As an **undergraduate Mathematics** or **Data Science** teacher, you can use this set of computer-based tools to help you in teaching **Introductory Statistics** and specifically **Linear Regression and Polynomial Regression**.

This lesson plan will help you to teach **Introductory Statistics for Data Science **through a** Linear Regression and Polynomial Regression **assignment**. **The lesson plan includes** a hands-on computer-based classroom activity** to be conducted on a dataset of annual production-based emissions of carbon dioxide (CO2) by China, measured in million tonnes per year, for the span of 1902-2018. This activity includes hands-on **Python code,** **a set of inquiry-based questions** that will enable your students to apply their understanding of **scatter plots, regression equations, correlation coefficients, linear regression, polynomial regression, **and the difference between them**.**

Thus, the use of this lesson plan allows you to integrate the teaching of a climate science topic with a core topic in **Mathematics, Statistics, and Data Science**.

**The tools in this lesson plan will enable students to:**

- Learn about linear regression and correlation
- Understand linear regression equations and related terms such as correlation coefficients
- Use linear and polynomial regression analyses and to describe production-based CO2 emissions in China from the Twentieth century to recent times (1900-2017)
- Discuss how these changes suggest that the planet is facing a significant increase in CO2 emissions in last 50 years

About

Step-by-Step User Guide

Questions

Credits

Review

About

Step-by-Step User Guide

Here is a step-by-step guide to using this lesson plan in the classroom/laboratory. We have suggested these steps as a possible plan of action. You may customize the lesson plan according to your preferences and requirements.

Teaching Module(25 mins)

- Use the teaching module, ‘Introduction-Linear Regression and Correlation’ by OpenStax
^{TM}, Rice University (for High School level) or ‘Chapter-3: Linear Regression’ provided by Ramesh Sridharan, Massachusetts Institute of Technology (for Undergraduate level), to introduce these topics of basic statistics. - Navigate to the sub-sections within the module to the basics of scatter plots, correlation coefficients, regression equations, and linear regression.
- Use the in-built practice exercises and quizzes to evaluate your students’ understanding of the topics.

Video micro-lectures (14 and 5 min)

Use the video micro-lecture, ‘Introduction to Simple Linear Regression’by dataminingincae INCAE Business School for a basic introduction to Simple Linear Regression and terms like dependant variable, independent variable, regression line, regression coefficients. Use the video micro-lecture, ‘ Polynomial Regression‘ by Art of Visualization for a basic introduction to Polynomial Regression and how it is useful to fit a nonlinear model to the data.

Classroom/ Laboratory activity(30 min)

- Use the provided Dataset china-co2-csv.csv and Python Notebook Simple-and-Polynomial-Regression.ipynb.
- The dataset includes Annual Production-based Emissions of Carbon Dioxide (CO2) by China, measured in million tonnes per year, for the span 1902-2018.Data Source: Carbon Dioxide Information Analysis Center (CDIAC) and Global Carbon Project. This can be found here.
- Use the Python Notebook and Dataset to:

- Read the Dataset using DataFrame
- Know the basics of the dataset like its dimensions, data types and memory usage
- Plot the scatter plot of yearly co2 emissions variable
- Use NumPy library to convert the DataFrame to NumPy Array which would be used in the further steps.

**Part 1**: **Linear Regression**

- Find the Regression Coefficients for Simple Linear Regression
- Plot the scatter plot and Regression Line as per the predicted coefficients
- Calculate RMSE (Root Mean-Squared Error-values)
- Discuss how well the Regression Line describes the data points.

**Part 2: Polynomial Regression**

- Explain how polynomial regression fits a nonlinear model to the data
- Compute the number of output features, then Transform data to polynomial features, fit a Regression for Transformed data, and then predict values
- Calculate RMSE (Root Mean-Squared Error-values)
- Discuss how well the Regression model describes the data points.
- Suggest the students to try different values for the degree of the Polynomial and see the difference between the results visually and also by comparing it using the RMSE value.

4. Encourage your students to answer topical questions by applying their understanding of scatter plots, correlation coefficients, linear regression and polynomial regression.

5. Use the regression analyses performed to initiate a discussion on the increase in CO2 emissions from 1980 to 2020 due to anthropogenic activities, which is one major reason behind global climate change

Questions

**Use this lesson plan to help your students find answers to:**

- Use the tools and the concepts learned so far to discuss and determine answers to the following questions:
- Use an example to describe linear regression analysis.
- Use an example to describe polynomial regression analysis.
- Determine the difference in the results of linear regression and polynomial regression analyses? What do the results suggest?
- Use linear and polynomial regression analyses to describe how the annual production-based CO2 emissions in China have changed from 1850 (pre-industrial)- 2018 (last datapoint).
- Discuss reasons for increasing CO2 emissions and their impact on Earth’s climate.

