CurveFitting
Fittingwith
withLinear
LinearModels
Models
2-7
2-7 Curve
LESSON PLAN
Warm Up (Slide #2)
Objective and PA State Standards
Vocab
(Slide #3)
(Slides #4 – 8)
Lesson Presentation
(Slides #9 – 24)
Text Questions - NONE
Worksheet–2.7A
(Slide #25)
Lesson Quiz
Holt
Algebra
Holt
Algebra
22
(Slides #26 – 28)
2-7 Curve Fitting with Linear Models
Warm Up
Write the equation of the line passing through
each pair of passing points in slope-intercept
form.
1. (5, –1), (0, –3)
2. (8, 5), (–8, 7)
Use the equation y = –0.2x + 4. Find x for each
given value of y.
3. y = 7
Holt Algebra 2
4. y = 3.5
2-7 Curve Fitting with Linear Models
Objectives
1. Fit scatter plot data using linear models with and
without technology.
2. Use linear models to make predictions.
Pa. Dept of Educ. Math Standards and Anchors:
2.6.A2.C/E
2.7.A2.C/E
M11.E.1.1.2
4.1.1
4.2.1
4.2.2
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Vocabulary
regression
correlation
line of best fit
correlation coefficient
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Researchers, such as
anthropologists, are often
interested in how two or more
measurements are related.
(ex. Climate, Size, Species)
The study of the relationship
between two or more variables
is called regression analysis.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Scatter plots like those below are helpful in determining
the strength and type of a relationship between variables.
Correlation is the strength and direction of the
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
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 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
(the “x” coordinate).
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.
Step 3 Sketch a Line of Best Fit
Notice that the data set is
negatively correlated...as
temperature rises in Albany, it
falls in Sydney.
••• ••
•• •
•••
o
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 (60,52) and (40,61).
Step 5 Find the slope of the line that models the data.
61 – 52
9
-.45
40 - 60
-20
Step 6 Use either point-slope or slope intercept form
to develop the equation
y – y1= m(x – x1)
y= mx + b
y – 52 = –0.45(x – 60)
52 = -.45(60) + b
y – 52 = –0.45x + 27
52 = -27 + b
y = –0.45x + 27 + 52
y = –0.45x + 79
52 + 27 = b
79 = b
y = –0.45x + 79
An equation that models the data is y = –0.45x + 79
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Check It Out! Example 1
Make a scatter plot for this set of data.
Identify the correlation, sketch a line of best
fit, and find its equation.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Check It Out! Example 1 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
Step 3 Sketch a Line of Best Fit
•
•
Holt Algebra 2
•
•
•• • •
••
2-7 Curve Fitting with Linear Models
Check It Out! Example 1 Continued
Step 4 Identify two points on the line.
For this data, you might select (20, 10) and (40, 25).
Step 5 Find the slope of the line that models the data.
Step 6 Develop the equation:
Using point-slope form.
Using slope-intercept form.
y – y1= m(x – x1)
y= m(x) + b
10= .75(20) + b
y – 10 = 0.75(x – 20)
y – 10 = 0.75x – 15
y = 0.75x – 5
Holt Algebra 2
10= 15 + b
y = 0.75x - 5
-5= b
2-7 Curve Fitting with Linear Models
You can use a graphing calculator to
graph scatter plots and lines of best fit.
Find video tutorial links
for both of these
calculator functions
SCATTER PLOTS and LINES OF BEST FIT
in Moodle
Algebra 2
Chapter 2
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 (which means “y”).
•
•• •
•
Holt Algebra 2
•• •
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.
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 it to predict the man’s height for a 41cm 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
2-7 Curve Fitting with Linear Models
Check It Out! Example 2
The gas mileage for randomly selected cars
based upon engine horsepower is given in the
table.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Check It Out! Example 2 Continued
a. Make a scatter
plot of the data
with horsepower
as the independent
variable.
The scatter plot is
shown on the right.
Holt Algebra 2
••
••
•
••
•
• •
2-7 Curve Fitting with Linear Models
Check It Out! 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
y ≈ –0.15x + 47.5.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Check It Out! Example 2 Continued
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.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Reading Math
A line of best fit may also be referred to as a
trend line.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Worksheet 2.7A
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Lesson Quiz: Part I
Use the table for Problems 1–3.
1. Make a scatter
plot with mass
as the independent
variable.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Lesson Quiz: Part II
2. Find the correlation coefficient and the
equation of the line of best fit on your scatter
plot. Draw the line of best fit on your scatter
plot.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Lesson Quiz: Part I
Use the table for Problems 1–3.
1. Make a scatter
plot with mass
as the independent
variable.
Holt Algebra 2
2-7 Curve Fitting with Linear Models
Lesson Quiz: Part II
2. Find the correlation coefficient and the
equation of the line of best fit on your scatter
plot. Draw the line of best fit on your scatter
plot.
r ≈ 0.67 ;
y = 0.07x – 5.24
Holt Algebra 2