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What is regression?

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Regression is a statistical method used in data analysis to model the relationship between a dependent variable and one or more independent variables. It aims to understand how the dependent variable changes as the independent variables vary.

In simpler terms, regression helps to predict the value of one variable based on the values of other variables. It is particularly useful for understanding and quantifying the relationship between variables, making predictions, and identifying patterns in data.

Here's how regression typically works:

  1. Data Collection: You collect data on the variables of interest. This involves gathering observations of both the dependent variable and the independent variables from your target population or sample.
  2. Data Exploration: You explore the data to understand its characteristics, such as distributions, relationships between variables, and potential outliers.
  3. Model Selection: Based on the nature of your data and the research question, you select an appropriate regression model. This could be linear regression, logistic regression, polynomial regression, etc.
  4. Model Training: You use your dataset to estimate the parameters of the regression model. This involves fitting the model to the data in order to find the best-fitting line, curve, or surface that describes the relationship between the variables.
  5. Model Evaluation: Once the model is trained, you evaluate its performance. This could involve assessing how well the model fits the data, checking for violations of assumptions, and using appropriate metrics to evaluate predictive accuracy.
  6. Inference or Prediction: Depending on your goals, you can use the regression model for two main purposes:
  • Inference: You can make inferences about the population parameters based on the sample data. For example, you might use regression to understand the relationship between smoking and lung cancer risk in a population.
  • Prediction: You can use the regression model to make predictions about the dependent variable for new or unseen data. For example, you might use regression to predict house prices based on features like square footage, number of bedrooms, etc.

Regression analysis provides valuable insights into the relationships between variables and allows us to make informed decisions based on data. It's widely used across various fields including economics, finance, marketing, healthcare, social sciences, and many others.

In supervised machine learning, regression techniques are primarily used when the target variable (dependent variable) is continuous, meaning it can take on a range of values. Here are some common types of regression used in supervised machine learning:

  1. Linear Regression: Linear regression is one of the simplest and most widely used regression techniques. It models the relationship between the dependent variable and one or more independent variables by fitting a linear equation to the observed data.
  2. Multi-Linear Regression: Multilinear regression, also known as multiple linear regression, is a statistical method used to model the relationship between a dependent variable and two or more independent variables.
  3. Polynomial regression: Polynomial regression extends linear regression by introducing polynomial terms of the independent variables. It's useful for capturing non-linear relationships between variables.
  4. Support Vector Regression: Support vector regression is a regression algorithm based on support vector machines (SVMs). It finds the hyperplane that best fits the data points while minimizing the margin violations.
  5. Decision Tree Regression: Decision tree regression models the relationship between the independent variables and the target variable by recursively partitioning the feature space into regions and fitting a simple model (typically a constant value) within each region.
  6. Random Forest Regression: Random Forest regression is an ensemble learning technique that combines multiple decision trees to improve prediction accuracy and robustness. It's useful for handling noisy data and capturing complex relationships between variables.

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