Regression analysis is a powerful technique for data science that can help you explore the relationships between variables, test hypotheses, and make predictions based on data. In this article, you will learn what regression analysis is, what types of regression models exist, and how you can use them in data science projects.
Regression analysis is a method of statistical modeling that seeks to determine the equation or function that best describes the relationship between one or more independent variables (also known as predictors or features) and a dependent variable (also known as response or outcome). This equation or function can range from linear to nonlinear, depending on the complexity of the data. Regression analysis can help answer questions such as how does house price depend on size, location, and features; how does demand for a product vary with its price, advertising, and seasonality; and how does a patient's blood pressure change with age, weight, and medication.
Regression analysis in data science is a statistical technique used to understand relationships between variables. It helps predict one variable based on the values of others. For example, it can forecast sales based on advertising expenditure. By analyzing historical data, regression identifies patterns and quantifies the impact of independent variables on the dependent one. This valuable tool aids in making informed decisions, ranging from business forecasts to scientific research, by providing insights into the relationships within your data.
There are various types of regression models, each having its own assumptions, advantages, and limitations. Linear regression is the most basic and widely used one, where the connection between the independent and dependent variables is assumed to be linear. Logistic regression is used when the dependent variable has two possible values, such as yes or no. Polynomial regression permits nonlinear relationships between the independent and dependent variables by using higher-order terms. Ridge regression adds a penalty term to the linear regression equation to reduce multicollinearity. Lasso regression uses a penalty term to perform feature selection or eliminate irrelevant independent variables. Each of these models offers unique benefits but can also lead to overfitting or underfitting if not chosen carefully.
10 types of regression models and when to use them: 1. Linear regression: when the outcome is a continuous variable 2. Logistic regression: when the outcome is binary 3. Multinomial logistic regression: when the outcome is a categorical variable with many levels 4. Ordinal logistic regression: when the outcome is an ordinal variable with more than 2 categories 5. Poisson regression: when the outcome is a count variable 6,7. LASSO and stepwise regression: when not all predictors are related to the outcome 8. Ridge regression: when the predictors are correlated 9. Cox regression: when the outcome is the time until an event occurs 10. Mixed model: when observations are not independent
Regression analysis is a powerful tool in data science, used to explore the data and understand the relationships between variables. It can also be used to test hypotheses or assumptions about the data, such as linearity, normality, homoscedasticity, and independence. Furthermore, regression analysis can build predictive models that estimate the value of the dependent variable based on the independent variables. It can also compare and select the best-fitting model among different types of regression models. Finally, regression analysis can provide recommendations or suggestions based on the data and quantify the impact or influence of the independent variables on the dependent variable.
Data scientists who want to learn and apply regression analysis can take advantage of several tools and resources, such as Python and R, both of which offer a variety of libraries and packages for regression analysis. Excel is another viable option, providing basic functions and features for regression analysis. Additionally, there are a number of online courses available, such as Coursera's Regression Models, edX's Data Science: Regression, and Udemy's Regression Analysis for Data Science. Finally, there are several books that can help deepen understanding and skills in regression analysis, including An Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani, Applied Linear Regression by Weisberg, and Regression Analysis by Example by Chatterjee and Hadi.
The best FREE books on regression analysis are: 1. Handbook of Regression Modeling in People Analytics by Keith McNulty (Good for beginners) 2. An Introduction to Statistical Learning by Gareth James and colleagues (A little bit more advanced + now there is an official python version) 3. Tidy Modeling with R by Max Kuhn and Julia Silge (for a modern approach using tidymodels)
Regression analysis is not a perfect technique and has some challenges and limitations that should be taken into account. For example, it can’t prove the causality or direction of the relationship between variables, and is sensitive to outliers in the data. Additionally, it can be affected by multicollinearity or high correlation among the independent variables. Furthermore, regression analysis involves many choices and decisions such as which type of regression model to use, which can lead to bias or error if not based on sound reasoning and evidence. To address these issues, you need to use methods such as experiments, robust regression, correlation analysis, hypothesis testing, and information criteria.
The key to regression analysis is having a well defined, clear hypothesis, good understanding of the available quantifiable data and feature selection methodology & engineering as per the data in hand.