6.4 Exponential Regression

Last updated about 1 year ago

16 questions

Note from the author:

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
Link to all CCSS Math
CCSS.HSS.ID.B.6.A
CCSS.HSF.LE.A.2
CCSS.HSF.LE.B.5
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
Student Activity Packet
Application Problems

Instructions

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
Link to all CCSS Math
CCSS.HSS.ID.B.6.A
CCSS.HSF.LE.A.2
CCSS.HSF.LE.B.5
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
Student Activity Packet
Application Problems

Intro/Warm-Up:

Learn It

Practice It

Desmos:

Application Problems

Level 2

6.4 Exponential Regression

Last updated about 1 year ago

16 questions

Note from the author:

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
Link to all CCSS Math
CCSS.HSS.ID.B.6.A
CCSS.HSF.LE.A.2
CCSS.HSF.LE.B.5
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
Student Activity Packet
Application Problems

Instructions

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
Link to all CCSS Math
CCSS.HSS.ID.B.6.A
CCSS.HSF.LE.A.2
CCSS.HSF.LE.B.5
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
Student Activity Packet
Application Problems

Intro/Warm-Up:

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.

Based on his regression, Fahad wrote the equation for the line of best fit:
 y = 275x + 881.
What is the slope of the line of best fit?_______ 
What does the slope represent in this scenario?_______ 

Estimate Fahad’s investment value after 15 years…
a.  Using the data points._______ 
b.  Using the line of best fit._______ 

Do you think the line of best fit gives you a good prediction? Why or why not?

Learn It

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?

Practice It

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.

Part 1: 
Model A_______ 
Model B_______ 
Model C_______ 

Desmos:

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. 

Application Problems

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.

Based on the model, approximately how many assets did robo advisors have under management in 2015?_______ billion

Here are the results of the exponential regression. Write the equation for the exponential model by substituting the values for a and b into the equation. Round to the nearest hundredth.
_______ 

Level 2

Complete the table by writing the equation and r2 values based on the regression results. Round to the nearest hundredth.

            Bond Fund        Stock Fund
            _______           _______ 

Equation:
            _______             _______ 

1.  Based on the regression model, what is the average annual rate of return of the Stock Fund?_______ 

2.  Amar decides to invest $100 in the Stock Fund. He learns it has a total expense ratio of 0.03%. Write an equation to model the predicted value of his investment after x years._______ 

3.  Based on the regression model, what is the predicted price of the Bond Fund after 15 years?_______ 
4.  Why does the exponential function of best fit for the Bond Fund appear almost linear?_______ 
5.  Which fund is more volatile?_______  Explain your reasoning._______ 
6.  Which fund do you think would be a better long-term investment? _______ Why?_______ 

6.4 Exponential Regression

6.4 Exponential Regression

Do you think the line of best fit gives you a good prediction? Why or why not?

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?

Do you think the line of best fit gives you a good prediction? Why or why not?

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?

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.

Do you think this model provides an accurate prediction for the future? Why or why not?

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.

Do you think this model provides an accurate prediction for the future? Why or why not?