Market Analysis with Econometrics and Machine Learning

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Questions and Answers

What is another term for the 'dependent variable'?

Response (correct)

Feature

Regressor

Predictor

In a regression model, 'x' and 'z' are typically considered features.

True

What is the purpose of a prediction model?

To make good predictions for new observations, also known as out-of-sample data.

A polynomial regression of degree 8 is also known as an ______________ function.

octic Signup and view all the answers

What is the problem with the octic curve in the plot?

Overfitting Signup and view all the answers

Match the following terms with their definitions:

Nominal variable = Categorical variable Dummy variable = One-hot encoded variable Explanatory variable = Regressor or feature estimate a model = Train a model Signup and view all the answers

The term 'feature' is only used in machine learning.

False Signup and view all the answers

What is the problem with a model that is highly influenced by the random errors in the training data?

It is likely to overfit the training data and not generalize well to new data. Signup and view all the answers

What is the main goal of a pure prediction problem?

To make good predictions of the dependent variable for new observations Signup and view all the answers

Linear regression is a powerful method for pure prediction problems.

False Signup and view all the answers

What is the name of the book that is recommended for starters in machine learning?

Introduction to Statistical Learning Signup and view all the answers

Machine learning is also known as ______________________ learning.

statistical Signup and view all the answers

What is the purpose of splitting a sample into a training and test data set?

To use cross validation for parameter tuning Signup and view all the answers

Econometrics and machine learning use the same expressions and terminology.

False Signup and view all the answers

Match the following machine learning methods with their characteristics:

Lasso Regression = Often used for prediction problems Random Forests = Can handle high-dimensional data Gradient Boosted Trees = Combines multiple weak models Deep Neural Networks = Can learn complex patterns Signup and view all the answers

In a linear regression, the dependent variable is denoted by ______________________.

y Signup and view all the answers

Study Notes

Prediction Problems and Machine Learning

In linear regression, we study how to consistently estimate the coefficients (e.g., β) to understand how an explanatory variable is related to or causally affects a dependent variable.
In contrast, in a pure prediction problem, we only want to find and estimate a model that allows us to make good predictions of the dependent variable for new observations.

Machine Learning Techniques

Machine learning has substantially advanced techniques for pure prediction problems, which can often outperform linear regressions.
Examples of powerful prediction methods include:
- Random forests
- Gradient boosted trees
- Lasso and ridge regression
- Deep neural networks
Established procedures for prediction problems include:
- Splitting the sample into a training and test data set
- Using cross-validation for parameter tuning

Thesaurus: Machine Learning vs. Econometrics

The machine learning literature uses different expressions than econometrics, including:
- Dependent variable = response
- Explanatory variable = regressor = predictor = feature
- Estimate a model = train a model
- Nominal variable = categorical variable = factor variable = non-numeric variable
- Dummy variable = one-hot encoded variable

Polynomial Regression for Prediction

A prediction model should make good predictions for new observations (out-of-sample data).
The trade-offs that affect out-of-sample prediction accuracy can be illustrated using a simulated data set with one explanatory variable.
The true data generating process can be a polynomial of degree 8 of the explanatory variable plus some iid error term.

Example: Overfitting

The octic curve can predict the training data points most closely, but it looks quite wiggly, which is a typical sign of overfitting.
Overfitting means that the form of the curve is strongly influenced by the realization of the random errors in the training data set.