# 5.6: Predicting with Linear Models

Difficulty Level:

**At Grade**Created by: CK-12## Learning Objectives

At the end of this lesson, students will be able to:

- Collect and organize data.
- Interpolate using an equation.
- Extrapolate using an equation.
- Predict using an equation.

## Vocabulary

Terms introduced in this lesson:

- surveys
- experimental measurements
- non-linear data
- linear interpolation
- polynomial interpolation
- linear extrapolation
- most accurate method

## Teaching Strategies and Tips

Use the introduction to motivate data collection and organization.

- Data are gathered from surveys and experimental measurements.
- Data are organized via tables and scatterplots, where it is easier to spot trends and patterns.

In Example 1:

- Point out that two data sets are being displayed simultaneously in the scatterplot. This is a common practice when two data sets are being compared.
- The two variables are
*Median Age of Males and Females At First Marriage by Year*. - Discuss with students whether the scatterplot is approximately linear and whether using a line of best fit to predict future values is appropriate. Do the same for Example 2.

Use Examples 3 and 4 to motivate linear interpolation.

- Ask students how they would go about estimating a value where there is no data point available.
- Possible discussion questions:
*Assume the data are linear. How would the line of best fit help? Should only a subset of the data be used? All of the data? How does the above considerations change for non-linear data?*

Use Example 5 to motivate linear extrapolation.

- Point out that the last data point is an outlier and therefore influences the extrapolation heavily.
- Work through the extrapolation a second time using a linear regression. Have students compare answers from the two models.
- Emphasize that extrapolation is not useful when used to predict values far into the future (or far into the past).

For additional data sets, visit:

## Error Troubleshooting

General Tip: On the TI graphing calculators, students should be using *LinReg**LinReg**LnReg*.

General Tip: Students can neglect to consider the accuracy of a prediction or estimate. Some estimates will not be good because the desired value is far removed from the rest of the data set.

### Image Attributions

## Description

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## Tags:

Activities
Answer Key
Answers
(48 more)
Assessment
circumference
CK.MAT.ENG.TE.1.Algebra-I.5
Common Misconceptions
Concept Check and Troubleshooting
dependent variable
diameter
Differentiated Instruction
Enrichment
extrapolate
family of lines
finding equations for lines
Inquiry Process
interpolate
line of best fit
linear equations
linear functions
linear regression
measurement error
negative reciprocal
outliers
Pacing
Parallel Lines
perpendicular lines
point slope form
point-slope form
Problem Sets
Problem Solving
Quizzes
reciprocal
scatter plot
Science Inquiry
slope
slope formula
slope-intercept form
Solution Key
Solutions
standard form
Survey
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
vertical shift
Worksheets
x-intercept
y-intercept

## Subjects:

## Date Created:

Feb 22, 2012## Last Modified:

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