Introduction
Linear regression and logistic regression are two types of regression analysis techniques that are used to solve the regression problem using machine learning. They are the most prominent techniques of regression. But, there are many types of regression analysis techniques in machine learning, and their usage varies according to the nature of the data involved.
This article will explain the different types of regression in machine learning, and under what condition each of them can be used. If you are new to machine learning, this article will surely help you in understanding the regression modeling concept.
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What is Regression Analysis?
Regression analysis is a predictive modelling technique that analyzes the relation between the target or dependent variable and independent variable in a dataset. The different types of regression analysis techniques get used when the target and independent variables show a linear or non-linear relationship between each other, and the target variable contains continuous values. The regression technique gets used mainly to determine the predictor strength, forecast trend, time series, and in case of cause & effect relation.
Regression analysis is the primary technique to solve the regression problems in machine learning using data modelling. It involves determining the best fit line, which is a line that passes through all the data points in such a way that distance of the line from each data point is minimized.
An example of a regression model in data analysis is linear regression, which can be used to predict a company’s future sales based on historical sales data and advertising spend. For instance, it might show that for every $1,000 spent on advertising, sales increase by $5,000.
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How does regression analysis work?
When conducting a regression analysis, you’re essentially delving into the relationship between two types of variables: the dependent variable and the independent variable(s). To kick things off, you need to pinpoint your dependent variable, which you believe is influenced by one or more independent variables.
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Defining Variables and Gathering Data
Imagine we’re using an example related to event satisfaction and ticket prices. Our dependent variable here is the level of satisfaction with the event, while the independent variable we’re interested in is the price of the event ticket. Now, to get a comprehensive dataset, surveys are an excellent tool. These surveys should cover questions related to both the dependent and independent variables you’ve identified, as types of regression in machine learning and what is regression in ml.
For our example, we’d gather data on historical levels of event satisfaction over the past few years and also collect information about ticket prices. We’re particularly keen on exploring how ticket prices might affect the satisfaction levels of individuals who know regression analysis and types of regression.
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Plotting Data
Now, let’s visualize this data. We’ll plot the satisfaction levels (dependent variable) on the y-axis and the ticket prices (independent variable) on the x-axis. By doing so, we can start to see if there’s any correlation between the two variables.
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Analyzing Correlations
Looking at the plotted data, we might notice patterns. If, hypothetically, we observe that higher ticket prices correspond to higher levels of event satisfaction, that’s interesting. But, we need to delve deeper to understand the degree of influence ticket prices have on satisfaction levels for machine learning regression models.
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Introducing the Regression Line
To do this, we draw a line through the data points. This line, known as the regression line, summarizes the relationship between our independent and dependent variables. It’s something we can calculate using statistical tools like Excel, which linear regression in machine learning.
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Understanding the Regression Line
The regression line tells us how the independent variable (ticket price) affects the dependent variable (event satisfaction). Excel provides us with a formula for this line, which might look something like this: Y = 100 + 7X + error term,regression models.
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Interpreting the Formula
Breaking this down, if there’s no change in the ticket price (X), the satisfaction level (Y) would still be 100. The 7X part indicates that for every unit increase in the ticket price, the satisfaction level increases by 7 points. But it’s essential to note that there’s always an error term involved. This acknowledges that other factors beyond ticket price influence event satisfaction regression techniques in machine learning.
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Considering Error
The presence of an error term reminds us that our regression line is an estimate based on available data. This means the larger the error term, the less certain we can be about the relationship between variables. In short, it’s a reminder that real-world scenarios are complex, and variables interact in ways we might not fully understand.
Types of Regression Analysis Techniques
There are many types of regression analysis techniques, and the use of each method depends upon the number of factors. These factors include the type of target variable, shape of the regression line, and the number of independent variables.
Below are the different regression techniques:
- Linear Regression
- Logistic Regression
- Ridge Regression
- Lasso Regression
- Polynomial Regression
- Bayesian Linear Regression
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The different types of regression models and when to use them in detail:
1. Linear Regression
Linear regression is one of the most basic types of regression in machine learning. The linear regression model consists of a predictor variable and a dependent variable related linearly to each other. In case the data involves more than one independent variable, then linear regression is called multiple linear regression models.
The below-given equation is used to denote the linear regression model:
y=mx+c+e
where m is the slope of the line, c is an intercept, and e represents the error in the model.
The best fit line is determined by varying the values of m and c. The predictor error is the difference between the observed values and the predicted value. The values of m and c get selected in such a way that it gives the minimum predictor error. It is important to note that a simple linear regression model is susceptible to outliers. Therefore, it should not be used in case of big size data.
There are different types of linear regression. The two major types of linear regression are simple linear regression and multiple linear regression. Below is the formula for simple linear regression.
