I am trying to play around to see how outliers in a dataset might affect a Linear Regression model. The issue I'm having is I don't exactly know how to add outliers to a dataset, I've only found loads of articles online about how to detect and remove them.

This is the code I have so far:

import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn import metrics
from sklearn.linear_model import LinearRegression
from sklearn.datasets import make_regression
# Generate regression dataset
X, y = make_regression(
n_samples=1000,
n_features=1,
noise=0.0,
bias=0.0,
random_state=42,
)
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.2, random_state=42
)
regressor = LinearRegression()
regressor.fit(X_train, y_train) # Training the algorithm
y_pred = regressor.predict(X_test)
print("R2 Score:", metrics.r2_score(y_test, y_pred))
print("Mean Absolute Error:", metrics.mean_absolute_error(y_test, y_pred))
print("Mean Squared Error:", metrics.mean_squared_error(y_test, y_pred))
print("Root Mean Squared Error:", np.sqrt(metrics.mean_squared_error(y_test, y_pred)))
plt.scatter(X_test, y_test)
plt.plot(X_test, y_pred, color="red", linewidth=1)
plt.show()

And this is the output:

My question is how can I add outliers to this clean dataset in order to see the effects outliers will have on the resulting model?

Any help would be appreciated, thanks!