting a New Car

The program predicts the transmission type of a new car with:

Variable	Value
Horsepower	120
Weight	3.0

The model calculates the probability of a Manual transmission and then classifies it as:

Manual, or
Automatic

using the threshold of 0.5.

15. Important Functions Used

Function	Purpose
`data()`	Loads a built-in dataset
`head()`	Displays the first few records
`str()`	`Displays dataset structure
`summary()`	Displays statistical summary
`factor()`	Converts categorical data into factors
`glm()`	Builds a generalized linear model
`predict()`	Predicts probabilities
`ifelse()`	Converts probabilities into classes
`table()`	Creates a confusion matrix

16. Result

Binary Logistic Regression was successfully implemented using the built-in mtcars dataset in R. A model was developed to predict whether a car has a Manual or Automatic transmission based on its horsepower and weight. The model was used to calculate predicted probabilities, classify observations, generate a confusion matrix, calculate classification accuracy, and predict the transmission type of a new car.

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Statistical Methods Lab ( R Language) PCCBL308 Semester 3 KTU BTech CB CU 2024 Scheme

Logistic Regression Using a Built-in R Dataset

Experiment: Logistic Regression Using a Built-in R Dataset

1. Experiment Title

2. Aim

3. Objectives

4. Theory

4.1 Logistic Regression

4.2 Logistic Regression Model

5. Built-in Dataset: `mtcars`

6. Problem Statement

7. R Program

Output

8. Explanation of the Program

Step 1: Loading the Dataset

Step 2: Selecting Variables

Step 3: Converting the Output Variable

9. Building the Logistic Regression Model

10. Predicting Probabilities

11. Converting Probability into a Class

12. Confusion Matrix

13. Accuracy

14. Predicting a New Car

15. Important Functions Used

16. Result

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Statistical Methods Lab ( R Language) PCCBL308 Semester 3 KTU BTech CB and CU 2024 Scheme - Dr Binu V P

Programs in R - using control statements - Assignment 2

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Logistic Regression Using a Built-in R Dataset

Experiment: Logistic Regression Using a Built-in R Dataset

1. Experiment Title

2. Aim

3. Objectives

4. Theory

4.1 Logistic Regression

4.2 Logistic Regression Model

5. Built-in Dataset: mtcars

6. Problem Statement

7. R Program

Output

8. Explanation of the Program

Step 1: Loading the Dataset

Step 2: Selecting Variables

Step 3: Converting the Output Variable

9. Building the Logistic Regression Model

10. Predicting Probabilities

11. Converting Probability into a Class

12. Confusion Matrix

13. Accuracy

14. Predicting a New Car

15. Important Functions Used

16. Result

Comments

Post a Comment

Popular posts from this blog

Statistical Methods Lab ( R Language) PCCBL308 Semester 3 KTU BTech CB and CU 2024 Scheme - Dr Binu V P

Programs in R - using control statements - Assignment 2

Programs to try using Functions in R - Assignment 3

5. Built-in Dataset: `mtcars`