- Here, y is the predicted value of the dependent variable (y) for any value of the independent variable (x)
- β0 is the intercepted, aka the value of y when x is zero
- β1 is the regression coefficient, meaning the expected change in y when x increases
- x is the independent variable
- ∈ is the estimated error in the regression
Simple linear regression can be used:
- To find the intensity of dependency between two variables. Such as the rate of carbon emission and global warming.
- To find the value of the dependent variable on an explicit value of the independent variable. For example, finding the amount of increase in atmospheric temperature with a certain amount of carbon dioxide emission.
In multiple linear regression, a relationship is established between two or more independent variables and the corresponding dependent variables. Below is the equation for multiple linear regression.
- Here, y is the predicted value of the dependent variable
- β0 = Value of y when other parameters are zero
- β1X1= The regression coefficient of the first variable
- …= Repeating the same no matter how many variables you test
- βnXn= Regression coefficient of the last independent variable
- ∈ = Estimated error in the regression
Multiple linear regression can be used:
- To estimate how strongly two or more independent variables influence the single dependent variable. Such as how location, time, condition, and area can influence the price of a property.
- To find the value of the dependent variables at a definite condition of all the independent variables. For example, finding the price of a property located at a certain place, with a specific area and its condition.
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2. Logistic Regression
Logistic regression is one of the types of regression analysis technique, which gets used when the dependent variable is discrete. Example: 0 or 1, true or false, etc. This means the target variable can have only two values, and a sigmoid curve denotes the relation between the target variable and the independent variable.
Logit function is used in Logistic Regression to measure the relationship between the target variable and independent variables. Below is the equation that denotes the logistic regression.
logit(p) = ln(p/(1-p)) = b0+b1X1+b2X2+b3X3….+bkXk
where p is the probability of occurrence of the feature.
For selecting logistic regression, as the regression analyst technique, it should be noted, the size of data is large with the almost equal occurrence of values to come in target variables. Also, there should be no multicollinearity, which means that there should be no correlation between independent variables in the dataset.
3. Ridge Regression
This is another one of the types of regression in machine learning which is usually used when there is a high correlation between the independent variables. This is because, in the case of multi collinear data, the least square estimates give unbiased values. But, in case the collinearity is very high, there can be some bias value. Therefore, a bias matrix is introduced in the equation of Ridge Regression. This is a powerful regression method where the model is less susceptible to overfitting.
Below is the equation used to denote the Ridge Regression, where the introduction of λ (lambda) solves the problem of multicollinearity:
β = (X^{T}X + λ*I)^{-1}X^{T}y
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4. Lasso Regression
Lasso Regression is one of the types of regression in machine learning that performs regularization along with feature selection. It prohibits the absolute size of the regression coefficient. As a result, the coefficient value gets nearer to zero, which does not happen in the case of Ridge Regression.
Due to this, feature selection gets used in Lasso Regression, which allows selecting a set of features from the dataset to build the model. In the case of Lasso Regression, only the required features are used, and the other ones are made zero. This helps in avoiding the overfitting in the model. In case the independent variables are highly collinear, then Lasso regression picks only one variable and makes other variables to shrink to zero.
Below is the equation that represents the Lasso Regression method:
N^{-1}Σ^{N}_{i=1}f(x_{i}, y_{I}, α, β)
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5. Polynomial Regression
Polynomial Regression is another one of the types of regression analysis techniques in machine learning, which is the same as Multiple Linear Regression with a little modification. In Polynomial Regression, the relationship between independent and dependent variables, that is X and Y, is denoted by the n-th degree.
It is a linear model as an estimator. Least Mean Squared Method is used in Polynomial Regression also. The best fit line in Polynomial Regression that passes through all the data points is not a straight line, but a curved line, which depends upon the power of X or value of n.
While trying to reduce the Mean Squared Error to a minimum and to get the best fit line, the model can be prone to overfitting. It is recommended to analyze the curve towards the end as the higher Polynomials can give strange results on extrapolation.
Below equation represents the Polynomial Regression:
l = β0+ β0x1+ε
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6. Bayesian Linear Regression
Bayesian Regression is one of the types of regression in machine learning that uses the Bayes theorem to find out the value of regression coefficients. In this method of regression, the posterior distribution of the features is determined instead of finding the least-squares. Bayesian Linear Regression is like both Linear Regression and Ridge Regression but is more stable than the simple Linear Regression.
People often wonder “what is regression in AI” or “what is regression in machine learning”. Machine learning is a subset of AI; hence, both questions have the same answer.
In the case of regression in AI, different algorithms are used make a machine learn the relationship between the provided data sets and make predictions accordingly. Hence, regression in AI is mainly used to add a level of automation to the machines.
Regression AI is often used in sectors like finance and investment, where establishing a relationship between a single dependent variable and multiple independent variables is a common case. A common example of regression AI will be factors that estimate a house’s price based on its location, size, ROI, etc.
Regression plays a vital role in predictive modelling and is found in many machine learning applications. Algorithms from the regressions provide different perspectives regarding the relationship between the variables and their outcomes. These set models could then be used as a guideline for fresh input data or to find missing data.
