7 Regression Techniques You Should Know
Regression is a type of maths that helps people understand how things are related to each other. It is used a lot in science, business, and other fields to figure out things like how much something will cost or how long it will take.
There are many different types of regression, but in this article, we will talk about 7 of the most important ones. These include linear regression, logistic regression, polynomial regression, ridge regression, lasso regression, and elastic net regression.
By the end of the article, you will know what these types of regression are and when to use them.
Linear Regression
Definition and explanation of linear regression
Linear regression is a mathematical approach for modeling a linear connection among one or more independent variables as well as a dependent variable. It is a type of supervised learning algorithm that is commonly used in predictive modeling and data analysis.
Linear regression is a way to use maths to understand how two things are related. It helps us find out if one thing (like how much someone weighs) affects another thing (like how tall they are). Linear regression can be used to predict what might happen in the future based on what has happened in the past.
Use cases and applications of linear regression
- Predictive modeling and forecasting
- Identifying relationships between variables
- Estimating causal effects
- Quality control
- Medical research
How to perform linear regression in popular data analysis software
Linear regression is a relatively simple and easy-to-use technique, making it a popular choice for many data analysts. It’s widespread in industries like finance, business, and advertising.
Performing linear regression in popular data analysis software such as R, Python, or Excel is a straightforward process.
In R and Python, there are specific packages, such as ‘lm’ and ‘LinearRegression’ that can be used to perform linear regression. These packages provide a variety of options for fitting a linear regression model and interpreting the results.
In Excel, the ‘Data Analysis’ tool can be used to perform linear regression, with options for inputting data and interpreting results.
Logistic Regression
Definition and explanation of logistic regression
Logistic Regression is a statistical method used to analyse a dataset in which there are one or more independent variables that determine an outcome. With a collection of independent factors, it’s employed to describe a binary result (1 / 0, Yes / No, False / True). Logistic regression is used in a variety of fields, including medical research, social sciences, and marketing.
This can be represented in
ln(p/(1-p)) = b0+b1X1+b2X2+b3X3….+bkXk
The key advantage of logistic regression is that it can be used to predict the probability of an outcome, rather than just the outcome itself. This makes it a useful tool for making predictions and understanding the impact of different variables on the outcome.
Use cases and applications of logistic regression
Among the most popular applications of logistic regression are:
- Predicting the likelihood of a customer making a purchase
- Identifying risk factors for a medical condition
- Understanding the impact of different marketing strategies on sales
- Analysing the likelihood of a student passing or failing a test
How to perform logistic regression in popular data analysis software (e.g. R, Python, Excel)
To do regression analysis in common data processing tools like R, Python, or Excel, you must first divide your information into variables that are both independent and dependent. Then, you will use the appropriate function or tool in the software to perform the logistic regression analysis.
For example, in R, you can use the glm() function to perform logistic regression, while in Python, you can use the statsmodels library. In Excel, you can use the Data Analysis ToolPak to perform logistic regression.
It’s important to note that before performing logistic regression, you should check the assumptions of the model, such as independence of errors, linearity of the logit, and absence of outliers.
Additionally, it’s important to interpret the results carefully, as logistic regression estimates the probability of an outcome, not the outcome itself.
Polynomial Regression
Definition and explanation of polynomial regression
Polynomial regression is a technique used to model the relationship between a dependent variable and one or more independent variables, using a polynomial equation. Unlike linear regression, which models the relationship as a straight line, polynomial regression allows for the relationship to be modeled as a curved line. This can be useful in cases where the relationship between the variables is not linear but rather follows a more complex pattern.
It can be represented by the equation below:
y=a+b*x^2
Use cases and applications of polynomial regression
Some common use cases for polynomial regression include:
- Modeling the relationship between temperature and energy consumption
- Modeling the relationship between duration and cost of stock
- Modeling the relationship between engine size and fuel efficiency
- the relationship between the number of rooms in a house and its price
How to perform polynomial regression in popular data analysis software (e.g. R, Python, Excel)
To perform a polynomial regression in popular data analysis software such as R, Python, or Excel, you must first ensure that the data is appropriately formatted for the model. This typically involves creating a new column for each polynomial term of the independent variable and then fitting the model using this new data.
In R, the “poly()” function can be used to create the polynomial terms, while in Python, the “PolynomialFeatures” class in the “sklearn.preprocessing” module can be used.
