Grade Level: 12^th

Textbook: Discovering Statistics

Cluster: Interpret Linear Models

• CCSS.Math.Content.HSS-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
• CCSS.Math.Content.HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
• CCSS.Math.Content.HSS-ID.C.9 Distinguish between correlation and causation.

 

In this learning progression students will learn about a line of regression for a set of data. They will learn about the different components of the equation, how to find the line of regression for a set of data both by and by using a graphing calculator, and the correlation coefficient.  Finally the students will apply what they have learned to a given set of data and explain the difference between correlation and causation in terms of a real life situation.

 

To learn the concept outlined in this standard the students will be presented with simple linear and non-linear functions that have real worlds application to practice identifying the meaning behind the different significant features of the graph and its equation. Then the transition will be made from simple linear equations to equations that are the linear regression of a set of data.	CCSS.Math.Content.HSS-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.   Example problem:
To learn this procedural fluency students must learn the individual processes involved with the end product. I will first introduce students to the concept of a linear regression. Then I will teach the students how to calculate this by hands. Once they have practice with this process for small sets of data I will teach them how to use their calculators to find this line for larger sets of data.	CCSS.Math.Content.HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.     Example problem: Find the linear regression and correlation coefficient for the following data set. Weight (kilograms) Age (Years) Blood fat content  1  1  84  46  354  2  1  73  20  190  3  1  65  52  405  4  1  70  30  263  5  1  76  57  451  6  1  69  25  302  7  1  63  28  288  8  1  72  36  385  9  1  79  57  402 10  1  75  44  365 11  1  27  24  209 12  1  89  31  290 13  1  65  52  346 14  1  57  23  254 15  1  59  60  395 16  1  69  48  434 17  1  60  34  220 18  1  79  51  374 19  1  75  50  308 20  1  82  34  220 21  1  59  46  311 22  1  67  23  181 23  1  85  37  274 24  1  55  40  303 25  1  63  30  244   Data From https://orion.math.iastate.edu /burkardt/data/regression/x09.txt
To meet this standard the students will work with examples of sets of data where there is a large correlation between two factors but neither is caused by the other. Some of these examples the variables will be related and some will be random. The students must experience this relational phenomenon for themselves to solidify this difference in their minds.	CCSS.Math.Content.HSS-ID.C.9 Distinguish between correlation and causation.   Example problem: The day of the year with the most reports of domestic violence is Super bowl Sunday. This means that there is a large correlation between these two factors. Does this mean that the Super Bowl causes domestic violence or vice a versa? Why or why not

 

 

 

Lesson Title: Interpreting the Data

Unit Title: Linear Regression

Teacher Candidate: Albany Thompson

Subject, Grade Level, and Date: Statistics, 12^th Grade,  2/27/14

 

This lesson will be the final lesson in this sequence. The student will only be able to perform these calculations and interpret the given data after completing the previous lesson in this section.

Central Focus: Finding the linear regression and correlation coefficient for a set of data.

Essential Question: Does a strong correlation imply causation? Does a weak correlation imply no causation?

• CCSS.Math.Content.HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
• CCSS.Math.Content.HSS-ID.C.9 Distinguish between correlation and causation.

Learning Outcomes	Assessment
By the end of this lesson students should be able to use their calculators to find a line of regression for a large set of data. They should also be able to find and interpret the correlation coefficient in terms of the original question.	I will assess the students’ mastery of the material by speaking with the students during the group work time and observing their process. I will also assess them informally during the end discussion when the students present their findings. The students will also be assessed based on the rubric found below.

 

Learning Targets	Student Voice
I will be able to find a line of regression. I will be able to calculate the correlation coefficient for a set of data. I will be able to explain the difference between correlation and causation.	The students will have the opportunity to explain their understanding to both the other students and myself during their group work time and the class discussion at the end of the lesson.

 

The students will be comfortable with the concept of linear regression and correlation from the previous lesson. I will assess their understanding of these topics through their answers to homework and quiz questions.

Academic Language Demands
Vocabulary & Symbols	Language Functions	Precision, Syntax & Discourse
linear regression correlation coefficient correlation causation	The language in this lesson functions to give the students the vocabulary to talk about data in a quantitative sense in order to make comparisons.	Mathematical Precision: The students will be able to discuss their findings with precision as a result of their calculations for comparison.   Syntax:   Discourse: Students will be able to talk about data in terms of its correlation to a straight line.

 

Language Target	Language Support	Assessment of Language Target
My goal for the students in this lesson is that they will be able to discuss their finding from their calculations with the precisions required for statistical analysis.	I will support the students’ use of appropriate language in a mathematical sense by conversing with them throughout the lesson and by targeting words that students have found confusing based on their prior exit slips.	I will assess the students’ mastery of the language target informally through their responses to their exit slips about the vocabulary that was taught in the lesson.

 

This lesson will be the culminating project for this section. It will incorporate all of the components that they have been learning about in this unit and give them an opportunity to apply their knowledge to model real life data and present their discoveries.

I will group students according to ability level to give al students the opportunity to be challenged in one way or another. I will also provide extra support to any students that have missed instruction or are just struggling in this section by assisting them with their calculations when need be.

• computer lab
• graphing calculators
• projector
• whiteboard
• whiteboard markers

Teaching & Instructional Activities
Time	Teacher Activity	Student Activity	Purpose
5 minutes	Group students and assign the lesson’s project Instructions below	Get in groupings and listen to instruction	Prepare students for their group work time.
35 minutes	Be available to answer student questions	Create model and prepare presentation	Group work time
10 minutes	Listen to presentations to assess student understanding	Listen to and give presentations of findings	Present findings, assess through products
5 minutes	Hand out and then collect exit slips	Fill out exit slips	Formatively assess student learning

 

 

Data taken from http://the-numbers.com/movie/budgets/

 

Instructions:

Choose one of the data charts from the website above to model with a linear regression. Then calculate the coefficient of correlation for this model. If necessary remove outliers from your data set to improve your model. Be prepared to give a short presentation about your findings and what they mean in the real world by the end of the period.

 

Modeling Activity Rubric

	0	1	2	3
Work time was used productively
The correct linear regression and coefficient were found
Explanation was given for the meaning of the findings any data points removed
The distinction between correlation and causation was made

 

Exit slip:

List 3 concepts that we covered today and indicate whether you would like to cover any of them again.

 

 

 

 

 

 

List two new terms from the lesson today and if possible define them

 

 

 

 

 

List one thing you found interesting from the lesson today.