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HomeBlogData ScienceLinear Regression in Machine Learning: A Comprehensive Guide
Statistical techniques have been used for Data Analysis and Interpretation for a long time. Linear Regression in Machine Learning analysis is important for evaluating data and establishing a definite relationship between two or more variables. Regression quantifies how the dependent variable changes as the independent variable itself take different values. Regression is referred to as simple or multiple regression depending on the number of independent variables, like single or multiple variables respectively.
Machine Learning is the solution when data is large, and relation becomes difficult to quantify manually. Here, the model is trained on available data of a number of independent variables with the statistical tool of Linear Regression to determine how the relationship can be obtained with great accuracy. This article has a practical example of Regression in Machine Learning for beginners. These days a comprehensive Data Science online course can help build the necessary foundation to the essential concepts of Regression in Machine Learning.
Linear Regression is an algorithm that belongs to supervised Machine Learning. It tries to apply relations that will predict the outcome of an event based on the independent variable data points. The relation is usually a straight line that best fits the different data points as close as possible. The output is of a continuous form, i.e., numerical value. For example, the output could be revenue or sales in currency, the number of products sold, etc. In the above example, the independent variable can be single or multiple.
Linear regression can be expressed mathematically as:
y= β0+ β 1x+ ε
Here,
The last parameter, random error ε, is required as the best fit line also doesn't include the data points perfectly.
Since the Linear Regression algorithm represents a linear relationship between a dependent (y) and one or more independent (y) variables, it is known as Linear Regression. This means it finds how the value of the dependent variable changes according to the change in the value of the independent variable. The relation between independent and dependent variables is a straight line with a slope.
Linear Regression can be broadly classified into two types of algorithms:
A simple straight-line equation involving slope (dy/dx) and intercept (an integer/continuous value) is utilized in simple Linear Regression. Here a simple form is:
y=mx+c where y denotes the output x is the independent variable, and c is the intercept when x=0. With this equation, the algorithm trains the model of machine learning and gives the most accurate output
When a number of independent variables more than one, the governing linear equation applicable to regression takes a different form like:
y= c+m1x1+m2x2… mnxn where represents the coefficient responsible for impact of different independent variables x1, x2 etc. This machine learning algorithm, when applied, finds the values of coefficients m1, m2, etc., and gives the best fitting line.
When the best fitting line is not a straight line but a curve, it is referred to as Non-Linear Regression.
The output which is obtained or predicted by an algorithm is referred to as yˆ (pronounced as yhat). The difference between the actual and predicted values is the error, i.e., y - yˆy^. Different values of y- yˆy^ (loss function) are obtained when the model repeatedly tries to find the best relation. The average summation of all loss function values is called the cost function. The machine learning algorithm tries to obtain the minimum value of the cost function. In other words, it tries to reach the global minimum.
where J = cost function, n= number of observations (i = 1 to n), ∑ = summation, predi = predicted output and yi = actual value.
As shown above, the error difference is squared for each value and then the average of the sum of squares of error gives us the cost function. It is also referred to as Mean Square Error (MSE).
Another important concept in Linear Regression is Gradient Descent. It is a popular optimization approach employed in training machine learning models by reducing errors between actual and predicted outcomes. Optimization in machine learning is the task of minimizing the cost function parameterized by the model's parameters. The primary goal of gradient descent is to minimize the convex function by parameter iteration.
A slower learning rate helps to reach the global minimum but takes an unusually long time and computationally proves expensive. The faster learning rate may make the model wander and lead to an undesired position, making it difficult to come back on the correct track to reach the global minimum. Hence the learning rate should be neither too slow nor too fast if the global minimum is to be reached efficiently. Interested in learning Data Science and its importance? Check out Data Science course.
