Build your ultimate AI agent
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.
Prerequisites
Curriculum
Course outline
1
Exploring Linear Trends
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.
- Introduction to Modeling Data50 XP
- Reasons for Modeling: Interpolation100 XP
- Reasons for Modeling: Extrapolation100 XP
- Reasons for Modeling: Estimating Relationships100 XP
- Visualizing Linear Relationships50 XP
- Plotting the Data100 XP
- Plotting the Model on the Data100 XP
- Visually Estimating the Slope & Intercept100 XP
- Quantifying Linear Relationships50 XP
- Mean, Deviation, & Standard Deviation100 XP
- Covariance vs Correlation100 XP
- Correlation Strength100 XP
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
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
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.
Introduction to Linear Modeling in Python
Course
Complete
