# Introduction to Linear Modeling in Python

Explore the concepts and applications of linear models with python and build models to describe, predict, and extract insight from data patterns.

4 Hours16 Videos59 Exercises
21,251 Learners

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## Course Description

One of the primary goals of any scientist is to find patterns in data and build models to describe, predict, and extract insight from those patterns. The most fundamental of these patterns is a linear relationship between two variables. This course provides an introduction to exploring, quantifying, and modeling linear relationships in data, by demonstrating techniques such as least-squares, linear regression, estimatation, and bootstrap resampling. Here you will apply the most powerful modeling tools in the python data science ecosystem, including scipy, statsmodels, and scikit-learn, to build and evaluate linear models. By exploring the concepts and applications of linear models with python, this course serves as both a practical introduction to modeling, and as a foundation for learning more advanced modeling techniques and tools in statistics and machine learning.
1. 1

### Exploring Linear Trends

Free

We start the course with an initial exploration of linear relationships, including some motivating examples of how linear models are used, and demonstrations of data visualization methods from matplotlib. We then use descriptive statistics to quantify the shape of our data and use correlation to quantify the strength of linear relationships between two variables.

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Introduction to Modeling Data
50 xp
Reasons for Modeling: Interpolation
100 xp
Reasons for Modeling: Extrapolation
100 xp
Reasons for Modeling: Estimating Relationships
100 xp
Visualizing Linear Relationships
50 xp
Plotting the Data
100 xp
Plotting the Model on the Data
100 xp
Visually Estimating the Slope & Intercept
100 xp
Quantifying Linear Relationships
50 xp
Mean, Deviation, & Standard Deviation
100 xp
Covariance vs Correlation
100 xp
Correlation Strength
100 xp
2. 2

### Building Linear Models

Here we look at the parts that go into building a linear model. Using the concept of a Taylor Series, we focus on the parameters slope and intercept, how they define the model, and how to interpret the them in several applied contexts. We apply a variety of python modules to find the model that best fits the data, by computing the optimal values of slope and intercept, using least-squares, numpy, statsmodels, and scikit-learn.

3. 3

### Making Model Predictions

Next we will apply models to real data and make predictions. We will explore some of the most common pit-falls and limitations of predictions, and we evaluate and compare models by quantifying and contrasting several measures of goodness-of-fit, including RMSE and R-squared.

4. 4

### Estimating Model Parameters

In our final chapter, we introduce concepts from inferential statistics, and use them to explore how maximum likelihood estimation and bootstrap resampling can be used to estimate linear model parameters. We then apply these methods to make probabilistic statements about our confidence in the model parameters.

Datasets

Femur length versus body heightDistance hiked versus hike durationGalaxy distances versus recession velocitiesSea surface height versus yearMass versus volume of solution

Collaborators  Jason Vestuto

Data Scientist, University of Texas at Austin

Jason Vestuto started life as a musician and later studied physics and taught himself to code to survive. Along the way, he has completed a couple of degrees in physics, and another in science education, and discovered that he learns best by trying to teach others. Presently, he works within the Space and Geophysics Lab of the University of Texas at Austin, as a python developer and data scientist focused on GPS satellite navigation and signal processing.
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