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Everything You Need To know About First Machine Learning Model - Linear Regression In ML

  • February 21, 2023
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Bharani Kumar Depuru is a well known IT personality from Hyderabad. He is the Founder and Director of Innodatatics Pvt Ltd and 360DigiTMG. Bharani Kumar is an IIT and ISB alumni with more than 18+ years of experience, he held prominent positions in the IT elites like HSBC, ITC Infotech, Infosys, and Deloitte. He is a prevalent IT consultant specializing in Industrial Revolution 4.0 implementation, Data Analytics practice setup, Artificial Intelligence, Big Data Analytics, Industrial IoT, Business Intelligence and Business Management. Bharani Kumar is also the chief trainer at 360DigiTMG with more than Ten years of experience and has been making the IT transition journey easy for his students. 360DigiTMG is at the forefront of delivering quality education, thereby bridging the gap between academia and industry.

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The input and output variables are the main focus of supervised learning, which uses an algorithm to forecast the results. For example, suppose a new input variable is introduced. A developing machine learning technology allows computers to learn autonomously from historical data. Machine learning uses various techniques to create mathematical models and make predictions based on previous information or data. It is utilized for many jobs, including image identification, speech recognition, email filtering, Facebook auto-tagging, recommender systems, and many others.

Linear Regression In Machine Learning

Data analysis and interpretation have used statistical methods for a very long period. In machine learning analysis, linear regression is crucial for assessing data and determining a clear relationship between two or more variables. Regression measures the extent to which the dependent variable varies from the independent variable. Regression is referred to as simple or multiple regression depending on the number of independent variables, such as single or multiple variables. In machine learning, the linear regression algorithm is a supervised learning method for approximating the mapping function to obtain the best predictions. We will learn about linear regression for machine learning in this article.

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What is Machine Learning?

In the actual world, we are surrounded by people who can learn from their experiences thanks to their capacity for learning, and we also have computers or other robots that carry out our orders. Can a machine, however, learn from past knowledge or experiences the same way people do? As a result, machine learning is now involved.

Some claim that machine learning is a subfield of artificial intelligence that focuses mostly on developing algorithms that allow a computer to learn from data and past experiences independently. However, in 1959, Arthur Samuel first used "machine learning." To put it simply, we may say that it is:

With the assistance of machine learning, a machine may predict outcomes without being explicitly programmed and automatically learn from data.

Without being explicitly coded, machine learning algorithms build a mathematical model from past sample data, or "training data," to assist in generating predictions or judgments. For example, one can use machine learning with statistics and computer science to construct prediction models. Machine learning either creates or incorporates learning-from-the-past algorithms. Consequently, as we provide more information, the performance will improve.

Linear Regression In Machine Learning

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What is the Importance of Machine Learning?

The objective of machine learning has been around for a while. The more you use the program, the more it uses algorithms to forecast outcomes and learn from experience.

Machine learning is a field that studies the research and creation of algorithms that can learn from data and make predictions.

Due to its ability to solve issues quickly and on a large scale that cannot be matched by a human mind alone, ML is helpful. Machines can be trained to recognize patterns in and relationships between incoming data by using enormous quantities of computational power, which you can use to perform a single activity or several focused tasks and automate repetitive tasks.

What is Regression?

Let's familiarise ourselves with regression first before learning about linear regression. Regression is a technique for estimating a target value from separate predictors. It is a statistical tool used to determine the association between one or more factors, frequently referred to as independent variables, and the result variable, also known as the dependent variable. The main applications of this approach are predicting and determining the causal connections between variables. The primary factors of regression algorithms' differences are the type of relationship between an independent and dependent variable and the number of independent variables. Check out 360digiTMG's linear regression if you want more information about linear regression. In this course, you will discover the necessity of linear regression and its function and practical applications. Both the mathematical and experimental components are emphasized throughout the course.

What Does Machine Learning's Linear Regression Mean?

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An algorithm that corresponds to supervised machine learning is linear regression. Based on the data points for the independent variables, it attempts to apply relations that would forecast the outcome of an event. The connection is often a straight line that fits the various data points as closely as possible. A continuous form, or numerical value, is the output. For instance, the outcome may be money-based revenue or sales, the volume of goods sold, etc. The independent variable in the example above can be one or many.

Numerous Names of Linear Regression:

Things can get complex once you start delving into linear regression.

Because linear regression has been around for a long time (more than 200 years), every angle you may explore has been, and frequently each grade has a new and different name.

A model in which the input variables (x) and the single output variable are assumed to have a linear relationship is known as linear regression (y). That y may be calculated from a linear combination of the input variables (x).

The technique is simple linear regression when only one input variable (x) exists. However, linear regression is frequently used in statistical literature when multiple input variables exist.

The most popular method, Ordinary Least Squares, can be used to prepare or train a linear regression equation using data. Therefore, a model created in this manner is frequently referred to as Ordinary Least Squares Linear Regression or simply Least Squares Regression.

Linear Regression In Machine Learning

Linear Regression Model:

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Learning a linear regression model entails calculating the coefficient values for the representation using the data at hand.

This section will quickly review four methods for creating a linear regression model. Of course, there needs to be more than this information to implement them from scratch, but it is sufficient to understand the computation and trade-offs involved.

