Simple Linear Regression Implementation

Nerd Cafe

The primary purpose of implementing a Simple Linear Regression model on the below dataset

356B

Salary_Data.csv

is to model and quantify the linear relationship between years of experience (independent variable) and salary (dependent variable) in order to make predictions. This serves the following specific goals:

1. Understanding Relationships

• You want to determine how salary changes with years of experience.

• A linear regression line provides an interpretable model that tells you how much increase in salary is expected for each additional year of experience.

2. Predict Future Outcomes

• Once trained, the model can be used to predict salary for unseen or future inputs (e.g., "What will be the salary of a person with 7.5 years of experience?").

3. Evaluate Model Accuracy

• By comparing predicted values with actual values on the test set, you can evaluate how well the model generalizes to new data.

• The y_test vs y_pred comparison helps calculate accuracy metrics like:

  • Mean Squared Error (MSE)

  • R² Score (coefficient of determination)

  • Mean Absolute Error (MAE)

4. Learn Model Parameters

• After fitting the model, the values of w₀ (intercept) and w₁ (slope) are learned from the training data.

• These parameters define the best-fit line:

which explains the trend in your dataset.

5. Validate Assumptions

• By plotting residuals or checking histograms, you can verify the assumptions of linear regression (linearity, normality, independence, homoskedasticity).

6. Foundational Learning

• This is a baseline model in machine learning. It introduces important concepts such as:

  • Supervised learning

  • Cost/loss functions

  • Optimization (e.g., gradient descent)

  • Model evaluation and visualization

Python code

The dataset contains two columns:

• Years of Experience: Number of years a person has worked.

• Salary: The corresponding salary.

Here's a preview of the first few rows:

import pandas as pd

# Load the CSV file
file_path = 'Dataset/Salary_Data.csv'
data = pd.read_csv(file_path)

# Display the first few rows of the dataset
data.head()

The output is:

	Years of Experience	Salary
0	1.1			39343
1	1.3			46205
2	1.5			37731
3	2.0			43525
4	2.2			39891

Let's build and visualize a simple linear regression model to predict salary based on years of experience.

1. Import Required Libraries

import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score, mean_squared_error

• pandas is used to load and manage the dataset.

• matplotlib.pyplot is for plotting the graph.

• sklearn.linear_model.LinearRegression is the core linear regression model.

• train_test_split splits the data into training and testing sets.

• r2_score and mean_squared_error are evaluation metrics.

2. Load the CSV File

df = pd.read_csv('Dataset/Salary_Data.csv')

• This reads the CSV file into a DataFrame called df.

3. Separate Features and Labels python Copy Edit

X = df[['Years of Experience']]
y = df['Salary']

• X contains the input feature: Years of Experience (2D array).

• y contains the target variable: Salary.

4. Split into Training and Testing Sets

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

• 80% of the data goes into training (X_train, y_train).

• 20% goes into testing (X_test, y_test).

• random_state=42 ensures reproducibility

5. Train the Linear Regression Model

model = LinearRegression()
model.fit(X_train, y_train)

• We create a linear regression model.

• .fit() trains the model using training data.

6. Make Predictions on Test Set

y_pred = model.predict(X_test)

• This uses the trained model to predict salaries for X_test.

7. Print the Model Equation

slope = model.coef_[0]
intercept = model.intercept_
print(f"Model Equation: Salary = {slope:.2f} * YearsExperience + {intercept:.2f}")

• slope is the coefficient (how much salary increases per year).

• intercept is the base salary when experience is 0.

• You get the equation in the form: Salary = a × YearsExperience + b

Output

Model Equation: Salary = 9423.82 * YearsExperience + 25321.58

8. Evaluate Accuracy

r2 = r2_score(y_test, y_pred)
mse = mean_squared_error(y_test, y_pred)
print(f"R² Score: {r2:.4f}")
print(f"Mean Squared Error: {mse:.2f}")

• R² Score: how well the model fits the data (1 = perfect).

• MSE: average of squared prediction errors (lower is better).

Output

R² Score: 0.9024
Mean Squared Error: 49830096.86

9. Predict Salary for a Specific Experience

specific_years = 5
predicted_salary = model.predict([[specific_years]])[0]
print(f"Predicted Salary for {specific_years} years of experience: ${predicted_salary:.2f}")

We predict the salary for 5 years of experience using our model.

Output

Predicted Salary for 5 years of experience: $72440.66

10. Plot the Data and the Regression Line

plt.figure(figsize=(10, 6))
plt.scatter(X, y, color='blue', label='Actual Data')
plt.plot(X, model.predict(X), color='red', linewidth=2, label='Regression Line')
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.title('Salary vs Years of Experience')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

• Blue points are actual data.

• Red line is the predicted regression line.

• Shows how well the line fits the data.