# 5.5: Fitting a Line to Data

Difficulty Level:

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

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

- Make a scatterplot.
- Fit a line to data and write an equation for that line.
- Perform linear regression with a graphing calculator.
- Solve real-world problems using linear models of scattered data.

## Vocabulary

Terms introduced in this lesson:

- scatterplot
- measurement error
- outlier
- linear regression, line of best fit

## Teaching Strategies and Tips

Before fitting a line to data, suggest that students always check the scatterplot first for signs of association between the variables. If the points are too scattered, any calculations will be meaningless.

Use the introduction and Example 1 to motivate linear regression.

- Data points are collected from measurement or experiment which is never perfect.
- A line of best fit is the line
*closest*to all the data points. This means that the line minimizes the square root of the sum of the squares of the distances from each point to the line.

Provide the class with examples they can relate to. For example:

- Compile a list of students’ ages and heights.
- Use a graphing utility to make a scatterplot of
*age*vs.*height*. - Ask the class whether the data set looks approximately linear. If so, perform a linear regression using a graphing utility.
- Use the line of best fit to make predictions of height from ages. Have students gather similar age and
*height*data from their older siblings as a way to check the model.

## Error Troubleshooting

In Examples 3 and 4, discourage students from using *any* two data points to determine the equation of the line of best fit.

- Two points on the line or two data points
*closest*to the line must be used. - Teachers are encouraged to show that the line of best fit does not always pass through every point in the data set; in fact, it is possible that the line doesn’t go through any data point.

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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

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

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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