{"id":223682,"date":"2025-05-12T12:00:20","date_gmt":"2025-05-12T16:00:20","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=223682"},"modified":"2025-05-12T12:04:07","modified_gmt":"2025-05-12T16:04:07","slug":"from-logistic-to-random-forests-mastering-non-linear-regression-models","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/from-logistic-to-random-forests-mastering-non-linear-regression-models\/","title":{"rendered":"From Logistic to Random Forests: Mastering Non-linear Regression Models"},"content":{"rendered":"\n

The post “From Logistic to Random Forests: Mastering Non-linear Regression Models” was originally published on QuantInsti<\/a> blog.<\/em><\/p>\n\n\n\n

Ever wish you had a crystal ball for the financial markets? While we can’t quite<\/em> do that, regression<\/strong> is a super useful tool that helps us find patterns and relationships hidden in data \u2013 it’s like being a data detective!<\/p>\n\n\n\n

The most common starting point is linear regression<\/strong>, which is basically about drawing the best straight line through data points to see how things are connected. Simple, right?<\/p>\n\n\n\n

In Part 1<\/a><\/strong> of this series, we explored ways to make those line-based models even better, tackling things like curvy relationships (Polynomial Regression) and messy data with too many variables (using Ridge and Lasso Regression). We learned how to refine those linear predictions.<\/p>\n\n\n\n

But what if a line (even a curvy one) just doesn’t fit? Or what if you need to predict something different, like a “yes” or “no”?<\/p>\n\n\n\n

Get ready for Part 2<\/strong>, my friend! <\/strong>Where we venture beyond the linear world and explore a fascinating set of regression techniques designed for different kinds of problems:<\/p>\n\n\n\n

    \n
  1. Logistic Regression:<\/strong> For predicting probabilities and binary outcomes (Yes\/No).<\/li>\n\n\n\n
  2. Quantile Regression:<\/strong> For understanding relationships at different points in the data distribution, not just the average (great for risk analysis!).<\/li>\n\n\n\n
  3. Decision Tree Regression:<\/strong> An intuitive flowchart approach for complex, non-linear patterns.<\/li>\n\n\n\n
  4. Random Forest Regression:<\/strong> Harnessing the “wisdom of the crowd” by combining multiple decision trees for accuracy and stability.<\/li>\n\n\n\n
  5. Support Vector Regression (SVR):<\/strong> A powerful method using “margins” to handle complex relationships, even in high dimensions.<\/li>\n<\/ol>\n\n\n\n

    Let’s dive into these powerful tools and see how they can unlock new insights from financial data!<\/p>\n\n\n\n

    \n\n\n\n

    Prerequisites<\/strong><\/h3>\n\n\n\n

    Hey there! Before we get into the good stuff, it helps to be familiar with a few key concepts. You can still follow along intuitively, but brushing up on these will give you a much better understanding. Here\u2019s what to check out:<\/p>\n\n\n\n

    1. Statistics and Probability<\/strong>
    Know the essentials\u2014mean, variance, correlation, and probability distributions. New to this?     Probability Trading<\/em><\/a> is a great intro.<\/p>\n\n\n\n

    2. Linear Algebra Basics<\/strong>
    Basics like matrices and vectors are super useful, especially for techniques like Principal Component Regression.<\/p>\n\n\n\n

    3. Regression Fundamentals<\/strong>
    Get comfy with linear regression and its assumptions.     Linear Regression in Finance<\/em><\/a> is a solid starting point.<\/p>\n\n\n\n

    4. Financial Market Knowledge<\/strong>
    Terms like stock returns, volatility, and market sentiment will come up a lot.     Statistics for Financial Markets<\/em><\/a> can help you brush up.<\/p>\n\n\n\n

    5. Explore Part 1<\/a> of This Series<\/strong>
    Check out     Part 1<\/a> for an overview of Polynomial, Ridge, Lasso, Elastic Net, and LARS. It\u2019s not mandatory, but it provides excellent context for different regression types.<\/p>\n\n\n\n

    Once you’re good with these, you\u2019ll be all set to dive deeper into how regression techniques reveal insights in finance. Let\u2019s get started!<\/p>\n\n\n\n

    \n\n\n\n

    What Exactly is Regression Analysis?<\/h2>\n\n\n\n

    At its core, regression analysis models the relationship between a dependent variable (the outcome we want to predict) and one or more independent variables (predictors).<\/p>\n\n\n\n

    Think of it as figuring out the connection between different things \u2013 for instance, how does a company’s revenue (the outcome) relate to how much they spend on advertising (the predictor)? Understanding these links helps you make educated guesses about future outcomes based on what you know.

    When that relationship looks like a straight line on a graph, we call it linear regression \u2013 nice and simple!<\/p>\n\n\n\n

    What Makes These Models ‘Non-Linear’?<\/h2>\n\n\n\n
    \n\n\n\n

    Good question! In Part 1<\/a>, we mentioned that ‘linear’ in regression refers to how the model’s coefficients are combined.<\/p>\n\n\n\n

    Non-linear models, like the ones we’re exploring here, break that rule. Their underlying equations or structures don’t just add up coefficients multiplied by predictors in a simple way. Think about Logistic Regression using that S-shaped curve (sigmoid function) to squash outputs between 0 and 1, or Decision Trees making splits based on conditions rather than a smooth equation, or SVR using ‘kernels’ to handle complex relationships in potentially higher dimensions.<\/p>\n\n\n\n

    These methods fundamentally work differently from linear models, allowing them to capture patterns and tackle problems (like classification or modelling specific data segments) that linear models often can’t.<\/p>\n\n\n\n

    \n\n\n\n

    Logistic (or Logit) regression<\/h2>\n\n\n\n

    You use Logistic regression when the dependent variable (here, a dichotomous variable) is binary (think of it as a “yes” or “no” outcome, like a stock going up or down). It helps predict the binary outcome of an occurrence based on the given data.<\/p>\n\n\n\n

    It is a non-linear model that gives a logistic curve with values limited to between 0 and 1. This probability is then compared to a threshold value of 0.5 to classify the data. So, if the probability for a class is more than 0.5, we label it as 1; otherwise, it is 0.<\/p>\n\n\n\n

    This model is generally used to predict the performance of stocks<\/a>.

    Note:<\/em> You can not use linear regression<\/strong> here because it could give values outside the 0 to 1 range. Also, the dependent variable can take only two values here, so the residuals won\u2019t be normally distributed about the predicted line.<\/p>\n\n\n\n

    Want to learn more? Check out this blog for more on logistic regression<\/a> and how to use Python code to predict stock movement.<\/p>\n\n\n\n

    \"From<\/figure>\n\n\n\n

    Source: https:\/\/www.saedsayad.com\/logistic_regression.htm<\/a><\/p>\n\n\n\n

    \n\n\n\n

    Quantile Regression: Understanding Relationships Beyond the Average<\/h2>\n\n\n\n

    Traditional linear regression<\/a> models predict the mean<\/strong> of a dependent variable based on independent variables. However, financial time series data often contain skewness<\/a> and outliers, making linear regression unsuitable.<\/p>\n\n\n\n

    To solve this problem, Koenker and Bassett (1978)<\/strong> introduced quantile regression. Instead of modeling just the mean, it helps us see the relationship between variables at different points (quantiles and percentiles) in the dependent variable’s distribution, such as:<\/p>\n\n\n\n