Quadratic Regression

Lesson 4: Modeling Behavior

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Do Now:
1. Grab a laptop and login.

You must have your OWN laptop.

2. Join the QUIZIZZ and have a desmos

STAAR tab open.

3. I will be checking your screens.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

On your sticky note, write your name AND prediction for the number of Americans that will be over 100 years old in 2030.
Once you are done, stick it on the poster in front.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Learning Goals

● Use a quadratic function to model data.
● Interpret characteristics of a quadratic function in terms of a problem situation.

● Use graphs of quadratic functions to make predictions.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Watch the video and Write the steps to finding the regression using Desmos.

Math Response

Your equation should look like:

y = mx + b

"m" and "b" should be replaced with the parameters from desmos.

Round to one decimal point.

Type answer here

Correct Answer: y=1.2x+31.1

Deg^°

Rad

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Let’s continue to analyze the data and make some predictions
about the volume of soda at different temperatures.

Lesson 4: Modeling Behavior

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This Might Be a Bad Idea . . .

A 12-ounce can of soda was put into a freezer. The table shows the volume of
the soda in the can, measured at different temperatures.

Poll

Based on graph on desmos, which regression equation would you use based on the shape?

• Linear

• Quadratic

Math Response

We have discovered that we should use the quadratic regression to describe the data.

Plug the data in to desmos.

1. Use the quadratic regression.

2. Write the quadratic equation using the parameters from desmos. Replace a, b, and c.

3. standard form: ax²+bx+c

Round to one decimal point.

Type answer here

Correct Answer: y=0.1x^2-8.4x+516.3

Deg^°

Rad

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

If you can't tell which regression to use based on the graph, run BOTH linear and quadratic regressions.

Look at the r-squared statistic.

The biggest on is the best regression.

Poll

Based on r² statistic on desmos, which regression equation would you use based on the shape?

• Linear

• Quadratic

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Once you have a regression equation, you can start making predictions.

Based on the graph, what will be the volume of the soda can at the following temperatures:


a. 20 degrees






b. 30 degrees

Draw

Show where the prediction would be for each temperature.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Let's practice if you can make predictions based on the graphs.

Hotspot

 The graph shows the results of the soccer teams practice per weekly versus matches they won. Based on the linear regression equation y = 3.52 + 3.14x, if a team practices 4.5 hours per week next year, which is the best prediction of the number of soc matches a team could expect to win?  

Hotspot

How much does it cost to have your lawn mowed for 2 hours?

Multiple Choice

Based on the graph, if Joe earned $400, how many hours did he work?

• 25 hours
• 35 hours
• 45 hours
• 15 hours

Multiple Choice

The scatter plot below shows the average yearly consumption of bottled water by people in the United States starting in 1990.

Using the line of best fit, predict the average consumption of bottled water in the year 2000?

• 20 gallons

• 18 gallons

• 22 gallons

• 19 gallons

Lesson 4: Modeling Behavior

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Using data from the US Census Bureau, the table
lists the number of Americans, in thousands,
who lived to be over 100 years old for the
specified years.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Skill Practice:
Work on the skill practice independently.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

1. Graph the table values on the grid

shown. Let x be the number of
years since 1994. Label the axes.

2. Use technology to calculate the

linear,exponential and quadratic
regression equations. Which model
best fits the data? Explain your
reasoning. Sketch the graph of the
best fit regression equation on the
coordinate plane on which you
created your scatter plot.

Lesson 4: Modeling Behavior

© Carnegie Learning, Inc.

3. State the domain and range of your function. How do they

compare to the domain and range of this problem situation?

4. Use your regression equation to predict the number of

Americans that will live to be over 100 years old in the year 2025.

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