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Multiple Linear Regression Using Python and Scikit-learn

This article was published as a part of the Data Science Blogathon.


Interesting in predictive analytics? Then research artificial intelligence, machine learning, and deep learning .

If you are on the path of learning data science, then you definitely have an understanding of what machine learning is. In today’s digital world everyone knows what Machine Learning is because it was a trending digital technology across the world.

Every step towards adaptation of the future world leads by this current technology, and this current technology is led by data scientists like you and me😌.

Here we only discuss machine learning, If you don’t know what it is, then we take a brief introduction to it:

Machine learning is the study of the algorithms of computers, that improve automatically through experience and by the use of data. its algorithm builds a model based on the data we provide during model building. This is the simple definition of machine learning, and when we go into deep then we find that there are huge numbers of algorithms that are used in model building. Generally, most used machine learning algorithms are based on the type of problem, the types are basically regression, classification, etc… But here we will only talk about regression algorithms.

Let’s take a brief introduction on what regression is? Regression is the statistical method in investing, finance, and other disciplines that attempts to determine the strength and the relation between the independent and dependent variables. Generally, independent variables are those variables where their values are used to obtain output and dependent are those whose value is dependent on independent values. When you are talking about regression algorithms then some mostly used regression algorithms are used to train the machine learning model, like simple linear regression, lasso, ridge, etc…

So, let’s talk about multiple linear regression and take a detailed understanding of how simple linear is differs from multiple linear regression.

Table of Contents

  • Simple linear regression vs multiple linear regression
  • Dataset
  • Reading dataset
  • Independent and dependent variables
  • Handling categorical variables
  • Splitting data
  • Applying model


Simple Linear Regression Vs Multiple Linear Regression

Now, before moving ahead let discuss the interaction behind the simple linear regression then we try to compare multiple and simple linear regression based on that intuition we actually doing our machine learning problem.

Simple Linear Regression

We considered a simple linear regression in any machine learning algorithm using example,

Now, suppose if we take a scenario of house price where our x-axis is the size of the house and the y-axis is basically the price of the house. In this basically, we have two features first one is f1 and the second one is f2, where,

                                                           f1 refers to the size of the house and,

                                                           f2 refers to the price of the house

So, if f1 becomes the independent feature and f2 become the dependent feature, usually we know that whenever the size of house increases then price also increases, suppose we draw scatter points randomly, by this scatter point basically we try to find the best fit line and this best fit line is given by the equation:

                            equation:   y = A + Bx

Suppose, y be the price of the house and x be the size of the house then this equation seems like this:

                            equation:  price = A + B(size)
                                        A is an intercept and B is slop on that intercept


When we discuss this equation, in which intercept basically, indicates the when the price of the house is 0 then what will be the base price of the house, and the slop or coefficient indicates that with the unit increases in size, then what will be the unit increases in slop.

Now, how is it different when compared to multiple linear regression?


Multiple Linear Regression

Multiple Linear Regression is basically indicating that we will be having many features Such as f1, f2, f3, f4, and our output feature f5. If we take the same example as above we discussed, suppose:

f1 is the size of the house.

f2 is bad rooms in the house.

f3 is the locality of the house.

f4 is the condition of the house and,

f5 is our output feature which is the price of the house.

Now, you can see that multiple independent features also make a huge impact on the price of the house, price can vary from feature to feature. When we are discussing multiple linear regression then the equation of simple linear regression y=A+Bx is converted to something like:

                            equation:  y = A+B1x1+B2x2+B3x3+B4x4

“If we have one dependent feature and multiple independent features then basically call it a multiple linear regression.”

Now, our aim to using the multiple linear regression is that we have to compute A which is an intercept, and B1  B2  B3  B4 which are the slops or coefficient concerning this independent feature, that basically indicates that if we increase the value of x1 by 1 unit then B1 says that how much value it will affect int he price of the house, and this was similar concerning others BBB4

So, this is a small theoretical description of multiple linear regression now we will use the scikit learn linear regression library to solve the multiple linear regression problem.


Now, we apply multiple linear regression on the 50_startups dataset, you can click here to download the dataset.

Reading dataset

Most of the dataset are in CSV file, for reading this file we use pandas library:

df = pd.read_csv('50_Startups.csv')

Here you can see that there are 5 columns in the dataset where the state stores the categorical data points, and the rest are numerical features.

Now, we have to classify independent and dependent features:

Independent and Dependent variables

There are total 5 features in the dataset, in which basically profit is our dependent feature, and the rest of them are our independent features:

#separate the other attributes from the predicting attribute
x = df.drop('Profit',axis=1)
#separte the predicting attribute into Y for model training 
y = ['profit']

Handling categorical variables

In our dataset, there is one categorical column State, we have to handle this categorical values present inside this column for that we will use pandas get_dummies() function:

# handle categorical variable
# dropping extra column
x= x.drop(‘State’,axis=1)
# concatation of independent variables and new cateorical variable.

Splitting Data

Now, we have to split the data into training and testing parts for that we use the scikit-learn train_test_split() function.

# importing train_test_split from sklearn
from sklearn.model_selection import train_test_split
# splitting the data
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state = 42)

Applying model

Now, we apply the linear regression model to our training data, first of all, we have to import linear regression from the scikit-learn library, there is no other library to implement multiple linear regression we do it with linear regression only.

# importing module
from sklearn.linear_model import LinearRegression
# creating an object of LinearRegression class
LR = LinearRegression()
# fitting the training data

finally, if we execute this then our model will be ready, now we have x_test data we use this data for the prediction of profit. 

y_prediction =  LR.predict(x_test)

Now, we have to compare the y_prediction values with the original values because we have to calculate the accuracy of our model, which was implemented by a concept called r2_score. let’s discuss briefly on r2_score:


It is a function inside sklearn. metrics module, where the value of r2_score varies between 0 and 100 percent,  we can say that it is closely related to MSE.

r2 is basically calculated by the formula given below:

                            formula:  r2 = 1 – (SSres  /SSmean )

now, when I say SSres it means, it is the sum of residuals and SSmean refers to the sum of means.


y = original values

y^ = predicted values. and,

If we take calculation from this equation, then we have to know that the value of the sum of means is always greater than the sum of residuals. If this condition satisfies then our model is good for predictions. Its values range between 0.0 to 1.

”The proportion of the variance in the dependent variable that is predictable from the independent variable(s).”

The best possible score is 1.0 and it can be negative because the model can be arbitrarily worse. A constant model that always predicts the expected value of y, disregarding the input features, would get an R2 score of 0.0.

# importing r2_score module
from sklearn.metrics import r2_score
from sklearn.metrics import mean_squared_error
# predicting the accuracy score
print(‘r2 socre is ‘,score)
print(‘mean_sqrd_error is==’,mean_squared_error(y_test,y_prediction))
print(‘root_mean_squared error of is==’,np.sqrt(mean_squared_error(y_test,y_prediction)))

You can see that the accuracy score is greater than 0.8 it means we can use this model to solve multiple linear regression, and also mean squared error rate is also low.

End Notes

hello, data scientists 😎 above we take a detailed discussion on multiple linear regression, and the example we used in it is the perfect example of multiple linear regression. I hope now you have a better understanding of multiple linear regression.

Hope you enjoyed this!

You can connect me on LinkedIn: www.linkedin.com/in/mayur-badole-189221199

Also, read my other articles: https://www.analyticsvidhya.com/blog/author/mayurbadole2407/

Thank You.

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