Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 16
Math
Unit 2
9th Grade
Lesson 16 of 22
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Calculate, with technology, the correlation coefficient for a data set. Explain why correlation does not determine causation.
The core standards covered in this lesson
HSS-ID.C.8 — Compute (using technology) and interpret the correlation coefficient of a linear fit.
HSS-ID.C.9 — Distinguish between correlation and causation.
The foundational standards covered in this lesson
8.SP.A.2 — Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3 — Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Below is a scatterplot comparing the number of hours of video games played over the course of a month and the score on the unit test.
Use the Desmos activity shown below to answer the question: Desmos, Andrew Knauft, “Correlation and Regression.”
How does the correlation coefficient help us to quantify the strength of correlation between two variables?
Correlation and Regression by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed June 21, 2017, 11:16 a.m..
Identify the calculation coefficient, and describe what this means in terms of how the variables are related.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
The scatterplot below displays data on the number of defects per cars and a measure of customer satisfaction (on a scale from to , with higher scores indicating greater satisfaction) for the brands of cars sold in the United States in 2009.
Data Source: USA Today, June 16, 2010, and July 17, 2010
r = -0.95
r = -0.24
r = 0.83
r = 1.00
Algebra I > Module 2 > Topic D > Lesson 19 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 15
Lesson 17
Topic A: Descriptive Statistics in Univariate Data
Describe statistics. Represent data in frequency graphs and identify the center of a data set.
HSS-IC.A.1 HSS-ID.A.1 HSS-ID.A.2
Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.
HSS-ID.A.1 HSS-ID.A.2
Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
HSS-ID.A.1
Describe the shape of the data in box plots and histograms. Choose an appropriate measure of center (or an appropriate shape) based on the shape and the relationship between the mean and the median.
HSS-ID.A.2 HSS-ID.A.3
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.3 HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2 HSS-ID.A.4
Interpret the standard deviation and interquartile range.
Calculate population percentages using the standard deviation.
HSS-ID.A.4
Given summary statistics, describe the best measures of center and spread. Describe reasoning.
HSS-ID.A.2
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)
HSS-ID.A.1 HSS-ID.A.2 HSS-ID.A.3 HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
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Topic B: Descriptive Statistics in Bivariate Data
Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.
HSS-ID.B.5
Describe relative and relative conditional frequencies of two-way tables.
Create scatterplots and identify function shapes in scatterplots.
HSS-ID.B.6
HSS-ID.C.8 HSS-ID.C.9
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6a HSS-ID.B.6b HSS-ID.C.7
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6b HSS-ID.B.6c
Describe the relationship between two quantitative variables in a contextual situation represented in a scatterplot using the correlation coefficient, least squares regression, and residuals as evidence.
HSS-ID.B.6a HSS-ID.C.7 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9 N.Q.A.1
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