  • Simple Linear Regression: With simple linear regression, we can utilize statistics to estimate the coefficients with a single input. You must perform the necessary statistical analysis on the data to determine means, standard deviations, correlations, and covariance. To traverse the data and do statistical calculations, it must all be accessible. Although entertaining as an exercise in Excel, this could be more practical.
  • Ordinary Least Squares: One can use Ordinary Least Squares to estimate the coefficient values with several inputs. The Ordinary Least Squares method aims to reduce the total squared residuals. For example, given a regression line across the data, we square the distance between each data point and the regression line and add the squared errors for all the data points. Ordinary least squares attempt to reduce this amount.
  • Gradient Descent: When we have one or more inputs, you can minimize the model'smodel's error on your training data iteratively to optimize the coefficient values. Gradient Descent is the procedure's name, and it functions by starting with random values for each coefficient. Each pair of input and output values has its sum of squared errors calculated. The scale factor utilized is the learning rate, and the coefficients are modified to minimize the error. The process can be repeated until a minimum sum squared error is reached or no further improvement is achievable.
  • Regularization: Regularization methods are extensions of the linear model'smodel's training. These aim to lower the complexity of the model while also minimizing the sum of the squared errors of the model on the training data (using conventional least squares) (like the number or an absolute size of the sum of all the coefficients in the model). These techniques work well when your input values are collinear, and ordinary least squares would overfit the training set.

Representation of a Linear Regression Model:

Because of how easily it can be represented, linear regression is a desirable model.

A linear equation that combines a particular set of input values (x) and yields the expected output for that set of input values serves as the representation (y). As a result, both the output value (y) and the input values (x) are numbers.

Each column or input value in the linear equation receives one scale factor, known as a coefficient and denoted by the capital Greek letter Beta (B). In addition, one more coefficient, commonly known as the intercept or bias coefficient, is added, providing the line an extra degree of freedom.

For instance, the model form for a straightforward regression problem (one x and one y) would be Y= 0 + 1x.

When there are multiple inputs, the line in higher dimensions is referred to as a plane or a hyper-plane (x). As a result, the representation takes the form of an equation, and the exact coefficient values (in the case above, 0 and 1) are employed.

Linear Regression In Machine Learning

Term Definitions for Linear Regression:

Before understanding the linear regression process, it's critical to understand the following terminology.

  • Cost Function:

    Based on the linear equation represented below, the best fit line can be determined.

    Linear Regression In Machine Learning

    Y stands for the dependent variable, which needs to be forecasted.

    The intercept b0 designates the point on a line that touches the y-axis.

    X stands for the independent factors that affect the prediction of Y, and b1 is the lifeline's slope.

    The letter e stands for the error in the final prediction.

    To create the best fit line for the data points, the cost function offers the optimal values for b0 and b1. It is possible to obtain optimal values for b0 and b1 by transforming the problem into a minimization problem. This issue has a minimal discrepancy between actual and forecasted values.

    Linear Regression In Machine Learning

    Linear Regression In Machine Learning

    To reduce the error, we choose the function mentioned above. Then, we divide the total number of data points by the square of the error difference and add the error across all data points. The obtained value then provides the averaged square error across all data points.

    We adjust the b0 and b1 to ensure that the MSE value is set at the lowest possible level, also known as MSE (Mean Squared Error).

  • Gradient Descent:

    Gradient descent is the next crucial phrase to comprehend while discussing linear regression. It is a technique for altering the values of b0 and b1 to lower the MSE. The goal is continuously iterating the b0 and b1 values until the MSE is minimized.

    We use the gradients from the cost function to update b0 and b1. We take partial derivatives concerning b0 and b1 to determine these gradients. The gradients are the partial derivatives utilized to update the values of b0 and b1.

    A bigger learning rate requires less time, but a lower learning rate takes longer to reach the minimum. Therefore, the duration is shorter, but it will likely exceed the minimum value.

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Examples of Linear Regression Applications:

Agriculture, banking, finance, education, marketing, and many more are examples of industries using linear regression. Real-world scenarios involving machine learning and forecasting output as a continuous variable typically require linear regression.

In banking, linear regression is used to forecast the likelihood of loan defaults, while it can be used in agriculture to indicate crop production and rainfall amounts. Linear regression is used in finance to forecast stock values and evaluate associated risks. In the healthcare industry, linear regression is useful for modeling healthcare expenditures, and forecasting patient hospital stays, among other things.

Players' performance in upcoming games can be predicted using linear regression in sports analytics. It can also be applied in education to forecast student success in various courses.

Additionally, companies utilize linear regression to forecast product sales, anticipate product demand, select marketing, and advertising tactics, and more.

Advantages of Linear Regression:

  • Linear regression works well to determine the nature of the association between various variables in linear datasets.
  • The implementation of linear regression models and linear regression algorithms are both simple.
  • By using dimensionality reduction strategies such as regularisation (L1 and L2) and cross-validation, linear regression models can avoid over-fitting.

Disadvantages of Linear Regression:

  • A significant drawback of linear regression is that it assumes linearity between the independent and dependent variables. It makes the often improbable assumption that the dependent and independent variables have a straight-line relationship.
  • It has noise and overfitting issues. Linear regression may not be the best option in datasets when the number of observations is smaller than the number of attributes since it can result in overfitting. It is so that the algorithm may consider the noise while creating the model.
  • Because the dataset is sensitive to outliers, it is crucial to pre-process and eliminate them before applying linear regression to the data.
  • It rejects the notion of multicollinearity. The algorithm assumes no link between the independent variables, so any multicollinearity between the variables must be reduced using dimensionality reduction techniques before applying linear regression.

Key Takeaway:

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