How Simple Linear Regression Works?

Greetings, fellow data enthusiasts! Today, we're diving into the fascinating world of data analysis and regression modeling. If you're new to the scene or looking to expand your toolkit, you're in for a treat. In this blog post, we're unraveling the mysteries of Simple Linear Regression – a fundamental technique that holds the key to understanding relationships between two variables. Get ready to embark on a journey of discovery as we demystify this concept and learn when and how to wield its power.

What is Simple Linear Regression?

Imagine you have two sets of numbers, and you're wondering if they're connected in some way. Simple Linear Regression steps in as your detective, helping you draw a straight line through those points to reveal the hidden story behind the numbers. It's like having a data compass that guides you toward understanding the relationship between two variables.

Knowing When to Call on Simple Linear Regression:

Now, let's address the big question – when should you use Simple Linear Regression? This technique is your go-to when you're exploring a scenario with just two numerical variables. It's like focusing a spotlight on a duo of data points, aiming to discover any patterns or connections between them

Simple linear regression using a real-world scenario.

We'll be uncovering the fascinating relationship between age and salary, step by step. Whether you're a beginner seeking clarity or a seasoned data explorer, get ready to demystify this concept and witness its power in action.

Setting the Scene:

Imagine you have a dataset containing information about individuals – their ages and corresponding salaries. Our goal is to unveil any patterns between these two variables, using the magic of simple linear regression. Buckle up as we unravel the mystery behind this essential technique!

The Essence of Simple Linear Regression:

At its core, simple linear regression is like a magnifying glass for relationships between two numeric variables. In our case, we're examining how changes in age might influence salary. Think of it as uncovering the hidden story behind the numbers.

Cracking the Regression Equation:

Meet the star of the show – the regression equation: y = xb1 + b. Here's what each part means in the context of our age-salary example:

Dependent Variable (y - Salary): This is what we're trying to understand or predict – in our case, it's the salary of an individual.

Independent Variable (x - Age): This is the factor we believe affects the dependent variable – here, it's the age of an individual.

Slope/coefficient (b1): This is a magical number that reveals the rate of change. In our case, it tells us how much the salary changes for each year of increase in age.

Intercept/constant (b): The starting point of the line – it gives us a salary value when the age is zero. While this might not make much sense in our scenario, it's an important part of the equation.

Cracking the Code of Best-Fit Line Selection:

In the process of determining the best-fit line in linear regression, we aim to identify the optimal straight line among the various possible lines available. To achieve this, we follow these steps:

1. For each potential line, we begin by calculating the differences between the actual data points and the corresponding points predicted by the linear regression model. These differences are then squared.

2. This squared difference is computed for every data point that is associated with the specific line under consideration.

3. The squared differences for all data points associated with a particular line are summed together. This sum is referred to as the "residual error" for that specific line.

We repeat steps 1 to 3 for all the candidate lines, calculating their respective residual errors.

Among all the candidate lines, the line that exhibits the minimum residual error is identified as the "best-fit line." This line represents the optimal approximation of the relationship between the variables being studied, as it minimizes the overall deviation between the actual data points and the model's predicted values.

Whether you're an experienced coder or new to the world of exploration, come along with me as we break down the code step by step and unravel the process of discovering the ideal line that captures the core of your data.

This code allows you to load data from a CSV file into a pandas DataFrame and inspect the first few rows of the DataFrame. You can replace 'age1.csv' with the actual path to your CSV file.

import pandas as pd
df = pd.read_csv('age1.csv')
df.head(10)

This code generates a scatter plot that visualizes the relationship between 'Age' and 'Income' using the data from the df DataFrame. It helps you understand the distribution of data points and any potential trends or patterns between the two variables.

import matplotlib.pyplot as plt
plt.scatter(df['Age'],df['Income'])
plt.xlabel('Age')
plt.ylabel('Income')
plt.title('Scatter Plot')
plt.show()

importing the LinearRegression class from the sklearn.linear_model module. This is a key step when working with linear regression using the popular scikit-learn library.

from sklearn.linear_model import LinearRegression

Organizing data is pivotal in data exploration and machine learning. By creating separate 'x' and 'y' DataFrames, variables like 'Age' and 'Income' find order, aiding seamless analysis with tools like scikit-learn and revealing insights efficiently.

x = df[['Age']]
y = df[['Income']]

reg = LinearRegression()
reg.fit(x,y)

By calling these two lines of code, you're setting the stage for the LinearRegression model to learn from your data and unveil the underlying patterns between the 'Age' and 'Income' variables. This is a pivotal step in predictive analysis and understanding data relationships.

predicting the 'Income' using the trained Linear Regression mode

reg.predict([[40]])

Accessing the coefficient of the Linear Regression model

reg.coef_

Retrieving the intercept of the Linear Regression model

reg.intercept_

40*672.22222222+(-2750)

using the coefficient and intercept values to manually compute the predicted 'Income' for an 'Age' of 40 based on the linear regression equation y = mx + b, where m is the coefficient and b is the intercept.

Diving into training and testing your Linear Regression model using scikit-learn's train_test_split function.

from sklearn.model_selection import train_test_split

x_train,x_test,y_train,y_test = train_test_split(x,y,train_size = 0.8 , random_state=0)

from sklearn.linear_model import LinearRegression
regression = LinearRegression()
regression.fit(x_train,y_train)

Code involves plotting the regression line along with the original data points.

import matplotlib.pyplot as plt
plt.plot(x_train, regression.predict(x_train),color = 'red')
plt.scatter(df['Age'],df['Income'])
plt.xlabel('Age')
plt.ylabel('Income')
plt.show()

This visualization provides a clear illustration of how well the regression line fits the original data points, helping you grasp the effectiveness of your Linear Regression model.