Transcript 2.5 Modeling Real World Data

Algebra II
Mr. Gilbert
Chapter 2.5
Modeling Real-World Data:
Using Scatter plots and line of fit
Standard & Honors
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Students shall be able to

Perform a simple
regression,
charting results
and saving the
equation.
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
2
Use a calculator to
determine what
kind of equation
best models
specific data.
Agenda
Warm up
 Home Work
 Lesson
 Practice
 Homework

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Click the mouse button4 or press the
Space Bar to display the answers.
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Homework Review
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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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Ti-83 Regression types
Source:http://academic.pg.cc.md.us/psc/TI83_booklet.pdf
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Example 1 Draw a Scatter Plot
Example 2 Find and Use a Prediction Equation
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Education The table below shows the approximate
percent of students who sent applications to two
colleges in various years since 1985. Make a scatter
plot of the data.
Years Since
1985
0
3
6
9
12
15
Percent
20
18
15
15
14
13
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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Safety The table below shows
the approximate percent of
drivers who wear seat belts in
various years since 1994. Make
a scatter plot of the data.
Years Since
1994
0
Percent
57 58 61 64 69 68 71 73
1
2
3
4
5
6
7
Source: National Highway Traffic Safety Administration
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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?
Years Since
1985
0
3
6
9
12
15
Percent
20
18
15
15
14
13
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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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?
Years Since
1985
0
3
6
9
12
15
Percent
20
18
15
15
14
13
Source: U.S. News & World Report
Answer: Except for (6, 15), this
line fits the data fairly well.
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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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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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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 2010
should be about 9%.
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How accurate is this prediction?
Answer: The fit is only approximate, so the prediction
may not be very accurate.
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Safety The table and scatter plot
show the approximate percent of
drivers who wear seat belts in
various years since 1994.
Years Since
1994
0
Percent
57 58 61 64 69 68 71 73
1
2
3
4
5
6
7
Source: National Highway Traffic Safety Administration
a. Draw a line of fit for the data.
How well does the line fit the data?
Answer: Except for (4, 69), this
line fits the data very well.
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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 + 55.5. 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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c. Predict the percent of drivers who will be wearing
seat belts in 2005.
Answer: 83%
d. How accurate is the prediction?
Answer: Except for the outlier, the line fits the data very
well, so the predicted value should be fairly accurate.
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Homework
See Syllabus 2.5
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