Regression and
Median-Fit Lines
(4-6)
Objective: Write equations
of best-fit lines using linear
regression. Write equations
of median-fit lines.
Best-Fit Lines
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You have learned how to find and write equations
for lines of fit by hand.
Many calculators use complex algorithms that find
a more precise line of fit called the best-fit line.
One algorithm is called linear regression.
Your calculator may also compute a number
called the correlation coefficient.
This number will tell you if your correlation is
positive or negative and how closely the equation
is modeling the data.
The closer the correlation coefficient is to 1 or -1,
the more closely the equation models the data.
Example 1
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The table shows Ariana’s hourly earnings for the
years 2001-2007. Use a graphing calculator to
write an equation for the best-fit line for the
data. Name the correlation coefficient.
Round to the nearest ten-thousandth. Let x be
the number of years since 2000.
Year
Cost
2001
$10
2002
$10.50
2003
$11
2004
$13
2005
$15
2006
$15.75
2007
$16.50
Example 1
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Before you begin, you need to make sure the
Diagnostic setting on your calculator is on.
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You can find this setting under the CATALOG
menu by pressing 2nd 0 on your calculator.
Alpha is set when you are in this menu. Press D
by using the x-1 button and then scroll down until
the arrow on the left is pointing to DiagnosticOn.
Press ENTER twice.
Example 1
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Enter the data in the table into your
calculator by pressing STAT.
Choose 1: Edit.
If there is data in the calculator
already, you will need to clear it out.
Scroll up until L1 is highlighted and press
CLEAR and the ENTER. Repeat this with
L2.
Enter the independent variable (x)
under L1 and the dependent variable
(y) under L2.
Year
Cost
2001
$10
2002
$10.50
2003
$11
2004
$13
2005
$15
2006
$15.75
2007
$16.50
Example 1
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You may then calculate the regression line by
pressing STAT again.
Right arrow over so that the heading CALC is
highlighted.
Scroll down to 4: LinReg(ax+b) and press ENTER
twice.
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The “a” value represents the slope.
The “b” value represents the y-intercept.
The “r” value represents the correlation coefficient.
Use “a” and “b” to write the equation for the bestfit line.
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y = 1.21x + 8.25
r = 0.9801
Check Your Progress
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Choose the best answer for the following.
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The table shows the average body temperature in
degrees Celsius of nine insects at a given
temperature. Use a graphing calculator to write
the equation for the best fit line for that data.
Name the correlation coefficient.
Temperature (˚C)
Air
25.7
30.4
28.7
31.2
31.5
26.2
30.1
31.5
18.2
Body
27.0
31.5
28.9
31.0
31.5
25.6
28.4
31.7
18.7
A.
B.
C.
D.
y = 0.85x + 1.28; 0.8182
y = 0.95x + 1.53; 0.9783
y = 1.53x + 0.95; 0.9873
y= 1.95x + 1.95; 0.8783
Interpolation and
Extrapolation
 We
can use points on the best-fit line to
estimate values that are not in the data.
 When we estimate values that are
between known values, this is called linear
interpolation.
 When we estimate a number outside of
the range of the data, it is called linear
extrapolation.
Example 2
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The table below shows the points earned by
the top ten bowlers in a tournament. Estimate
how many points the 15th-ranked bowler
earned.
Rank
1
2
3
4
5
6
7
8
9
10
Score
210
197
164
158
151
147
144
142
134
132
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y = -7.9x + 201.2
y = -7.9(15) + 201.2
y = -118.5 + 201.2
y = 83
Median-Fit Lines
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second type of fit line that can be
found using a graphing calculator is a
median-fit line.
 The equation of a median-fit line is
calculated using the medians of the
coordinates of the data points.
Example 3
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Find the equation of a median-fit line for the data
on the bowling tournament in Example 2. Then
predict the score of the 20th ranked bowler.
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Enter the data into the calculator the same way
using the STAT button.
After the data has been entered, go back to STAT
and right arrow over so that CALC is highlighted.
Choose 3: Med-Med.
Once again, the “a” value is the slope and the “b”
value is the y-intercept.
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y = -9x + 209.5
y = -9(20) + 209.5
y = -180 + 209.5
y = 30
Check Your Progress
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Choose the best answer for the following.
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An air taxi keeps track of how many passengers it carries
to various islands. The table shows the number of
passengers who have traveled to Kelley’s Island in
previous years. Use a regression line to determine how
many passengers should the airline expect to go to
Kelley’s Island in 2015?
Air Taxi to Kelley’s Island
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Number of
Passengers
1020
1115
1247
1657
1324
1568
1987
1562
1468
1693
A.
B.
C.
D.
1186 passengers
1702 passengers
1890 passengers
2186 passengers
y = 68.7x + 1154.9
y = 68.7(15) + 1154.9
y = 1030.5 + 1154.9
Check Your Progress
 Choose
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the best answer for the following.
Use the data from the table and a medianfit line to estimate the number of
passengers the airline will have in 2015.
A.
B.
C.
D.
1100 passengers
1700 passengers
1900 passengers
2100 passengers
y = 63.9x + 1142.5
y = 63.9(15) + 1142.5
y = 958.5 + 1142.5