Worksheet

Author
Affiliation

Camille Mondon

Toulouse School of Economics

Published

January 12, 2026

1 LDA on Insurance Data

Exercise 1 The data set we consider comes from an insurance company and contains information about 2220 young drivers who have a car insurance contract. The available variables are:

  • TYPE: the type of insurance contract (A: good, B: medium, C: minimum)
  • VALUE: the value of the insured vehicle (1 = very low, 2 = low, 3 = medium, 4 = high)
  • SEX: the sex of the insured (1 = man, 0 = woman)
  • AGEV: the age of the vehicle
  • AGEI: the age of the insured

You may use either R or Python to answer the following questions.

  1. Load the data insurance.csv1 and provide a short description of the variables. You should:
  • Display the first few rows of the dataset.
  • Compute summary statistics for each variable.
  • Provide counts for each category of the TYPE variable.

Hint: You may use summary() and table() in R, or describe() and value_counts() in Python.

  1. Randomly split the dataset into a training sample and a test sample.
  • Use approximately 70% of the observations for training and 30% for testing.
  • Ensure that all levels of the TYPE variable are represented in both samples.

Hint: In R, you can use sample() or the caret package. In Python, you can use train_test_split from sklearn.model_selection.

  1. Using the training sample, predict the type of insurance contract (TYPE) using the explanatory variables VALUE, SEX, AGEV, and AGEI.
  • Fit a Linear Discriminant Analysis (LDA) model on the training sample.
  • Compute predicted classes for the test sample.
  • Evaluate the model’s accuracy using a confusion matrix.

Hint: In R, use MASS::lda(). In Python, use sklearn.discriminant_analysis.LinearDiscriminantAnalysis.

Remark

Remark 1.

  • Ensure that categorical variables have the correct type before applying LDA.
  • Standardizing numerical variables is not required for LDA but may affect the interpretation of coefficients.
  1. Interpret the results obtained from LDA:
  • Comment on which variables appear most influential in discriminating between the insurance contract types (using the \(R^2\) equivalent in LDA).
  • Interpret the variables in the discriminant subspace using the correlations.
  • Discuss any misclassification patterns observed in the test sample.
  • Reflect on the overall accuracy of LDA and its usefulness for predicting TYPE.

Hint: Use the confusion matrix to identify which classes are most often misclassified. You may also inspect the LDA coefficients to assess variable importance.

  1. Why isn’t it possible to draw a ROC curve? How can you modify the insurance variables so that it becomes possible?

Footnotes

  1. You can download it here.↩︎