Linear Regression in Machine Learning: Everything You Need to Know

Different machine learning technology are used in several walks of our daily lives to find solutions to everyday problems in a way that is backed by data, analysis, and experience. These machine learning algorithms play a very important role in not only identifying text, images, and videos but are instrumental in improving medical solutions, cybersecurity, marketing, customer services, and many other aspects or areas that concern our regular lives.

There are primarily two types of machine learning algorithms that all of the algorithms are divided into. These are supervised and unsupervised machine learning algorithms. Our focus in this blog will only be on supervised machine learning algorithms, and especially – linear regression. Let us start by understanding supervised machine learning algorithms. 

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What are supervised learning algorithms?

These machine learning algorithms are ones that we train to predict a well-established output that is dependent on the data that is inputted by the user. The algorithm trains the model to deliver outputs on a given data set. At the start, the system has access to both input and output data. The job of the system is to define rules that are going to map the input to the output.

The training of the model continues until the performance is at its optimal level. After the training, the system is able to assign outputs objects that it didn’t encounter while it was being trained. In the ideal scenario, this process is quite accurate and doesn’t take a lot of time. There are two types of supervised learning algorithms, namely, classification and regression. 

We will discuss both briefly, before jumping straight into our primary topic of discussion. 

1. Classification

These are supervised machine learning algorithms that have a simple goal of reproducing class assignments. The learning technique is often considered for situations in which data separation is required. It separates data into classes by predicting responses. For example, the weather forecast for a given day, identifying a specific type of photo from an album, and separating spam from email. 

2. Regression

The learning technique is used to serve the objective of reproducing output values. In other words, it is used in situations in which we need to fit data to a specific value. For example, it is often used to estimate the price of different items. Regression can be used to predict more things than you can possibly imagine. 

Types of regressions

Logistic and linear regressions are the two most important types of regression that exist in the modern world of machine learning and data science. However, there are others as well, but they are used quite sparingly. There is no denying the fact that we can perform numerous regressions on a given data set or use for different situations.

Every form of regression has its pros and cons and is suitable for specific conditions. While we will focus only on linear aggression, you need to know the complete background to familiarise yourself with its workings. 

It is the reason we are taking the discussion step by step. 

What is regression analysis?

Regression analysis is nothing but a predictive modelling methodology that aims to investigate the relation that exists between independent variables or predictors and dependent variables or targets. This analysis is used in a host of different things, including time series modelling, forecasting, and others.

For instance, if you want to study the relationship between road accidents and casual driving, there is no better technique than regression analysis for this job. It plays a very important role in both analyzing and modelling data. This is done by fitting a line or curve to different data points in a way that we can minimize the difference in data point distances from the line, or the curve. 

What’s the need for regression analysis? 

Regression analysis is used to predict the relationship between variable, only if they are two or more in number. Let’s understand how this works with a simple example. Suppose you are given a task that requires you to come up with a company’s sales growth in estimation for a given period keeping in mind the existing economic conditions.

Now the company data tells you that the sales grew around two times the growth in the economy. We can use this data to estimate the company’s growth in sales in the future by taking insights from the past and current information. 

Using regression analysis can offer you a number of benefits when working with data or making a prediction on the data set. It can be used to point towards the significant relationships between independent and dependent variables. It is used to indicate the impact of dependent variable experiences from multiple independent variables.

It allows the comparison of the effects of different variables that belong to different measurement scales. These things go a long way in helping data scientists, researchers, and data analysts in building predictive models based on the most appropriate set of variables. 

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What do you need to keep in mind to choose the right regression model?

Well, things are usually a lot easier when you just have two or three techniques to choose from. However, if we so many options at our disposal, then the decision becomes a lot more overwhelming. Now you can’t just choose linear regression because the outcome is continuous. Or go for logistic regression if the outcome is binary. There are more things to consider when we choose a regression model for our problem.

As we have already mentioned, there are more regression models available then we can get our heads around. So what is it that we should keep in mind while making the selection? There are a few things that are important – data dimensionality, type of dependent and independent variable, and other properties of the data in question. Here are a few important things to consider while choosing the right regression model:

Data exploration is the key to building predictive models. No wonder it must be amongst the first thing you should do before you make the selection. Explore data for identifying variable impact and relationship.

Evaluate different regression models for prediction through cross-validation. Separate your data set into training and validation groups. The mean squared difference between predicted and observed values will provide an insight into the prediction accuracy.

Use Ridge, ElasticNet, and other regression regularisation methods to choose the right model for data sets that have variables with high multicollinearity and dimensionality.

To make a comparison between different regression models ad their suitability, we can analyze parameters, such as AIC, BIC, R-square, error term, and others. There is one more criterion, which is called Mallow’s Cp. It compares the model with different submodels to look out for bias. 

Never go with the automatic model selection method if the data set that you are working with has a number of puzzling variables. If you do it, you would be moving towards putting those variables in the model all at once. 

Your objective is also important for selecting the right regression model. Whether you need a powerful model, a simple one, or a statistically significant one, will depend on your objective.

What is linear regression?

Let’s know more about what is linear regression. It is one of the machine learning techniques that fall under supervised learning. The rise in the demand and use of machine learning techniques is behind the sudden upsurge in the use of linear regression in several areas. Did you know that multilayer perceptron layers are known to perform linear regression? Let us now shed some light on the assumptions that linear regression is known to make about the data sets it is applied to. 

