Linear regression is one of the algorithms in Machine Learning required in making predictions of real or numerical variables like the product, price, salary, sales, age, etc. It is considered to be the easiest and most popular statistical method used for predictive analysis.

Before talking about linear regression, you need to know what regression is.

Regression in machine learning comprises the mathematical methods used by data scientists while predicting a continuous outcome (y), dependent on the value of one or more predictor variables (x). And because of its ease-of-use and time-consuming characteristics in predicting and forecasting, linear regression is considered the most popular form of regression method. So if you understand how linear regression in machine learning works, you can surely go for linear regression in machine learning courses to understand it in depth.

How Does Linear Regression In Machine Learning Work?

The linear relationship of the dependent and the independent variable is portrayed by linear regression. It brings out how the value of the dependent variable changes with the change in the value of independent variables.

Mathematically, linear regression is represented as-

y= a0 a1x ε

where,

Y= Target Variable ( Dependent Variable)

a0= Line Intercept ( Provides an additional degree of freedom)

a1= Coefficient of Linear Regression ( Each input value’s scale factor)

X= Predictor Variable ( Independent Variable)

E= Error

In the above expression, the values of Y and X variables are the training datasets used to represent the linear regression model.

What Are The Different Types Of Linear Regression?

Depending on the number of the independent variables, there are two types of linear regression-

1. Simple Linear Regression: If the prediction of the value of the numerical dependent variable relies on a single independent variable, then such an algorithm is considered simple linear regression.

2. Multiple Linear RegressionIf the prediction of the value of the numerical dependent variable relies on more than one independent variable, then such an algorithm is considered multiple linear regression.

Learning Of The Model Linear Regression

To estimate the values of the coefficients used in the representation with the only data available, we require the learning of a linear regression model. There are four techniques essential for the preparation of a linear regression model. The model is so well-studied in machine learning classes that there are other techniques too, except for the following four techniques:

1. Ordinary Least Squares:

The procedure used in minimizing the sum of the squared residuals is known as Ordinary Least Squares. If there is more than one input, it is required to estimate the coefficients’ values.

It means being provided with the data of a regression line, the distance from the regression line, and each of the data points is calculated. Then, it is squared, and all the squared errors are added together. The ordinary least squares seek to minimize this particular quantity.

The optimal value for the coefficient is then estimated using the linear algebra operations, and the data is treated as a matrix using the above approach. It implies that you must have adequate memory to fit all the data available to perform matrix operations. It may be unfamiliar for you to accomplish the ordinary least squares yourself except in linear algebra. For fast calculation, this method is highly recommended to you.

If you are provided with one or more inputs, then by frequentlyminimizing the error of the model of your training data, you can optimize the values of the coefficients. This operation is considered as the Gradient Descent.

It works by taking the random value of each coefficient at the beginning, and then the calculation for each pair of output and input values is done by summing up the squared errors. As a scale factor, a learning rate is being used, and the coefficients are then updated in the direction en route to minimize the error. This method is continuously repeated until the minimum sum squared error, or there is no possibility of any further improvement.

While using this method, for determining the size of the development step to grab on each iteration of the process, you need to select a learning rate (alpha) parameter. Because of its simple, straightforward understanding characteristics, Gradient Descent is practiced in regression learning. It is mainly used when provided with a large dataset, either in the number of rows or columns, which may not fit into the memory.

3. Regularisation:

The regularisation method of the training of the linear model seeks to have an extension as it could be useful in reducing the complexity of the model (accurate size or number of the sum of all coefficients of the model). It also aids in minimizing the sum of the squared error of the training data model (by using the ordinary least squares method).

There are two popular procedures of regularisation in regression learning, and those are:

a. Lasso Regression: In this procedure, the Ordinary Least Squares is modified for minimizing the absolute sum of all the coefficients. It is also called L1 regularization.

b. Ridge Regression: In this process, the Ordinary Least Squares is modified for minimizing the squared absolute sum of all the coefficients. It is also called L2 regularization.

The above methods effectively use collinearity in your output values, and the ordinary least squares overfit the training data.

4. Simple Linear Regression:

Among all the other processes, simple linear regression is the simplest as when you have a single output; then, with the help of simple linear regression, you can use statistics to estimate the value of coefficients. The statistical properties like means, correlations, standard deviations, and covariance are required to be calculated, and you must make sure that all the data are available to calculate and traverse the statistics. It usually is not very useful in practice but is fun while doing an exercise in excel.

Assumptions Of Linear Regression

Here are some assumptions, or you could say some formal checks while building a linear regression model that ensures you get the best possible result from a particular dataset.

a. Linear relationship between the target and the features helps in assuming the linear relationship between the dependent and independent variables.

b. No or small multi-collinearity between the features: Multicollinearity is considered the high correlation between the features. It isn’t easy to determine which predictor variable affects the target variable and which one is not. It is thus assumed that the model has less or no multi-collinearityamong the independent variables.

c. Homoscedasticity Assumption: Homoscedasticity is a situation where the error term for all the values of the features is the same. With it, the distribution of data in a scattered plot should not be transparent.

d. The normal distribution of error terms: According to the assumption of the linear regression model, there should be a normal distribution of error terms.  This is because not having a normal distribution may result in the confidence interval being either too wide or too narrow, causing difficulties in finding coefficients.

e. No Autocorrelation: Autocorrelation occurs if there is a dependency between residual errors, and it may drastically reduce the model’s accuracy. So, the model of linear regression assumes no correlation in the error terms.

CONCLUSION

It is easily understandable from the above explanations that linear regression in machine learning is an algorithm that is entirely based on advanced learning. To know what linearregression in machine learning is in more detail, go for the university of texas ai and machine learning online course from Great Learning.