Lecture 1: Data Science Fundamentals

PSTAT100 Data Science Concepts and Analysis

John Inston
johninston@ucsb.edu

University of California, Santa Barbara

April 7, 2026

Course Introduction

👋 Introduction

Welcome to PSTAT100 Data Science Concepts and Analysis! 🎉

🤝 About Me

  • My name is John Inston.
    • Pronouns: I use he/him/his pronouns.
  • I am a 4th year PhD candidate 👴 in the Department of Statistics and Applied Probability.
  • My research interests include stochastic games 🎲 and numerical optimization 💻.


📧 Contact Information

✉️ Email: johninston@ucsb.edu

🌐 Website: johnrobininston.com

Office Hours

🏢 OH: South Hall 5431T R 1PM to 3PM.

👩‍🏫 Teaching Staff

I am being assisted this term by the following wonderful teaching assistants:

❗ Due to space availability section switching must be confirmed in advance with your TA.

ℹ️ Prerequisites

Programming Language

  • This course will be taught in python 🐍.
    • A working knowledge of python is not required but it is expected that you have some familiarity with similar programming languages.
    • You are also expected to create documents using Jupyter notebooks or Quarto markdown.

Prerequisite Courses

  • PSTAT 120A
    • Probability Theory
    • Statistics
  • CS 9 or CS 16
    • Python Programming
    • Data Structures
    • Algorithms
  • Math 4A
    • Linear Algebra

📝 Supplementary materials summarizing these topics will be made available in the online lecture notes for review.

ℹ️ Course Information

📝 Course Materials

  • You will be provided with:
    • 📝 Lecture Notes (slides, online, pdf)
    • 📚 Suggested reading (textbooks, online notebooks)
    • 🧪 Lab and assignment solutions
  • You can access all course material through the Canvas page.
    • All material that is not assessed will also be made available on the course website.

👩‍⚖️ Course Policies

  • Communication is key! 💬

  • No plagiarism! ❌

  • 🤖 AI tools are encouraged for learning.

  • Be respectful. 🤝

Please make sure to read through the course policies detailed in the syllabus.

📝 Assessments

📝 Assignments (40%)

  • 4 assignments throughout the quarter.
    • These will be released and submitted on Canvas
    • Due at the end of weeks 2, 4, 6, and 8.

💻 Labs (30%)

  • 8 lab worksheets
    • Submitted to Canvas by the end of the week.
    • In lab sessions your TA will help you with problems.

📊 Project (30%)

  • You are required to complete a data analysis project.
    • Individual or group.
    • Details of this project will be specified in the coming weeks.

✅ Topic Outline

The following is a tentative course outline:

  1. Introduction to Data Science
    • Python Fundamentals
    • Data Lifecycle
  2. Data Preparation
    • Data Cleaning
    • Missingness
  3. Exploratory Data Analysis
    • Data Visualization
    • Data Summarization
  4. Statistical Foundations
    • Probability
    • Hypothesis Testing
  1. Regression
    • Simple / Multiple Linear Regression
    • Ridge / Lasso / Elastic Net Regression
  2. Classification Methods
    • Logistic Regression
    • Support Vector Machines
  3. Tree-Based Methods
    • Decision Trees / Random Forests
  4. Unsupervised Learning
    • PCA & Clustering
  5. Introduction to Deep Learning
  6. Data Science Ethics
    • Privacy, Fairness and Bias

📈 Maximizing Your Learning

💼 Professional Skills

In addition to technical topics we will also develop your professional skills as a data scientist including:

  • Technical document production.
  • 🗣️ Precise and clear communication.
  • 🤝 Collaboration and team work.
  • Version control (GitHub).
  • Independent learning.

🎯 Course Aims

Your course aims should be:

  • 🛠️ Build a toolkit for your future career.
  • Independently learning new tools and techniques based on the problem at hand.
  • To have a project to showcase your skills and knowledge for job applications.
    • And have the start of a project portfolio on GitHub!

