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2-7 Curve Fitting with Linear Models
Section 2.7
Curve Fitting with Linear Models
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Homework
• Pg 146 #5-11, 22-24
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Researchers, such as
anthropologists, are
often interested in how
two measurements are
related. The statistical
study of the relationship
between variables is
called regression.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
A scatter plot is helpful in understanding the
form, direction, and strength of the relationship
between two variables. Correlation is the
strength and direction of the linear relationship
between the two variables.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
If there is a strong linear relationship between two
variables, a line of best fit, or a line that best fits
the data, can be used to make predictions.
Helpful Hint
Try to have about the same number of points
above and below the line of best fit.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 1: Meteorology Application
Albany and Sydney are
about the same distance
from the equator. Make
a scatter plot with
Albany’s temperature as
the independent
variable. Name the type
of correlation. Then
sketch a line of best fit
and find its equation.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 1 Continued
Step 1 Plot the data points.
Step 2 Identify the correlation.
Notice that the data set is
negatively correlated–as the
temperature rises in Albany, it
falls in Sydney.
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Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 1 Continued
Step 3 Sketch a line of best fit.
Draw a line that splits
the data evenly above
and below.
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Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 1 Continued
Step 4 Identify two points on the line.
For this data, you might select (35, 64) and
(85, 41).
Step 5 Find the slope of the line that models the
data.
Use the point-slope form.
Point-slope form.
y – y1= m(x – x1)
y – 64 = –0.46(x – 35)
y = –0.46x + 80.1
Substitute.
Simplify.
An equation that models the data is y = –0.46x + 80.1.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
The correlation coefficient r is a measure of how
well the data set is fit by a model.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 2: 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.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 2 Continued
a. Make a scatter
plot of the data
with femur
length as the
independent
variable.
The scatter plot is
shown at right.
Holt Algebra 2
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2-7 Curve Fitting with Linear Models
Example 2 Continued
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 Algebra 2
2-7 Curve Fitting with Linear Models
Example 2 Continued
The slope is about 2.91, so for each 1 cm
increase in femur length, the predicted increase
in a human being’s height is 2.91 cm.
The correlation coefficient is r ≈ 0.986 which
indicates a strong positive correlation.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Example 2 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.
Holt Algebra 2