Section 1.1: Preparing the Dataset

To illustrate the graphs discussed here, we will create a dataset using the make_regression function from scikit-learn. Our dataset will consist of 100 samples, each with four features, all of which are informative. Additionally, we will apply Gaussian noise with a standard deviation of 10 and set the random state to 25—these parameters are somewhat arbitrary.

import numpy as np

import matplotlib.pyplot as plt

from sklearn.datasets import make_regression

# Create a regression dataset

X, y = make_regression(

n_samples=100,

n_features=4,

n_informative=4,

noise=10,

random_state=25

)

# Display the first 5 observations

print(X[:5])

Section 1.2: Scatter Plots

Scatter plots are excellent for visualizing the relationships between two numerical variables. They help us understand how one variable may influence another. Each point in the scatter plot represents an individual observation.

# Generate line of best fit

m, b = np.polyfit(X[:, 2], y, 1)

best_fit = m * X + b

# Plotting

plt.subplots(figsize=(8, 5))

plt.scatter(X[:, 2], y, color="blue")

plt.plot(X, best_fit, color="red")

plt.title("Impact of Feature at Index 2 on Target Label")

plt.xlabel("Feature at Index 2")

plt.ylabel("Target Label")

plt.show()

In this case, we are particularly interested in whether there is a relationship between the two variables. Just as in our personal relationships, not all connections are identical. If a relationship exists, we can further analyze its characteristics for deeper insights.

Key aspects to consider include:

• The strength of the relationship
• The nature of the relationship (positive or negative)
• Whether it follows a linear or non-linear pattern
• Presence of any outliers

The visual representation above indicates a positive, fairly strong, linear relationship, with no apparent outliers.

Section 1.3: Histograms

Histograms are a staple in statistical data representation. They effectively display the general distribution of a numerical feature within a dataset by grouping data into intervals. Each observation is assigned to an appropriate interval, reflected in the height of the corresponding bar.

plt.subplots(figsize=(8, 5))

plt.hist(X[:, 0], bins=10) # Default of 10 bins

plt.xlabel("Feature at Index 0")

plt.title("Distribution of Feature at Index 0")

plt.ylabel("Number of Occurrences")

plt.show()

When examining histograms, pay attention to skewness and modality:

• Skewness indicates the asymmetry of the probability distribution.
• Modality refers to the number of peaks within the dataset.

Our visualizations suggest a symmetrical and unimodal distribution. It's essential to note that the bin width for our histogram is arbitrary; adjusting the number of bins can change the narrative the histogram conveys.

Section 1.4: Box Plots

Box plots offer another effective way to understand data spread. They highlight outliers, the interquartile range, and the median, all while utilizing minimal space, making it easier to compare distributions across different groups.

plt.subplots(figsize=(8, 5))

plt.boxplot(X, vert=False)

plt.ylabel("Features")

plt.show()

Our box plot allows us to assess the skewness of each feature and identify outliers, as well as the minimum and maximum values. In our case, all features appear symmetrical, although outliers are present in the first and fourth features, warranting further investigation in real-world scenarios.

Data visualization is crucial for effectively conveying insights. It is vital that our visualizations are easily comprehensible to the intended audience. A key strategy for achieving this is to ensure your graphs answer questions that matter to your audience. While this article covers only a few types of graphs, it provides a solid foundation for creating high-quality visual insights.

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