Curriculum  /  Math  /  9th Grade  /  Unit 2: Descriptive Statistics  /  Lesson 18

Descriptive Statistics

Lesson 18

Math

Unit 2

9th Grade

Lesson 18 of 22

Objective

Use residuals to assess the strength of the model for a data set.

Common Core Standards

Core Standards

  • HSS-ID.B.6b — Informally assess the fit of a function by plotting and analyzing residuals.
  • HSS-ID.B.6c — Fit a linear function for a scatter plot that suggests a linear association.

Criteria for Success

  1. Explain that the least squares regression line is the predicted model for the data, whereas the data points are the actual data.
  2. Describe that while you can fit various functions to a set of data and develop an algebraic model, the focus in this unit is on fitting and analyzing a linear model. 
  3. Relate the standard deviation (distance from the mean) with comparing the actual data points in a scatterplot from the distance from the line of best fit. 
  4. Calculate the residuals between the actual data and the line of best fit. 
  5. Describe that by plotting and analyzing the residuals, you can make a conjecture about whether a particular function is appropriate for a set of data and variables. 
  6. Analyze a residual plot for randomness. If a residual plot has a random pattern, the function is likely an appropriate model for the relationship between the two variables. 
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Anchor Problems

25-30 minutes

Problem 1

Below is a set of data. 
On the left is an incorrect line of best fit, and on the right is the least squares regression line. 

$${y=x+1}$$$${y=.9x+2.5}$$
A student explains that the line on the left is more appropriate, because it goes through three points in the data set. 

What calculations can you do to convince this student that even though the line of best fit does not go through any of the points on the graph on the right, it is a better model for the data? 

Guiding Questions

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Problem 2

What function will be the best fit for this set of data? How can we use residuals to determine this?

Guiding Questions

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Meerkats have a gestation time of days.

  1. Use the equation of the least squares line, $${y=6.643+0.03974x}$$ , to predict the longevity of the meerkat. Remember $$x$$ equals the gestation time in days and $$y$$ equals the longevity in years.
  2. Approximately how close might your prediction be to the actual longevity of the meerkat? What was it (from class) that told you roughly how close a prediction might be to the true value?
  3. The longevity of the meerkat is actually 10 years. Use this value and the predicted value that you calculated in part a. to find the residual for the meerkat.

References

EngageNY Mathematics Algebra I > Module 2 > Topic D > Lesson 15 — Exit Ticket #1

Algebra I > Module 2 > Topic D > Lesson 15 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..

Additional Practice

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.

Next

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.

Lesson 19
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Descriptive Statistics in Univariate Data

Topic B: Descriptive Statistics in Bivariate Data

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