1. Autocorrelation:

This assumption made by linear regression indicates little to no autocorrelation in data. Autocorrelation takes place when residual errors are dependent on each other in one or the other way.

2. Multi-collinearity:

This assumption says that data multi-collinearity either doesn’t exist at all or is present scarcely. Multi-collinearity happens when independent features or variables show some dependency.

3. Variable relationship:

The model has an assumption that there is a linear relationship between feature and response variables.

A few instances where you can use linear regression include the estimation of the price of a house depending on the number of rooms it has, determining how well a plant will grow depending on how frequently it is watered, and so on. For all these instances, you would already have an idea about the type of relationship that exists between different variables.

When you use linear regression analysis, you back your idea or hypothesis with data. When you develop a better understanding of the relationship between different variables, you are in a better position to make powerful predictions. If you don’t already know, let us tell you that linear regression is a supervised machine learning technique as well as a statistical model.

In machine learning terms, the regression model is your machine, and learning relates to this model being trained on a data set, which helps it learn the relationship between variables and enables it to make data-backed predictions.

How does linear regression work?

Before we run the analysis, let us assume that we have two types of teams – those that perform their jobs well and those that don’t. There are could several reasons why a team isn’t good at what it is doing. It could be because it doesn’t have the right skill set or it doesn’t have the experience required to perform certain duties at work. But, you can never be certain of what it is. 

We can use linear regression to find out candidates that have all that’s required to be the best fit for a particular team that is involved in a particular line of work. This will help us in selecting candidates that are highly likely to be good at their jobs. 

The objective that regression analysis serves is creating a trend curve or line that is suitable for the data in question. This helps us in finding out how one parameter (independent variables) is related to the other parameter (dependent variables).

Before anything else, we need to first have a closer look at all the attributes of different candidates and find out whether they are correlated in some way or the other. If we find some correlations, we can go ahead start making predictions based on these attributes. 

Relationship exploration in the data is done by using a trend curve or line and plotting the data. The curve or line will show us if there is any correlation. We can now use linear regression to refute or accept relationships. When the relationship is confirmed, we can use the regression algorithm to learn his relationship. This will enable us to make the right predictions. We will be able to more accurately predict whether a candidate is right for the job or not.

Importance of training a model

The process involved in training a linear regression model is similar in many ways to how other machine learning models are trained. We need to work on a training data set and model the relationship of its variables in a way that doesn’t impact the ability of the model to predict new data samples. Model is trained to improve your prediction equation continuously.

It is done by iteratively looping through the given dataset. Every time you repeat this action, you simultaneously update the bias and weight value in the direction that the gradient or cost function indicates. The stage of the completion of training is reached when an error threshold is touched or when there is no reduction in cost with the training iterations that follow.

Before we start training the model, there are a few things that we need to prepare. We need to set the number of iteration required as well as the rate of learning. Apart from this, we also have to set default values for our weights. Also, record the progress that we are able to achieve with every repeat. 

What is regularisation?

If we talk about the linear regression variants that are preferred over others, then we will have to mention those that have added regularisation. Regularisation involves penalizing those weights in a model that have larger absolute values than others.

Regularisation is done to limit overfitting, which is what a model often does as it reproduces the training data relationships too closely. It doesn’t allow the model to generalize never seen before samples as it is supposed to. 

When do we use linear regression?

The power of linear regression lies in how simple it is. It means that it can be used to find answers to almost every question. Before using a linear regression algorithm, you must ensure that your data set meets the required conditions that it works on.

The most important of these conditions is the existence of a linear relationship between the variables of your data set. This allows them to be easily plotted. You need to see the difference that exists between the predicted values and achieved value in real are constant. The predicted values should still be independent, and the correlation between predictors should be too close for comfort. 

You can simply plot your data along a line and then study its structure thoroughly to see whether your data set meets the desired conditions or not.

Linear regression uses

The simplicity by which linear aggression makes interpretations at the molecular level easier is one of its biggest advantages. Linear regression can be applied to all those data sets where variables have a linear relationship. 

Businesses can use the linear regression algorithm is their sales data. Suppose you are a business that is planning to launch a new product. But, you are not really sure at what price you should sell this product. You can check how your customers are responding to your product by selling it at a few well thought of price points. This will allow you to generalize the relationship between your product sales and price. With linear regression, you will be able to determine a price point that customers are more likely to accept. 

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Linear regression can also be used at different stages of the sourcing and production of a product. These models are widely used in academic, scientific, and medical fields. For instance, farmers can model a system that allows them to use environmental conditions to their benefit. This will help them in working with the elements in such a way that they cause the minimum damage to their crop yield and profit.

In addition to these, it can be used in healthcare, archaeology, and labour amongst other areas. is how the interpretation on a linear model 

Conclusion

Regression analysis is a widely adopted tool that uses mathematics to sort out variables that can have a direct or indirect impact on the final data. It is important to keep it in mind while analysis is in play! Linear regression is one of the most common algorithms used by data scientists to establish linear relationships between the dataset’s variables, and its mathematical model is necessary for predictive analysis.

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