As the models are trained to understand a variety of relationships between different variables, they are often extremely helpful in predicting the portfolio performance or stocks and trends. These implementations fall under machine learning in finance.
The very common use of regression in AI includes:
- Predicting a company’s sales or marketing success
- Generating continuous outcomes like stock prices
- Forecasting different trends or customer’s purchase behaviour
Hope this helped to understand what regression is in AI or what is regression in machine learning.
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Why do we use Regression Analysis?
Regression analysis is a powerful statistical tool used in various fields to understand the relationship between variables. Let’s find out what is the main purpose of regression analysis: –
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Understanding Relationships
First and foremost, regression analysis helps us understand how one variable (dependent variable) changes concerning another variable (independent variable). Imagine you’re investigating how study hours affect exam scores. Regression analysis can tell you if there’s a significant relationship between these two factors for supervised machine learning regression and classification.
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Predictive Insights
One of the primary reasons we use regression analysis is for prediction. By analyzing historical data, regression models can forecast future outcomes. For instance, if we have data on past sales and advertising spending, regression analysis can predict future sales based on different advertising budgets.
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Quantifying Relationships
Regression analysis provides us with coefficients that quantify the relationship between variables. These coefficients indicate the strength and direction of the relationship. For instance, a positive coefficient suggests that as one variable increases, the other also tends to increase regression types in machine learning.
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Identifying Significant Factors
In complex systems with multiple variables, regression analysis helps identify which factors significantly influence the outcome. By analyzing the coefficients and statistical significance, we can determine which variables have a meaningful impact. This information is crucial for decision-making and resource allocation.
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Model Validation
Another essential aspect of regression analysis is model validation. Once we develop a regression model, we need to ensure its accuracy and reliability. Through various statistical tests, we assess how well the model fits the data and whether it can be trusted for making predictions.
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Risk Assessment
Regression analysis is also valuable in risk assessment. By analyzing historical data and identifying patterns, businesses can assess and mitigate risks more effectively. For example, a financial institution may use regression analysis to predict the likelihood of default based on various financial indicators.
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Optimization
In many scenarios, regression analysis helps optimize processes and strategies. By understanding the relationships between variables, organizations can fine-tune their operations for better outcomes. For instance, a manufacturing company may use regression analysis to optimize production processes and minimize costs and regression and its types.
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Continuous Improvement
Lastly, regression analysis supports continuous improvement initiatives. By analyzing data over time, organizations can identify trends, detect anomalies, and make necessary adjustments to improve performance. This iterative process helps businesses stay competitive and adapt to changing environments.
What are the Benefits of Regression Analysis?
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Quantifying Relationships
Regression analysis allows researchers to quantify the relationship between a dependent variable and one or more independent variables. By providing numerical coefficients, it helps in understanding the strength and direction of these relationships. For instance, in a study examining the relationship between study hours and exam scores, regression analysis can determine how much exam scores change with each additional hour of study.
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Prediction and Forecasting
One of the primary benefits of regression analysis is its predictive capability. By establishing a relationship between variables based on historical data, regression models can be used to forecast future outcomes. For instance, in finance, regression analysis is utilized to predict stock prices based on factors like company performance, market trends, and economic indicators.
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Identifying Significant Variables
Regression analysis helps in identifying which independent variables have a significant impact on the dependent variable. Through statistical tests such as t-tests or F-tests, researchers can determine the significance of each variable in explaining the variation in the dependent variable. This helps in focusing resources and efforts on the most influential factors.
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Model Evaluation
Regression analysis provides tools for assessing the goodness of fit of the model. Metrics like R-squared, adjusted R-squared, and root mean square error (RMSE) measure how well the model fits the data. These evaluations help in determining the reliability and accuracy of the regression model, guiding researchers in decision-making processes.
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Control and Optimization
In experimental research or process optimization, regression analysis helps in identifying the optimal settings for independent variables to achieve a desired outcome. By analyzing the relationship between inputs and outputs, regression models assist in controlling and optimizing processes, leading to improved efficiency and performance.
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Risk Management
Regression analysis is instrumental in risk management by identifying factors that contribute to risk exposure. For instance, in insurance, regression models help in assessing the relationship between variables such as age, health status, and lifestyle habits with the likelihood of filing a claim. This enables insurers to set premiums and manage risks effectively.
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Decision Support
Regression analysis provides valuable insights to support decision-making processes. Whether it’s determining marketing strategies based on consumer behavior, allocating resources efficiently, or assessing the impact of policy changes, regression analysis aids in making informed decisions grounded in empirical evidence of regression analysis in machine learning
Conclusion
In addition to the above regression methods, there are many other types of regression in machine learning, including Elastic Net Regression, JackKnife Regression, Stepwise Regression, and Ecological Regression.
These different types of regression analysis techniques can be used to build the model depending upon the kind of data available or the one that gives the maximum accuracy. You can explore these techniques more or can go through the course of supervised learning on our website.
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