1. Algebra II Mr. Gilbert Chapter 2.5 Modeling Real-World Data:
Using Scatter plots and line of fit
Standard & Honors
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2. Students shall be able to
Perform a simple regression, charting results and saving the equation.
Use a calculator to determine what kind of equation best models specific data.
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3. Agenda
Warm up
Home Work
Lesson
Practice
Homework
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4. Click the mouse button or press the Space Bar to display the answers.
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Click the mouse button or press the Space Bar to display the answers.
Transparency 7

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Transparency 7a

6. Homework Review
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7. Communicate Effectively
Line of fit: a line that closely approximates the data points.
Prediction Equation: the equation that defines the line of fit.
Regression Analysis: a method to find the line of fit.
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8. Ti-83 Regression types
Source:
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9. Example 1 Draw a Scatter Plot
Example 2 Find and Use a Prediction Equation
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Lesson 5 Contents

10. Education The table below shows the approximate percent of students who sent applications to two colleges in various years since Make a scatter plot of the data. 13 14 15 18 20
Percent 12 9 6 3
Years Since 1985
Source: U.S. News & World Report
Graph the data as ordered pairs, with the number of years since 1985 on the horizontal axis and the percentage on the vertical axis.
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Example 5-1a

11. Safety The table below shows the approximate percent of drivers who wear seat belts in various years since Make a scatter plot of the data. 73 71 68 69 64 61 58 57
Percent 7 6 5 4 3 2 1
Years Since 1994
Source: National Highway Traffic Safety Administration
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Example 5-1b

12. Draw a line of fit for the data. How well does the line fit the data?
Education The table and scatter plot below show the approximate percent of students who sent applications to two colleges in various years since 1985.
Draw a line of fit for the data. How well does the line fit the data? 13 14 15 18 20
Percent 12 9 6 3
Years Since 1985
Source: U.S. News & World Report
The points (3, 18) and (15, 13) appear to represent the data well. Draw a line through these two points.
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Example 5-2a

13. Draw a line of fit for the data. How well does the line fit the data?
Education The table and scatter plot below show the approximate percent of students who sent applications to two colleges in various years since 1985.
Draw a line of fit for the data. How well does the line fit the data? 13 14 15 18 20
Percent 12 9 6 3
Years Since 1985
Source: U.S. News & World Report
Answer: Except for (6, 15), this line fits the data fairly well.
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Example 5-2b

14. Find a prediction equation. What do the slope and y-intercept indicate?
Find an equation of the line through (3, 18) and (15, 13). Begin by finding the slope.
Slope formula
Substitute.
Simplify.
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Example 5-2c

15. Distributive Property
Point-slope form
Distributive Property
Add 18 to each side.
Answer: One prediction equation is
The slope indicates that the percent of students sending applications to two colleges is falling at about 0.4% each year. The y-intercept indicates that the percent in 1985 should have been about 19%.
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Example 5-2d

16. Predict the percent in 2010.
The year 2010 is 25 years after 1985, so use the prediction equation to find the value of y when
Prediction equation
Simplify.
Answer: The model predicts that the percent in should be about 9%.
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Example 5-2e

17. How accurate is this prediction?
Answer: The fit is only approximate, so the prediction may not be very accurate.
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Example 5-2f

18. Answer: Except for (4, 69), this line fits the data very well.
Safety The table and scatter plot show the approximate percent of drivers who wear seat belts in various years since 1994.
a. Draw a line of fit for the data. How well does the line fit the data? 73 71 68 69 64 61 58 57
Percent 7 6 5 4 3 2 1
Years Since 1994
Source: National Highway Traffic Safety Administration
Answer: Except for (4, 69), this line fits the data very well.
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Example 5-2g

19. b. Find a prediction equation. What do the slope and
b. Find a prediction equation. What do the slope and y-intercept indicate?
Answer: Using (1, 58) and (7, 73), an equation is y = 2.5x The slope indicates that the percent of drivers wearing seatbelts is increasing at a rate of 2.5% each year. The y-intercept indicates that, according to the trend of the rest of the data, the percent of drivers who wore seatbelts in 1994 was about 56%.
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Example 5-2h

20. d. How accurate is the prediction? Answer: 83%
c. Predict the percent of drivers who will be wearing seat belts in 2005.
d. How accurate is the prediction?
Answer: 83%
Answer: Except for the outlier, the line fits the data very well, so the predicted value should be fairly accurate.
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Example 5-2i

21. Homework
See Syllabus 2.5
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