After understanding the concept of Linear Regression and its adoption to solve many engineering and business problems, we now will consider the process of applying Linear Regression in a Machine Learning project. Let us import the necessary libraries:
import pandas as pd import matplotlib.pyplot as plt import seaborn as sns from sklearn.model_selection import train_test_split from sklearn.linear_model import LinearRegression from sklearn import metrics
We will load the dataset using the following command:
# Loading the data car_data = pd.read_csv('/content/car_data.csv')
Let us check the first few rows of the dataset:
car_data.head()
We can describe the dataset using .info() command
# Getting some information about the dataset
car_data.info()
Let us convert categorical variables i.e., "Fuel_Type", "Seller_Type" and "Transmission" (dtype=object), into numerical variables before applying a regression algorithm.
# encoding Columns car_data.replace({'Fuel_Type':{'Petrol':0,'Diesel':1,'CNG':2}},inplace=True) car_data.replace({'Seller_Type':{'Dealer':0,'Individual':1}},inplace=True) car_data.replace({'Transmission':{'Manual':0,'Automatic':1}},inplace=True)
To understand the relationship between different attributes in the dataset, we will plot a correlation matrix using the following code:
corrMatrix = car_data.corr() sns.heatmap(corrMatrix, annot=True, cmap=”viridis”) plt.show()
Splitting the Dataset
We will use an 80:20 split for training and testing the model
X = car_data.drop(['Car_Name','Selling_Price'],axis=1) Y = car_data['Selling_Price'] X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state=42)
We can call the Linear Regression module from the sklearn library using the following commands:
# loading the linear regression model lin_reg_model = LinearRegression() Now we can fit the model to our dataset lin_reg_model.fit(X_train,Y_train)
Once the training is completed, we can make predictions and print the r-squared error for regression-
# prediction on Training data training_data_prediction = lin_reg_model.predict(X_train)
# R squared Error train_error_score = metrics.r2_score(Y_train, training_data_prediction) print("R squared Error - Training : ", train_error_score)
# prediction on Training data
Y_pred = lin_reg_model.predict(X_test)
# R squared Error
test_error_score = metrics.r2_score(Y_test, Y_pred) print("R squared Error - Test: ", test_error_score)
To plot the best fit line, we will use the following code:
# create scatterplot with regression line
sns.regplot(Y_test, Y_pred, scatter_kws={"color": "green"}, line_kws={"color": "blue"})
Normally most statistical tests and results rely upon some specific assumptions regarding the variables involved. Naturally, if these assumptions are not considered, the results will not be reliable. Linear Regression also comes under same consideration. There are some common assumptions to be considered while using Linear Regression:
All the above assumptions are critical because if they are not followed, they can lead to drawing conclusions that may become invalid and unreliable. You can check out Data Science Bootcamp course KnowledgeHut for a better understanding of the course.
Linear Regression is popular in statistics. It offers several benefits in Data Science as follows:
A Linear Regression machine learning model is computationally simple and does not require much engineering overhead. Hence, it is easy to implement and maintain.
Since Linear Regression is computationally inexpensive, it can be applied to cases where scaling is needed, such as applications that handle big data.
Linear Regression is easy to interpret and very efficient to train. It is relatively simple, unlike deep learning neural networks which require more data and time to efficiently train.
As Linear Regression models are easy to train and do not require much computational power, these can be retrained quickly with new data and hence, can be applied to scenarios where real-time predictions are important.
Linear Regression finds applications in several domains such as agriculture, banking and finance, education, marketing, and many more. Linear Regression is applicable in real-world scenarios where machine learning problems can be used to predict the output as a continuous variable.
In agriculture, Linear Regression can be used to predict the amount of rainfall and crop yield, while in banking, it is implemented to predict the probability of loan defaults. For the Finance sector, Linear Regression is used to predict stock prices and assess associated risks. In the healthcare sector, Linear Regression is helpful in modeling healthcare costs, predicting the length of stay in hospitals for patients, etc. In the domain of sports analytics, Linear Regression can be used to predict the performance of players in upcoming games. Similarly, it can be used in education to predict student performances in different courses. Businesses also use Linear Regression to forecast product demands, predict product sales, decide on marketing and advertising strategies, and so on.
