# 5.6: Predicting with Linear Models

**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*\begin{align*}(ax+b)\end{align*}*LinReg*\begin{align*}(a+bx)\end{align*}*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.

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