In Excel, the “Data Analysis” tool can be used to perform polynomial regression, but it will require manual creation of the polynomial terms.
Once the model has been fitted, you can then use it to make predictions, calculate R-squared values and other statistical measures to evaluate the model and plot the results to visualise the relationship between the variables. Understanding and being able to use polynomial regression techniques can help you to make more accurate predictions and understand complex data relationships.
Ridge Regression
Definition and explanation of ridge regression
Ridge Regression is a type of linear regression that addresses the problem of multicollinearity, which occurs when two or more predictor variables are highly correlated.
In Ridge Regression, a penalty term, also known as a regularisation term, is added to the least squares function to shrink the coefficient estimates toward zero. This helps to reduce the variance of the estimates and prevent overfitting.
Can be represented by the equation:
y=a+b*x+e
Where e is the
Use cases and applications of ridge regression
One of the main use cases of Ridge Regression is in linear models with a large number of predictor variables. It is also commonly used in scenarios where the data is noisy or has high multicollinearity. Some specific applications of Ridge Regression include:
1. Predicting financial performance based on a large number of economic indicators
2. Identifying risk factors for a disease based on a large number of potential predictors
3. Improving the accuracy of predictions in a machine learning model by reducing the variance of the estimates
How to perform ridge regression in popular data analysis software (e.g. R, Python, Excel)
To perform Ridge Regression in R, the user can use the ‘glmnet’ package, which has a built-in Ridge Regression function. In Python, the user can use the ‘scikit-learn’ library and the Ridge Regression function. In Excel, the user can use the ‘Data Analysis ToolPak’ and select ‘Regression’ to perform Ridge Regression.
Lasso Regression
Definition and explanation of lasso regression
Lasso regression, also known as Least Absolute Shrinkage and Selection Operator, is a type of regularised linear regression that aims to reduce the complexity of the model by setting some of the coefficient estimates to zero. This technique can be used in cases where there are a high number of predictor variables, also known as feature selection.
Use cases and applications of lasso regression
- Feature selection in high-dimensional data sets
- Reducing multicollinearity in linear regression models
- Identifying the most important predictors in a model
- Image and text data analysis
- Model interpretability
How to perform lasso regression in popular data analysis software (e.g. R, Python, Excel)
To perform lasso regression in R, the “glmnet” package can be used. In Python, the “sklearn” package has a “Lasso” function.
In Excel, the “Data Analysis Toolpak” has a “Regression” function that can be used to perform lasso regression with the appropriate settings. It’s important to note that when using Lasso regression, the choice of the regularisation parameter is crucial. One of the most common ways to select the regularisation parameter is by using cross-validation.
Elastic Net Regression
Definition and explanation of elastic net regression
Elastic Net Regression is a combination of both Ridge and Lasso regression techniques. It is a linear regression technique that adds a penalty term to the ordinary least squares objective function, similar to Ridge and Lasso. The penalty term is a combination of both L1 and L2 regularisation terms. This allows Elastic Net to balance the strengths of Ridge and Lasso, resulting in a more robust model.
Use cases and applications of elastic net regression
- High-dimensional data analysis, such as image or text data analysis.
- Multicollinearity situations, where multiple independent variables are highly correlated with each other.
- Feature selection, as the L1 regularisation term tends to shrink the coefficients of less important features to zero.
- Predictive modelling, for example in finance, marketing, and healthcare industries.
- Time-series forecasting, for example in stock market analysis or weather prediction.
How to perform elastic net regression in popular data analysis software (e.g. R, Python, Excel)
In terms of performing Elastic Net Regression, it can be done using popular data analysis software such as R, Python, and Excel. In R, the package “glmnet” can be used to perform Elastic Net Regression. In Python, the “Scikit-learn” library has a “ElasticNet” class for performing Elastic Net Regression. In Excel, the “Solver” add-in can be used to perform Elastic Net Regression.
Conclusion
In conclusion, we have discussed 7 important regression techniques that every data analyst should be familiar with.
Linear Regression, Logistic Regression, Polynomial Regression, Ridge Regression, Lasso Regression, and Elastic Net Regression are examples of such approaches. Each of these techniques has its own unique use cases and applications and can provide valuable insights when analysing data.
The importance of understanding and using these techniques cannot be overstated. Regression techniques are a fundamental part of data analysis and are widely used in various fields such as finance, economics, and marketing.