The success of every attempt to apply any machine learning model to a specific problem depends on the best practice of implementation. Best practices mean sticking to the characteristics of the selected algorithms, the right type of data being used, and some specific causes related to the problem at hand. Some of the tips for best practices are listed below:
The different assumptions in the application of Linear Regression in machine learning have already been discussed above. When applying a regression algorithm, the assumptions must be considered.
A simple model is easy to build and execute, takes less time, and can be applied to similar different datasets.
Using visualizations to analyze and evaluate the performance of models frequently helps to understand the correctness of the model and can be used to improve the same by removing any shortcomings.
When applied to a large dataset, the model takes more time to reach its accuracy and high computational power. If the performance on a large dataset is not satisfactory, the time and power spent are of no use. Hence, starting with a small sample dataset initially is better to try out the model.
The estimate obtained on this dataset gives a good indication of correct progress or otherwise. The findings of this approach help to take corrective action in the new model if required.
If the market conditions change in due course of time, the algorithm's controlling parameters also need to be changed. In such situations, it is better to go for a multi-linear model so that new affecting parameters can be included to build up the model.
It is always a good practice to apply Linear Regression to real-life problems like stock prediction, probability of promotion chances, growth percentage of crop yield, and so on. The results obtained can be matched to some previous example outcomes for gaining confidence.
The success of any algorithm is as good as the data used. One can choose appropriate data to be given to the model based on the outcome of the project in mind. A lot of open-source websites provide a variety of datasets suitable for applying regression algorithms in machine learning.
While regression analysis is utilized in practically every area, from finance to education and from banking to advertising, there are some beginner machine learning projects for Linear Regression as mentioned below:
Banks employ Machine learning to predict loan defaults and decide upon loan applications. Lending in the form of loans is a major source of revenue for banks, credit unions, and other financial organizations, which accounts for a sizable portion of the bank's assets. However, when these loans default, the financial institutions suffer severe consequences. Download Lona Default Prediction Database.
Predicting house prices may assist in determining the selling price of a property in a certain location and in determining the best time to buy a home. Download the House Price Prediction dataset.
Stock market analysis and forecasting are extremely challenging tasks. Stock prices are dynamic and affected by a variety of factors. When forecasting stocks, most stockbrokers use methodological and fundamental analysis and time series analysis. Download the Stock Markert Prediction dataset.
Sales forecasting is crucial because it assists companies in discovering which strategies work effectively and where a particular strategy needs to be modified to ensure future success. Download the Market Sales Forecasting dataset.
Businesses usually promote their products through websites and social media channels. However, their main challenge lies in finding the correct demographic to target for internet marketing. Since advertising is expensive, targeting advertisements to an audience that is unlikely to purchase the products can be a loss for the company. Download the Advertising dataset.
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In this article, we discussed Linear Regression for Machine Learning, its concepts, terminologies, and the types of Linear Regression. We understood the assumptions as well as the advantages and disadvantages of Linear Regression. Further, we learned how Linear Regression works with an example of Multiple Linear Regression on the car prices dataset. And finally, explored the best practices along with some beginner-level projects to try and gain confidence in Linear Regression problems. Check out KnowledgeHut’s Data Science Bootcamp cost, where you are offered a variety of Data Science training that will give you the experience you need to land a top Data scientist role.
The output is a continuous value, integer, or probability percentage based on the selected problems. Thus, it can be sales amount, profit percentage, probability of success or failure in some activities like admission possibility, winning an election, etc. With the best fit line of regression, the output value for any new value of the input variable can be easily calculated.
There are many benefits of Linear Regression, including simplicity of understanding and implementation. It can be applied to obtain relations in linear or multi-linear parameters and thus can be applied to various business problems.
A Linear Regression model will use a mathematical equation to derive a relation between a predicted variable which varies with independent variables. The best fit line will be obtained based on the given data after applying the algorithm, and this line can then be used to give expected predictions.
Many datasets can be used for Linear Regression, like stock price prediction, house price prediction, disease prediction probability, medical insurance costs, etc.
Although it is not easy to specify a particular best ML model for regression yet, one can select a regression model that best fits to predict outcomes of numerical nature. A multi-Linear Regression model would probably be a good choice in most cases.
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