What is Linear Regression?
Linear regression is a predictive analysis method that measures probabilities to assess the likelihood of an event. It focuses on two key aspects: the quality of predictor variables and their significance. Predictor variables must effectively forecast the outcome variable, and their impact on the outcome must be significant. With these factors, linear regression explains the relationship between a dependent variable and one or more independent variables, leading to probability measurements.
There are six types of linear regression algorithms
- Simple linear regression
- Multiple linear regression
- Logistic regression
- Ordinal regression
- Multinomial regression
- Discriminant analysis
Multiple Linear Regression
Multiple linear regression involves assessing multiple independent variables to predict a single dependent variable. It’s a step up from simple linear regression, which examines one independent and one dependent variable. For both, the independent variables must be interval, ratio, or dichotomous, while the dependent variable must be either interval or ratio.
Ordinal Regression
Ordinal regression analyzes a single ordinal dependent variable and one or more independent variables, which should be nominal or dichotomous. It can handle multiple independent variables based on the data used in the algorithm.
Multiple Linear Regression in Machine Learning
Multinomial regression involves one nominal dependent variable and one or more independent variables, which can be interval, ratio, or dichotomous. This regression type is used when the dependent variable has multiple categories without a specific order.
Discriminant Analysis
Discriminant analysis involves one nominal dependent variable and one or more independent variables, which are interval or ratio. Researchers select discriminant analysis based on the fit between their data and research goals, ensuring the chosen method aligns with their objectives for accurate and successful results in linear regression.
How Does Linear Regression Work?
Linear regression, specifically simple linear regression, involves analyzing the relationship between one dependent variable and one independent variable. The model is trained with formulas that define how variables interact. This training enables the model to determine the relationship between the independent and dependent variables. Once trained, data is input into the model to predict outcomes based on these relationships. Unlike decision trees, which explore various possible outcomes, linear regression focuses on predicting the probability of a specific outcome based on predefined data. To benefit from linear regression, you need a clear theory and relevant data to test that theory.
When Should Linear Regression be Used?
Use linear regression when you have a clear goal and relevant data. Input your dependent and independent variables into the model to determine if the desired outcome is likely. If unsure, explore other algorithms to develop a theory first, then use linear regression to test and refine it. Applications include budgeting, agriculture, and inventory management.
For example, in budgeting, linear regression can help predict fuel costs. Track money spent on gas and miles driven to estimate how much gas is needed for future trips. Calculate the cost by multiplying miles by the gas cost determined from the regression analysis.
Agriculture
In agriculture, linear regression can help farmers identify what types of variables are going to affect things such as their crops. For example, let’s say a farmer was looking into their crop yield and wanted to know how much certain independent variables affected his crop yield. In this case, he could run an analysis where he identifies how much these independent variables have affected crop yield in the past to get an understanding of what is likely to affect his crop yield. He might test against amount of rainfall, amount of sunshine, pesticides used, farming practices used, and other independent variables to see how much these independent variables have affected his crop yield. As a result, he would be able to get an accurate understanding as to what would affect his yield, and possibly be able to create a plan to offset anything that may negatively impact his yield.
Retail – Ordering
In retail, linear regression can be used to help companies identify how much products they should be ordering with each order. They would be able to measure the number of products sold against how long it took for those products to sell. In this case, the dependent variable would be the passing of a set period of time (the time between orders) and the independent variable would be the number of products sold in that timeframe. Through this algorithm, the retailer could identify how many products were consistently being sold in that time period so that they could identify how many products they needed to order. This way, they order enough to keep up with supply and demand, but not so much that they find themselves buried in excess products that their customers are not purchasing.
Logistic regression machine learning
Logistic regression is a form of linear regression specifically designed for situations where the dependent variable is binary, meaning it has only two possible outcomes, often represented as 0 and 1. Unlike other types of linear regression, logistic regression is used to estimate the probability of a specific outcome by modeling the relationship between one or more independent variables (which can be nominal, ordinal, interval, or ratio) and a binary dependent variable.
The key difference between logistic regression and other forms of linear regression is that logistic regression is constrained to produce probabilities that are between 0 and 1, which makes it particularly useful for binary classification tasks. The logistic model uses a logistic function to map any linear combination of the independent variables to a probability value, which then indicates the likelihood of the dependent variable being 0 or 1.
One of the challenges with logistic regression is that the output is often more difficult to interpret than the results from other linear regression models. This is because the relationship between the dependent and independent variables is expressed in terms of odds and probabilities, rather than direct numerical predictions. As such, a solid understanding of statistical concepts and binary classification is necessary to interpret the results effectively.
Logistic regression is commonly used in fields like medicine, social sciences, and finance, where the goal is to determine the likelihood of a particular event occurring, such as the presence or absence of a disease, the success or failure of a marketing campaign, or the default or non-default of a loan.
How Does Logistic Regression Work?
Logistic regression is similar to simple linear regression but focuses on a dichotomous (binary) dependent variable.
- Identify Variables
The dependent variable must be binary, while independent variables can be ratios, nominals, ordinals, or intervals.
- Input Data:
Input the variables into the logistic regression model.
- Plot Data:
The model plots the data on a graph with the dependent variable on the y-axis and independent variables on the x-axis.
- Generate Curve:
Instead of a straight line, logistic regression uses a curved line that starts at the bottom left and curves up to the right, showing the probability of the dependent variable’s outcomes.
When Can Logistic Regression Be Used?
Logistic regression is widely used in machine learning within medical and social fields. In medicine, it’s applied to predict outcomes like mortality in trauma cases (e.g., Trauma and Injury Severity Score) or the likelihood of developing diseases such as diabetes or coronary heart disease, based on patient characteristics. This helps doctors decide on appropriate diagnostic and treatment paths. In socioeconomics, logistic regression can predict factors like labor force participation, home ownership, or mortgage management.that may be relevant to a person’s lifestyle. Through taking a dependent, such as what they are looking into a person’s likelihood of experiencing, and applying independent variables such as their demographic classification, the logistic regression algorithm can identify probabilities.