**Introduction to Linear Regression**

Linear regression is a type of supervised learning algorithm, commonly used for predictive analysis. As the name suggests, linear regression performs regression tasks. Now, what is regression? Well, regression is nothing but a technique that displays the relationship between two variables.

Here’s the table of contents for this module:

**What Is Linear Regression?****Line of Best Fit****Coefficient of X****Hands-on: Boston Housing Prices Dataset**

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Without much delay, let’s get started.

**What Is Linear Regression?**

As mentioned above, linear regression is a predictive modeling technique. It is used whenever there is a linear relation between the dependent and the independent variables.

Y = b_{0}+ b_{1}* x

It is used in estimating exactly how much of *y* will change, when *x* changes a certain amount.

As we see in the picture, a flower’s sepal length is mapped onto the x-axis and the petal length is mapped on the y-axis. Let us try and understand how the petal length changes with respect to the sepal length with the help of linear regression. Let us have a better understanding of linear regression with another example given below.

**Example: **

Say, there is a telecom network called Neo. Its delivery manager wants to find out if there’s a relationship between the monthly charges of a customer and the tenure of the customer. So, he collects all customer data and implements linear regression by taking monthly charges as the dependent variable and tenure as the independent variable. After implementing the algorithm, what he understands is that there is a relationship between the monthly charges and the tenure of a customer. As the tenure of the customer increases, the monthly charges also increase. Now, the best fit line helps the delivery manager find out more interesting insights from the data. With this, he can predict the values of *y* for every new value of *x*.

Let us say, the tenure of a customer is 45 months, and with the help of the best fit line the delivery manager can predict that the customer’s monthly charges would be somewhere around $64.

Similarly, if the tenure of a customer is 69 months, then with the help of the best fit line the delivery manager can predict that the customer’s monthly charges would be somewhere around $110.

This is how linear regression works. Now, the question is how to find the best fit line?

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**Line of Best Fit**

The line of best fit is nothing but the line that best expresses the relationship between the data points. Let us see how to find the best fit line in linear regression.

This is where the residual concept comes into the picture which is shown in the image below:

Red lines in the above image denote residual values, which are the differences between the actual values and the predicted values. How does residual help in finding the best fit line?

To find out the best fit line, we have something called **residual sum of squares (RSS)**. In RSS, we take the square of residuals and sum them up.

The line with the **lowest value of RSS** is the best fit line.

Now, let us see how the coefficient of *x* influences the relationship between the independent and the dependent variables.

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**Coefficient of X**

In simple linear regression, if the coefficient of *x* is positive, then we can conclude that the relationship between the independent and the dependent variables is positive.

Here, if the value of *x* increases, the value of *y* also increases.

Now, if the coefficient of *x* is negative, then we can say that the relationship between the independent and the dependent variables is negative.

Here, if the value of *x* increases, the value of *y* decreases.

Now, we will apply these concepts to build a linear regression model with the help of Boston Housing Prices dataset.

**Hands-on: Boston Housing Prices Dataset**

**Environment:**Python 3 and Jupyter Notebook**Library:**Pandas**Module:**Scikit-learn

**Understanding the Dataset**

Before we get started with the hands-on, let us explore the dataset. We will be using the **Boston House Prices Dataset**, with **506 rows** and **13 attributes** with a target column.

**Let’s take a quick look at the dataset.**

**This data frame contains following columns:**

**Crim:**Per capita crime rate by town**Zn:**Proportion of residential land zoned for lots over 25,000 sq. ft.**Indus:**Proportion of non-retail business acres per town**Chas:**Charles River dummy variable (= 1 if tract bounds river; 0, otherwise)**Nox:**Nitrogen oxides concentration (parts per 10 million)**Rm:**Average number of rooms per dwelling**Age:**Proportion of owner-occupied units built before 1940**Dis:**Weighted mean of distances to five Boston employment centers**Rad:**Index of accessibility to radial highways**Tax:**Full-value property tax rate per $10,000**Ptratio:**Pupil–Teacher ratio by town**Black:**1000(Bk – 0.63) ^2, where Bk is the proportion of Blacks by town**Lstat:**Lower status of the population (percent)**Medv:**Median value of owner-occupied homes in $1000s

**In this example, we will train two models to predict the price.**

**Model Building **

Now that we are familiar with the dataset, let us build the linear regression models.

**Simple Linear Regression Model**

Consider ‘lstat’ as independent and ‘medv’ as dependent variables

*Step 1: Load the Boston dataset*

*Step 2: Have a glance at the shape*

*Step 3: Have a glance at the dependent and independent variables*

*Step 4: Visualize the change in the variables*

*Step 5: Divide the data into independent and dependent variables*

*Step 6: Split the data into train and test sets*

*Step 7: Shape of the train and test sets*

*Step 8: Train the algorithm*

*Step 9: Retrieve the intercept*

*Step 10: Retrieve the slope*

*Step 11: Predicted value*

*Step 12: Actual value*

*Step 13: Evaluate the algorithm*

** Multiple Linear Regression Model**

Here, consider ‘medv’ as the dependent variable and the rest of the attributes as independent variable

*Step 1: Load the Boston dataset*

*Step 2: Set up the dependent and the independent variables *

*Step 3: Have a glance at the independent variable*

*Step 4: Have a glance at the dependent variable*

*Step 5: Divide the data into train and test sets: *

*Step 6: Have a glance at the shape of the train and test sets:*

*Step 7: Train the algorithm:*

*Step 8: Having a look at the coefficients that the model has chosen: *

*Step 9: Concatenating the DataFrames to compare:*

*Step 10: Comparing the predicted value to the actual value: *

*Step 11: Evaluate the algorithm*

**What Did We Learn?**

In this module, we have discussed the use of linear regression, what linear regression is, the line of best fit, and the coefficient of *x*. Toward the end, we have built two linear regression models: simple linear regression and multiple linear regression. In the next module, we will talk about logistic regression. Let’s meet there!

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