💪 Python Bootcamp

What about if I am not familiar with Python? 🤔


When and Where?

I will be hosting a Python Bootcamp this Thursday from 1:00pm to 3:00pm in South Hall 5421.

❗ Attendance is optional!

Who is this for?

  • Encouraged for anybody who is unfamiliar with Python or needs a refresher.
  • Focus will be on IDE setup, basic functionality and document creation.

Data Science Fundamentals

📊 Data Science

What is Data Science?

Let’s see what Claude thinks:

Claude’s Definition of Data Science.

Fundamental Aims

Simply put…

Data science is the practice of using data to extract insights and knowledge. 👍

How does it work?

  • Data science is an interdisciplinary field, requiring:
    • Statistics
    • Mathematics
    • Computer science
    • Domain knowledge
  • Required to manage and interpret large, complicated data sets.

🤔 Notice that these disciplines loosely correspond to the prerequisites for this course.

Data Science Disciplines

Intersection of the Disciplines

Data Science Venn Diagram.

🔢 Data

What is Data?

Definition: Data

Data is (digital) information (such as measurements or statistics) used as a basis for reasoning, discussion, or calculation.

  • Raw data is often difficult or even impossible to interpret.
    • Hence, the need for Data Science!

For example…

Data Growth

🫩 Sooo much data!

  • The amount of data being collected, stored, and processed is growing exponentially!

  • Larger variety of increasingly complicated data types.

Worldwide Data Growth.

🔢 Datasets

Datasets

Definition: Dataset

A dataset is a collection of observations taken on observational units, consisting of values measured on a set of variables.

Terminology

  • An observational unit is the entity that is being measured.
    • People in a study, cars on a production line, etc.
  • An observation is a collection of values (e.g. a vector) measured on various variables.
    • One person, car in particular is an observation.
    • Variables might be the person’s age, the car’s engine size, etc.

Let’s look at our first example dataset.

Dataset Example - cats.csv

🐈 A New Cat Dataset

First 5 rows of cats.csv
Breed Age (Years) Weight (kg) Color Gender
0 Russian Blue 19 7 Tortoiseshell Female
1 Norwegian Forest 19 9 Tortoiseshell Female
2 Chartreux 3 3 Brown Female
3 Persian 13 6 Sable Female
4 Ragdoll 10 8 Tabby Male


Identifying Observations and Variables

  • The cats dataset was provided by Waqar Ali on Kaggle.

  • Here the observational unit is a cat.

  • This dataset of 1000 observations (rows, individual cats) each with 5 variables (columns).

Semantics vs Structure

What is the difference?

  • In general, we distinguish between the semantics and structure of a dataset.

  • The semantics of a dataset refers to the meaning behind the data.

    • Interpretation and representation.

  • The structure of a dataset refers to the way the data is organized.

    • Shape, organization and storage.

🔢 Types of Data

🔢 Quantitative Data

  • Quantitative Data (Numerical): Represents measurable quantities.
    • Discrete: Counted items that are distinct and whole (e.g., number of children, product sales).
    • Continuous: Measured items that can be any value within a range (e.g., height, weight).

⚖️ Qualitative Data

  • Qualitative Data (Categorical): Represents descriptive characteristics or labels.
    • Nominal: Named categories with no inherent order (e.g., gender, hair color, blood type).
    • Ordinal: Categories with a logical order or ranking (e.g., satisfaction surveys, education level).

🏢 Structured vs. Unstructured Data

  • Structured vs. Unstructured Data:
    • Structured: Organized, formatted data (e.g., Excel sheets, SQL databases).
    • Unstructured data: Data without a fixed schema (e.g., video, audio, free text).

Data Type Example - cats.csv

🐈 The Cats Strike Back!

First 5 rows of cats.csv
Breed Age (Years) Weight (kg) Color Gender
0 Russian Blue 19 7 Tortoiseshell Female
1 Norwegian Forest 19 9 Tortoiseshell Female
2 Chartreux 3 3 Brown Female
3 Persian 13 6 Sable Female
4 Ragdoll 10 8 Tabby Male

Identifying Variable Types

  • The Breed, Color, and Gender variables are qualitative variables since they are categorical.

