OBJECTIVES & STANDARDS
Math Objectives
Use technology to find the exponential function that best fits a data set
Analyze how well a regression model fits a data set using r2 values
Use regression models to summarize trends and make predictions
Common Core Math Standards
Personal Finance Objectives
Analyze long-term trends in the stock market
Use exponential regression to summarize trends for different portfolios, funds, and asset types
National Standards for Personal Financial Education
Investing
3b: Investigate the long-run average rates of returns on small-company stocks, large-company stocks, corporate bonds, and Treasury bonds
DISTRIBUTION & PLANNING
Distribute to students
OBJECTIVES & STANDARDS
Math Objectives
Use technology to find the exponential function that best fits a data set
Analyze how well a regression model fits a data set using r2 values
Use regression models to summarize trends and make predictions
Common Core Math Standards
Personal Finance Objectives
Analyze long-term trends in the stock market
Use exponential regression to summarize trends for different portfolios, funds, and asset types
National Standards for Personal Financial Education
Investing
3b: Investigate the long-run average rates of returns on small-company stocks, large-company stocks, corporate bonds, and Treasury bonds
DISTRIBUTION & PLANNING
Distribute to students
GRAPH: Fahad’s Investment
The data points below represent the value of Fahad’s investment account over the last 15 years. Fahad wants to summarize the trends in his account, so he finds the line of best fit.
Do you think the line of best fit gives you a good prediction? Why or why not?
Measuring Goodness of Fit
We can measure how well a model, like Fahad’s line of best fit, matches the data points given by using a statistical measure called r squared
Read the notes below and answer the questions that follow.
In your own words, what does r^2 (r squared) tell you?
Summarize: Looking at a graph, how might you know if a model had an r squared value close to 1?
Part I:
Part II: Fahad’s Investments and r squared
Let’s return to Fahad’s investment from the start of the lesson. Fahad used a linear regression model to explain his investment’s value, but we could also use an exponential model. Compare the models and answer the questions.
What is the r^2 value of the linear model? What does that tell you?
Which model is a better fit for the data set? Justify your response.
DESMOS: Exponential Regression in Investing
Link in google classroom
In earlier lessons, you learned how to find the line that best fits a data set using a linear regression model. We can do the same thing with exponential functions. Follow your teacher’s instructions to complete this Desmos activity which will be graded separetly in X2.
Part I: Robo Advisors
Robo advisors have been growing in popularity ever since they were first made available to the public approximately 15 years ago. The data points show how many billions of dollars were managed by robo-advisors each year since 2010 in the US. The curve is an exponential regression model for the data.
Do you think this model provides an accurate prediction for the future? Why or why not?
