Transcript 1.4 Scatter Plots - Biloxi Public Schools

Bell Ringer
Find each slope:
1. (5, –1), (0, –3)
2. (8, 5), (–8, 7)
1.4 Objectives
Fit scatter plot data using linear models
with and without technology.
Use linear models to make predictions.
A line of best fit may also
be referred to as a trend line.
FOURCurve
KINDSFitting
OF CORRELATIONS
WILL
with Linear (YOU
Models
1-4
LEARN ABOUT IN TRANSITION)
Positive Correlation
Constant Correlation
Holt McDougal Algebra 2
Negative Correlation
No Correlation
1-4 Curve Fitting with Linear Models
Scatter Plots + Calculator
• 1) STAT 
• #1 
• L1 (x) , L2 (y) (enter data;
use arrow keys to select
column) 
• STAT 
• CALC 
• 4enter LinReg(ax+b) 
• 2nd 
Holt McDougal Algebra 2
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8) y= 
plot1 
on 
TYPE
X list L1 & Y list L2 
mark (select on) 
GRAPH
Example 1
Albany and Sydney are about the same distance
from the equator. (a)Make a scatter plot with
Albany’s temperature as the independent variable.
(b)Name the type of correlation. (c)Then sketch a
line of best fit and (d)find its equation.
How to:
Calculator data entry
Enter ______ in list L1 by pressing STAT
and then 1.
Enter _______ in list L2 by pressing 
Make scatter plot in the following
way:
Press 2nd
Y=
PLOT 1
set up desired type
when done, press GRAPH
c
o
n
t
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n
u
e
d
That’s to much
work with paper &
pencil
Tables:
ACT
Does yours look like this ? example 1 continued
Albany and Sydney are about the
same distance from the equator.
(a)Make a scatter plot with Albany’s
temperature as the independent variable.
(b)Name the type of correlation.
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(c)Then sketch a line of best fit and
(d)find its equation. (hint: what is m? b?)
o
Example 2
(a)Make a scatter plot for this set of data.
(b)Identify the correlation
(c)sketch a line of best fit
(d)find its equation.
example 2 continued
Step 1 Plot the data points.
Step 2 Identify the correlation.
Notice that the data set is
positively correlated–as time
increases, more points are
scored
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example 2 continued
Step 3 Sketch a line of best fit.
Draw a line that splits the
data evenly above and below.
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Step 4 Identify the equation
for the data.
end
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Example 3: Anthropology Application
Anthropologists can use the femur, or thighbone, to
estimate the height of a human being. The table shows
the results of a randomly selected sample.
(a)Make a scatter plot for
this set of data.
(b)Identify the correlation
(c)sketch a line of best fit
(d)find its equation.
example 3 continued
a. Make a scatter
plot of the data
with femur length
as the
independent
variable.
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Fitting3 with
Linear Models
Continued
1-4 CurveExample
b. Find the correlation coefficient r and the line of
best fit. Interpret the slope of the line of best fit in
the context of the problem.
Enter the data into lists L1
and L2 on a graphing
calculator. Use the linear
regression feature by
pressing STAT, choosing
CALC, and selecting
4:LinReg. The equation of
the line of best fit is
h ≈ 2.91l + 54.04.
Holt McDougal Algebra 2
Example 3 with
Continued
Linear Models
1-4 Curve Fitting
What does the slope indicate about
problem?
Holt McDougal Algebra 2
Example 3 Continued
c. A man’s femur is 41 cm long. Predict the
man’s height.
The equation of the line of best fit is
h ≈ 2.91l + 54.04. Use the equation to predict the
man’s height.
For a 41-cm-long femur,
h ≈ 2.91(41) + 54.04 Substitute 41 for l.
h ≈ 173.35
The height of a man with a 41-cm-long femur
would be about 173 cm.
end
Example 4
The gas mileage for
randomly selected cars
based upon engine
horsepower is given
in the table.
a. Make a scatter
plot of the data
with horsepower
as the independent
variable.
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with
Linear Models
Example
4 Continued
1-4 Curve Fitting
b. Find the correlation coefficient r and the line of
best fit. Interpret the slope of the line of best
fit in the context of the problem.
Enter the data into lists L1 and
L2 on a graphing calculator. Use
the linear regression feature by
pressing STAT, choosing CALC,
and selecting 4:LinReg. The
equation of the line of best fit is
y ≈ –0.15x + 47.5.
Holt McDougal Algebra 2
Example 4 Continued
The slope is about –0.15, so for each 1 unit
does the slope
indicatedrops
?
increase What
in horsepower,
gas mileage
≈
0.15 mi/gal.
c. Predict the gas mileage for a 210-horsepower
engine.
The equation of the line of best fit is
y ≈ –0.15x + 47.5. Use the equation to predict
the gas mileage. For a 210-horsepower engine,
y ≈ –0.15(210) + 47.50.
Substitute 210 for x.
y ≈ 16
The mileage for a 210-horsepower engine would be
about 16.0 mi/gal.
end
Exit Question: complete on graph paper attached to
Exit Question sheet
(a)Make a scatter plot for this set of data using your
calculator
(b)find its equation.