  • The Age and Weight variables are quantitative variables since they are numerical.

    • Both are continuous variables since they can take on any value within a range.
    • ❗ We note however that they have both been discretized into bins.

🔄 Transformations

Variable Transformations

  • Variables can be transformed from one type to another, often for:
    • Improved interpretability.
    • Removing excessive detail.
    • Subsequent analysis (e.g. PCA).

🐈 Return of the Cat Dataset

Suppose we are interested in transforming the quantitative age variable into the categories young, middle-aged, and senior.

  • We create a new variable AgeGroup with the following values:
    • Young: 0-5 years
    • Middle-Aged: 6-10 years
    • Senior: 11+ years

Transformations Example - cats.csv

🐕 Transformed Cat Dataset

First 5 rows of cats.csv with AgeGroup variable
Breed Age (Years) Weight (kg) Color Gender AgeGroup
0 Russian Blue 19 7 Tortoiseshell Female Senior
1 Norwegian Forest 19 9 Tortoiseshell Female Senior
2 Chartreux 3 3 Brown Female Young
3 Persian 13 6 Sable Female Senior
4 Ragdoll 10 8 Tabby Male Middle-Aged

Interpretation of the Transformed Variable

  • We have now transformed the numerical Age (Years) variable into a qualitative AgeGroup variable.

  • We will revisit variable transformations in more detail later in the course when we discuss data preparation.

Data Type Hierarchy

Variable Classification.

🔢 Tabular Data

  • We will primarily be working with tabular data.
    • Spreadsheet style datasets containing both quantitative and qualitative data.
    • We will occasionally deal with more complex structures such as databases.

Complicated Data

😵‍💫 More Complicated Data Types

In reality there is a wide variety of different data types:

  • Time series data - stock prices, weather patterns, etc.
  • Spatial data - map data, satellite imagery, etc.
  • Textual data - social media posts, news articles, etc.
  • Image data - photos, videos, etc.
  • Audio data - audio recordings, podcasts, etc.
  • Video data - videos, etc.
  • Network / graphical data - social media networks, etc.


Each data type has its own unique set of challenges and techniques for data scientists to apply.

Complicated Data Example - MNIST

🖐️ Handwritten Digits

MNIST database, a subset of the larger NIST made available by Yann LeCun on Kaggle.

  • The database is of handwritten digits.
    • White text on a black background.
  • The data is complicated!
    • There are 70,000 observations total (60,000 training and 10,000 testing).
    • Each observation consists of 28x28 pixels, with a total of 784 pixels per observation.
    • Each pixel is a grayscale value between 0 and 255 (0 = black, 255 = white).

Handwritten Digits

🖐️ Handwritten Digits

MNIST Data Visualization.

📖 Data Literacy

My point is…

The world of data is confusing! 😵‍💫

  • Different data types with different formats and different dimensions.
  • Each has unique challenges and techniques for data scientists to learn.
  • We do not have time to go over everything, but we will cover some of the most important cases!
  • It is a long road to build up your data literacy.


Definition: Data Literacy

Data Literacy is the ability to explore, understand, and communicate with data in a meaningful way. (Tableau)

Data Science Lifecycle

🔄 Data Science Lifecycle

What is the Data Science Lifecycle?

The data science lifecycle (DLS) is the following multi-step process used to extract actionable insights from data:

  1. ❓ Hypothesize:
    • Formulate a question of interest.
  2. 🧹 Collect and Prepare:
    • Sample or acquire data.
    • Understand your dataset (origins, limits).
    • Clean up and organize your data.
  3. 📈 Explore and Analyze:
    • Explore the data to understand its structure.
    • Analyze data relationships.
  4. 🗣️ Interpret and Communicate:
    • Interpret the results of the analysis.
    • Communicate your results.

Data Science Lifecycle.

Guidelines

Don’t feel restricted!

