# Multiple Variables Linear Regression in Python: Explained with coding outline

Linear regression is a popular statistical model used to understand the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data. In this article, we will walk through the steps to implement linear regression with multiple variables in Python.

Before we begin, make sure you have the following packages installed:

- NumPy: a library for numerical computing with Python
- Pandas: a library for data manipulation and analysis
- Matplotlib: a library for creating plots and charts

You can install these packages using `pip install numpy pandas matplotlib`

.

# Step 1: Import the necessary libraries and load the data

First, we will import the required libraries and load the data into a Pandas DataFrame.

`import numpy as np`

import pandas as pd

import matplotlib.pyplot as plt

# Load the data into a Pandas DataFrame

data = pd.read_csv('data.csv')

# Step 2: Explore and visualize the data

Next, we will explore and visualize the data to get a better understanding of the relationships between the variables.

`# Print the first few rows of the data`

print(data.head())

# Get the number of rows and columns in the data

print(data.shape)

# Get the statistical summary of the data

print(data.describe())

# Plot a scatter plot of the data

plt.scatter(data['x1'], data['y'], color='b')

plt.xlabel('x1')

plt.ylabel('y')

plt.show()

plt.scatter(data['x2'], data['y'], color='b')

plt.xlabel('x2')

plt.ylabel('y')

plt.show()

# Plot a histogram of the data

data.hist()

plt.show()

# Step 3: Preprocess the data

Before we can fit a linear regression model to the data, we need to preprocess it. This includes splitting the data into training and test sets and standardizing the variables.

`# Split the data into training and test sets`

from sklearn.model_selection import train_test_split

X = data.iloc[:, :-1]

y = data.iloc[:, -1]

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

# Standardize the variables

from sklearn.preprocessing import StandardScaler

scaler = StandardScaler()

X_train = scaler.fit_transform(X_train)

X_test = scaler.transform(X_test)

# Step 4: Fit a linear regression model

Now, we can fit a linear regression model to the training data using the `LinearRegression`

class from scikit-learn.

`from sklearn.linear_model import LinearRegression`

# Create a linear regression model

model = LinearRegression()

# Fit the model to the training data

model.fit(X_train, y_train)

# Print the coefficients

print(model.coef_)

# Print the intercept

print(model.intercept_)

# Step 5: Evaluate the model

After fitting the model, we can evaluate its performance on the test set using various metrics.

`# Make predictions on the test set`

y_pred = model.predict(X_test)

# Calculate the mean squared error

from sklearn.metrics import mean_squared_error

mse = mean_squared_error(y_test, y_pred)

print(f'Mean squared error: {mse:.2f}')

# Calculate the root mean squared error

rmse = np.sqrt(mse)

print(f'Root mean squared error: {rmse:.2f}')

# Calculate the coefficient of determination (R^2 score)

from sklearn.metrics import r2_score

r2 = r2_score(y_test, y_pred)

print(f'R^2 score: {r2:.2f}')

# Step 6: Visualize the results

Finally, we can visualize the results by plotting the predicted values against the actual values.

`# Plot the predicted values against the actual values`

plt.scatter(y_test, y_pred, color='b')

plt.xlabel('Actual values')

plt.ylabel('Predicted values')

plt.show()

sThat’s it! You have successfully implemented linear regression with multiple variables in Python. You can use this model to make predictions on new data or fine-tune the model by adjusting the parameters or trying different algorithms.