Credits

1 | Teaching Module, “Introduction- Linear Regression and Correlation” | Provided by OpenStax^{TM}, Rice University |

2 | Teaching Module, “Chapter 3: Linear Regression” | Provided by Ramesh Sridharan, MIT from ‘Statistics for Research Projects’ |

3 | Video micro-lecture, ‘Introduction to Simple Linear Regression’ | by dataminingincae, INCAE Business School |

4 | Video micro-lecture, ‘Polynomial Regression’ | by Art of Visualization |

5 | Dataset annual production-based emissions of carbon dioxide (CO2) by China, measured in million tonnes per year, for the span of 1902-2018. | Carbon Dioxide Information Analysis Center (CDIAC) and Global Carbon Project |

Review

About

Step-by-Step User Guide

Questions

Credits

Review

About

Step-by-Step User Guide

Here is a step-by-step guide to using this lesson plan in the classroom/laboratory. We have suggested these steps as a possible plan of action. You may customize the lesson plan according to your preferences and requirements.

Teaching Module(25 mins)

- Use the teaching module, ‘Introduction-Linear Regression and Correlation’ by OpenStax
^{TM}, Rice University (for High School level) or ‘Chapter-3: Linear Regression’ provided by Ramesh Sridharan, Massachusetts Institute of Technology (for Undergraduate level), to introduce these topics of basic statistics. - Navigate to the sub-sections within the module to the basics of scatter plots, correlation coefficients, regression equations, and linear regression.
- Use the in-built practice exercises and quizzes to evaluate your students’ understanding of the topics.

Video micro-lectures(14 and 5 min)

(14 and 5 min)Use the video micro-lecture, ‘Introduction to Simple Linear Regression’by dataminingincae INCAE Business School for a basic introduction to Simple Linear Regression and terms like dependant variable, independent variable, regression line, regression coefficients. Use the video micro-lecture, ‘ Polynomial Regression‘ by Art of Visualization for a basic introduction to Polynomial Regression and how it is useful to fit a nonlinear model to the data.

Classroom/ Laboratory activity(30 min)

- Use the provided Dataset china-co2-csv.csv and Python Notebook Simple-and-Polynomial-Regression.ipynb.
- The dataset includes Annual Production-based Emissions of Carbon Dioxide (CO2) by China, measured in million tonnes per year, for the span 1902-2018.

Data Source: Carbon Dioxide Information Analysis Center (CDIAC) and Global Carbon Project

- Use the Python Notebook and Dataset to:

- Read the Dataset using DataFrame
- Know the basics of the dataset like its dimensions, data types and memory usage
- Plot the scatter plot of yearly co2 emissions variable
- Use NumPy library to convert the DataFrame to NumPy Array which would be used in the further steps.

**Part 1**: **Linear Regression**

- Find the Regression Coefficients for Simple Linear Regression
- Plot the scatter plot and Regression Line as per the predicted coefficients
- Calculate RMSE (Root Mean-Squared Error-values)
- Discuss how well the Regression Line describes the data points.

**Part 2: Polynomial Regression**

- Explain how polynomial regression fits a nonlinear model to the data
- Compute the number of output features, then Transform data to polynomial features, fit a Regression for Transformed data, and then predict values
- Calculate RMSE (Root Mean-Squared Error-values)
- Discuss how well the Regression model describes the data points.
- Suggest the students to try different values for the degree of the Polynomial and see the difference between the results visually and also by comparing it using the RMSE value.

4. Encourage your students to answer topical questions by applying their understanding of scatter plots, correlation coefficients, linear regression and polynomial regression.

5. Use the regression analyses performed to initiate a discussion on the increase in CO2 emissions from 1980 to 2020 due to anthropogenic activities, which is one major reason behind global climate change

Questions

**Use this lesson plan to help your students find answers to:**

- What are derivatives and their functions?
- Using an example, describe polynomial differentiation.
- Is the extent of the Arctic Sea Ice decreasing since 1980?
- Has the speed of melting of Arctic Sea Ice changed from 1980- 2017?
- Discuss the Ice Albedo Feedback and Global Warming to explain the differences in rates of melting of and extent of Arctic Sea Ice over the past four decades.

Credits

1 | Teaching Module; ‘Differentiation: definition and basic derivative rules’ | Developed by Khan Academy |

2 | Teaching Module; ‘Derivatives and the Shape of a Graph’ | Provided by OpenStax^{TM}, Rice University |

3 | Classroom Activity; ‘Arctic Sea Ice’ | Provided by Sustainability Math by Thomas J. Pfaff, Professor of Mathematics, Ithaca College, USA |

4 | Reading; ‘Polynomials and their Derivatives’ | By Donald Byrd, Indiana University Informatics |

5 | Visualization; ‘Charctic Interactive Sea Ice Graph’ | From National Snow and Ice Data Center (NSIDC) |

6 | Image(s) | Armin Rose/Shutterstock NOAA Climate.gov image, based on data from the National Snow and Ice Data Center |

Review

TROP ICSU is a project of the International Union of Biological Sciences and Centre for Sustainability, Environment and Climate Change, FLAME University.