  • This lifecycle is not necessarily sequential.
    • You may start with a data set that needs processing before forming your hypothesis.
    • You may need to reformulate your hypothesis as your understanding deepens.
  • Think of this as a guide to help structure your approach.

In reality, the data science lifecycle has a more complex structure.

Real Data Science Lifecycle.

❓ Hypothesize

Deceptively Simple

  • Typically we begin with a question we want to answer.
    • 💉 Does this new drug improve patient outcomes?
    • 🛳️ What impact has increased shipping had on marine mammal populations?
    • 🎓 Does this new policy improve student performance?
  • The scope of your hypothesis should inform the data you collect.
    • Am I considering a specific population?
    • Do I wish to generalize?
    • Does this data already exist?

Step 1: Hypothesize.

🧹 Collect and Prepare

This takes time!

  • Design experiment / survey or collect second-hand data.
    • There are whole courses dedicated to experimental design.
  • ➡️ Our hypothesis informs the data we collect.
    • ⬅️ With second-hand data, this is often reversed.
  • 🧹 Data preparation is often a time consuming process.
    • Errors are challenging to locate.
    • Missing data needs to be handled appropriately.
    • Formatting and readability issues.

Step 2: Collect and Prepare.

📈 Explore and Analyze

Understanding the data

  • Analyze the data to understand its structure.
    • Visualizations.
    • Descriptive statistics.
  • Identify relationships between variables.
    • Inferential modelling.
    • Hypothesis testing.
  • Sometimes we wish to forecast future outcomes.
    • Predictive modelling.
  • Sometimes we solely focus on model outcomes.
    • Model selection and evaluation.
    • Machine learning models.

Step 3: Explore and Analyze.

🗣️ Interpret and Communicate

Refer back to your hypothesis

  • Interpret our results.
    • How do our results fit our hypothesis?
    • How significant are our results?
    • How do our results compare to other studies?
  • Communicate our results.
    • Write a report.
    • Present your findings.
  • Ensure reproducibility.
    • Share your code and data.
    • Maximize transparency.
  • Let’s look at an example…

Step 4: Interpret.

DSL Example - mammals.csv

mammals.csv

Suppose we are provided with the following data set:

The first few rows of the mammals data set.
species body_weight brain_weight slow_wave paradox total_sleep lifespan gestation predation exposure danger
0 African elephant 6654.000 5712.0 NaN NaN 3.3 38.6 645.0 3 5 3
1 African giant pouched rat 1.000 6.6 6.3 2.0 8.3 4.5 42.0 3 1 3
2 Arctic fox 3.385 44.5 NaN NaN 12.5 14.0 60.0 1 1 1
3 Arctic ground squirrel 0.920 5.7 NaN NaN 16.5 NaN 25.0 5 2 3
4 Asian elephant 2547.000 4603.0 2.1 1.8 3.9 69.0 624.0 3 5 4


  • The mammals.csv data set (web source) comes from Allison and Cicchetti (1976) and contains data for 62 mammals.
  • What questions might we be able to answer with this data?

Suppose we are interested in how the size of an animal’s brain scales with their body size.

DSL Example - Prepare

Data Cleaning

  • The data is already immaculately cleaned and organized.
  • We therefore check the dimensions and inspect the data for any missing values.
Dimensions:  
 (62, 11)
Missingness analysis:  
 species          0
body_weight      0
brain_weight     0
slow_wave       14
paradox         12
total_sleep      4
lifespan         4
gestation        4
predation        0
exposure         0
danger           0
dtype: int64

DSL Example - Hypothesize

Make sure we understand our limitations!

  • We need to understand the limitations of the data.
    • The data only contains mammals.
    • The data is aggregated at the species level.
    • The data was not collected to represent mammals as a whole.
  • What does this mean?
    • We cannot generalize our findings to all mammals.
  • How does this impact the questions we can ask?

Final Hypothesis

Does this data suggest evidence of a relationship between a mammal’s brain size and body weight?

