Algebra II Mr. Gilbert

1
Algebra IIMr. Gilbert

• Chapter 2.5
• Modeling Real-World Data
• Using Scatter plots and line of fit
• Standard Honors

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.

3
Agenda

• Warm up
• Home Work
• Lesson
• Practice
• Homework

4
Transparency 7
Click the mouse button or press the Space Bar to
display the answers.
5
Transparency 7a
6
Homework Review
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.

8
Ti-83 Regression types
Sourcehttp//academic.pg.cc.md.us/psc/TI83_bookle
t.pdf
9
Lesson 5 Contents
Example 1 Draw a Scatter Plot Example 2 Find and
Use a Prediction Equation
10
Example 5-1a
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.
Graph the data as ordered pairs, with the number
of years since 1985 on the horizontal axis and
the percentage on the vertical axis.
11
Example 5-1b
Safety The table below showsthe approximate
percent ofdrivers who wear seat belts invarious
years since 1994. Make a scatter plot of the
data.
12
Example 5-2a
Education The table and scatter plot below show
the approximate percent of students who
sentapplications to two colleges in various
years since 1985. Draw a line of fit for the
data. How well does the line fit the data?
The points (3, 18) and (15, 13) appear to
represent the data well. Draw a line through
these two points.
13
Example 5-2b
Education The table and scatter plot below show
the approximate percent of students who
sentapplications to two colleges in various
years since 1985. Draw a line of fit for the
data. How well does the line fit the data?
Answer Except for (6, 15), this line fits the
data fairly well.
14
Example 5-2c
Find a prediction equation. What do the slope
andy-intercept indicate?
Find an equation of the line through (3, 18) and
(15, 13). Begin by finding the slope.
15
Example 5-2d
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.
16
Example 5-2e
Predict the percent in 2010.
Answer The model predicts that the percent in
2010 should be about 9.
17
Example 5-2f
How accurate is this prediction?
Answer The fit is only approximate, so the
prediction may not be very accurate.
18
Example 5-2g
Answer Except for (4, 69), this line fits the
data very well.
19
Example 5-2h
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.
20
Example 5-2i
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.
21
Homework
See Syllabus 2.5