Using Linear Models

Lesson 1.19: Linear
Modeling with Data

Obj: 4C, (4A, 4B): I can formulate linear regressions
and use them to make predictions.

EQ: How do I use technology to find a linear regression?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

What role will you be for your group today?

• Scribe

• Facilitator

• Resourcer

• Includer

Part 1: Correlation VS

Causation (4B)

Vocabulary

Causation: When an article says that causation was found, this means that the
researchers are saying that changes in one thing they measured directly cause
changes in the other. (Cause and Effect)

Correlation (Association) - When researchers find an association, which can
also be called a correlation, what they are saying is that they found a relationship
between two, or more, things. The trouble is, there could be other “hidden
variables” affecting this relationship that the researchers don't know about.

Word Cloud

Give an Example of Cause and Effect.

Causation or Association?

​Answer the polls on the next slides for each scenario independently, then discuss what you chose for each and why with your team.

Poll

Which best describes the relation?

The time period you write with a mechanical pencil. & The amount of lead remaining.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When the number of bus stops increases, the number of car sales decreases.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

How tall someone is. & How much someone weighs.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

How much knowledge someone has. & How old they are.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When fewer firefighters report to a house fire, the damage caused by the fire decreases.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

Putting money into a raffle. & Temporarily or permanently having less money.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When ice cream sales increase, incidents of sunburn increase.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When it rains several inches, the water level of a lake increases.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When the student population at a school increases, the number of teachers at the school increases.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When the amount of sugar in quart of apple juice is reduced, there are fewer calories in each serving.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When there are more efficient workers on a project, the project is completed in less time.

• Association/Correlation

• Causation

Poll

Which best describes the relation?

When there is more protein in an athlete’s diet, the athlete scores more points in a game.

• Association/Correlation

• Causation

Causation or Association?

Which best describes each relation?
1. The time period you write with a mechanical pencil. & The amount of lead remaining
2. When the number of bus stops increases, the number of car sales decreases.
3. How tall someone is. & How much someone weighs.
4. How much knowledge someone has. & How old they are.
5. When fewer firefighters report to a house fire, the damage caused by the fire decreases.
6. Putting money into a raffle. & Temporarily or permanently having less money.
7. When ice cream sales increase, incidents of sunburn increase.
8. When it rains several inches, the water level of a lake increases.
9. When the student population at a school increases, the number of teachers at the school increases.
10. When the amount of sugar in quart of apple juice is reduced, there are fewer calories in each
serving.
11. When there are more efficient workers on a project, the project is completed in less time.
12. When there is more protein in an athlete’s diet, the athlete scores more points in a game.

Discuss what you chose for each poll and why with your team for the scenarios above.

Reorder

Reorder the following from least to greatest.

• 0.02

• 0.2

• 1/4

• 100%

• 3/2

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Part 2: Correlation

Coefficient (4A)

Correlation Coefficient: a number between -1 and +1
to represent the % of accuracy between the data and
line of best fit. This is represented by “r”

r Examples

Scatter Plot Examples

Give an example of a weak
correlation coefficient

Multiple Select

According to the chart, which of the following are considered weak correlation coefficients?

• r = 0.25

• r = 0.87

• r = -0.72

• r = 0.43

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Part 3: Linear Regressions

(4C)

desmos.com/calculator
+
table
Input data
y1 ~ mx1 + b
write formula

This example:
y = 5x - 4

Desmos Graph with Data Graphed:
https://www.desmos.com/calculator/62uyrmlpnv

Practice

Using the linear regression equation derived, what is y when x = 3?

Using the linear regression equation derived, what is y when x = 5?

Using the linear regression equation derived, what is y when x = 20?

Using the linear regression equation derived, what is x when y = 15?

Drag and Drop

The linear regression is ​

Placeholder

; when x = 3, y = ​

Placeholder

; when x = 5, y = ​

Placeholder

; when x = 20, y = ​

Placeholder

; x = ​

Placeholder

, when y = 15.

Drag these tiles and drop them in the correct blank above

161.5

y = 11.3x - 8

25.9

48.5

218

2.1

y = 0.1x + 0.8

Poll

What is your favorite color?

• Red

• Blue

• Purple

• Black

• Other

Poll

How satisfied are you with these lesson slides?

• Very Satisfied

• Satisfied

• Neutral

• Dissatisfied

• Very Dissatisfied

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

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