DSL Example - Explore

Summarizing the data

  • Both variables are quantitative and continuous.
    • We can therefore use descriptive statistics to summarize the data (more on this later).
Summary statistics:  
        body_weight  brain_weight
count    62.000000     62.000000
mean    198.789984    283.134194
std     899.158011    930.278942
min       0.005000      0.140000
25%       0.600000      4.250000
50%       3.342500     17.250000
75%      48.202500    166.000000
max    6654.000000   5712.000000
Correlation:  
               body_weight  brain_weight
body_weight      1.000000      0.934164
brain_weight     0.934164      1.000000
  • Some observations:
    • Correlation is high suggesting a positive relationship between the variables.
    • Data appears heavily skewed (we will discuss this later).
  • We can also produce a scatter plot to visualize the relationship between the variables.

DSL Example - Visualize

  • There is a clear linear relationship between the variables on the log scale.

  • The plot shows a positive relationship between the variables.
  • To better see the relationship, we can use log-log axes.

DSL Example - Analyze

Linear Model

Our visualization suggests that the relationship could be modeled as

\[ \begin{aligned} \log(\text{brain}) & = \beta_0 + \beta_1 \log(\text{body})\\ \text{brain} & = \exp(\beta_0 + \beta_1 \log(\text{body})) \\ \text{brain} & = c\cdot\exp(\log(\text{body}^{\beta_1})) \\ \implies \text{brain} & \propto \text{body}^{\beta_1}. \end{aligned} \]

This suggests that the relationship is a power law.

  • To determine the parameters of the model, we can use linear regression.
    • We will discuss this in more detail later.
    • Let’s have a quick look at the fitted model details.

DSL Example - Model

                             OLS Regression Results                             
================================================================================
Dep. Variable:     np.log(brain_weight)   R-squared:                       0.921
Model:                              OLS   Adj. R-squared:                  0.919
Method:                   Least Squares   F-statistic:                     697.4
Date:                  Tue, 07 Apr 2026   Prob (F-statistic):           9.84e-35
Time:                          22:12:32   Log-Likelihood:                -64.336
No. Observations:                    62   AIC:                             132.7
Df Residuals:                        60   BIC:                             136.9
Df Model:                             1                                         
Covariance Type:              nonrobust                                         
=======================================================================================
                          coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------
Intercept               2.1348      0.096     22.227      0.000       1.943       2.327
np.log(body_weight)     0.7517      0.028     26.409      0.000       0.695       0.809
==============================================================================
Omnibus:                        2.698   Durbin-Watson:                   1.667
Prob(Omnibus):                  0.260   Jarque-Bera (JB):                1.933
Skew:                           0.405   Prob(JB):                        0.380
Kurtosis:                       3.301   Cond. No.                         3.73
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
  • R-squared = 0.921 — \(\log(\text{body weight})\) explains 92.1% of the variance in \(\log(\text{brain weight})\).
  • F-statistic p-value = 9.84e-35 — the model is highly statistically significant overall.
  • Slope = 0.7517
    • p-values of 0.000, so highly significant.

DSL Example - Interpret

Our fitted model is:

\[ \text{brain} \propto \text{body}^{0.7517}. \]

  • This means that a 1% increase in body weight is associated with a ~0.75% increase in brain weight.

  • This leads us to draw the following conclusion:

For these 62 mammals there is evidence that brain weight changes in proportion to a power of body weight.

  • Note that this conclusion is not very strong since:
    • Data set is relatively small.
    • Not representative of mammals in general.
    • Aggregated data, not individual level.

Conclusion

Conclusion

✅ What we covered

  • Course information.
  • What is data science?
    • Data and Datasets
    • Key terminology.
    • Data types.
  • The data science lifecycle.

📅 What’s next?

  • Handling data in Python.
  • Data structure.
  • Data preparation.

References

Allison, T., and D. V. Cicchetti. 1976. “Sleep in Mammals: Ecological and Constitutional Correlates.” Science 194 (4266): 732–34. https://doi.org/10.1126/science.982039.