REGRESSION LINE WITH SNAZZY MUSIC

LessonSummary: This lesson is designed to introduce the student to lines of regression and the concept of correlation coefficient through the use of music. Students will also be exposed to using the TI-83/84.

KeyWords: Math and music, Regression Line, Correlation coefficient

Background Knowledge: Students will have to know the concept of plotting points.

Benchmarks:

Data Analysis and Probability Standard - Grades: 8-10

  1. Create, interpret and use graphical displays and statistical measures to describe data; e.g. scatterplots.

E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis

  1. Construct convincing arguments based on analysis and interpretation of graphs.

Data Analysis and Probability Standard - Grades: 11-12

  1. Create and analyze tabular and graphical displays of data using appropriate tools, including graphing calculators.

C. Design and perform a statistical experiment, simulation or study; collect and interpret data; and use descriptive statistics to communicate and support predictions and conclusions.

Grade Level Indicators:

9.2 – Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

9.6 – Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation.

10.2 – Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.

11.1 - Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation.

11.4 – Create a scatterplot of bivariate data, identify trends, and find a function to model the data.

11.5 – Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation.

11.8 – Analyze and interpret univariate and bivariate data to identify patterns, not trends, draw conclusions, and make predictions.

11.9 – Evaluate validity of results of a study based on characteristics of the study design, including sampling methods, summary statistics and data analysis techniques.

Learning Objectives:

1. From a set of student-generated points, students will create a list in the graphing calculator.

  1. Students will create a scatterplot of these points on the graphing calculator.
  1. Students will determine the linear regression equation and correlation coefficient for their data using the graphing calculator.
  1. Students will interpret the r-value of the data and write a summary of its meaning.

Materials:

CD Player / Computer with CD drive

CD – Music compiled by teacher

Worksheet: Rate the Song

Worksheet: Name the Song

Worksheet: Partner Coordinates

Worksheet: Scatterplot

Worksheet: Instructions – Line of Best Fit

Worksheet: Scatterplot Data Sheet

Graphing Calculators (one for every two students)

Pencil

Ruler

Suggested Procedures:

Day before:

Announce that students will spend the next class period listening to music.

Day One:

  1. Have music playing as students enter the room.
  2. Distribute worksheets Rate the Song and Name the Song and discuss the directions for this portion of the activity.
  3. Play 30 seconds of each song (or to the chorus). Allow students time after each song to rate it and determine the title and artist.
  4. After all 25 songs are played, collect Rate the Song worksheet.
  5. Students are then to trade and grade Name the Song worksheets with a classmate. (Each song is worth two points—one for the title and one for the artist.) Answers will be provided by the students/teacher.
  6. Student with the highest score will be awarded a special prize to be determined by the individual teacher.
  7. Before tomorrow’s class, teacher will assign each student either an x- or y-coordinate on the Rate the Song worksheet.

Day Two:

  1. Distribute the Rate the Song worksheets.
  2. Students will find a partner with the opposite coordinate of their own.
  3. Distribute one Partner Coordinates worksheet to each pair of students. Students will fill in their coordinates for each song.
  4. Distribute one Scatterplot worksheet to each pair of students. Students will plot their points.
  5. Distribute graphing calculators and Instructions-Line of Best Fit worksheet. Students will follow directions on the worksheet.

Day Three:

  1. Students will complete the scatterplot data sheet. They will analyze the data and draw conclusions regarding the correlation coefficient.
  2. Students will draw the regression line on the Scatterplot worksheet.
  3. The teacher will discuss the differences in the data and students will discuss the meaning.
  4. Collect worksheets for grades.

Assessment:

Informal : Listen to student discussion

Formal: Collect and grade worksheets

Extension:

Barbie Bungee

Project AMP Dr. Antonio R. Quesada Director, Project AMP