Best Fit Lines in Data Analysis
Lesson 4.6
Best Fit Line
C
o
n
c
e
p
t
:
U
s
i
n
g
&
I
n
t
e
r
p
r
e
t
i
n
g
B
e
s
t
F
i
t
L
i
n
e
s
E
Q
s
:
-
How do we determine a line of best fit from a
scatter plot? (S.ID.6 a,c)
-What does the slope and intercept tell me about the
data? (S.ID.7)
V
o
c
a
b
u
l
a
r
y
:
S
c
a
t
t
e
r
P
l
o
t
,
S
l
o
p
e
,
I
n
t
e
r
c
e
p
t
,
Line of best fit
1
4.2.4: Fitting Linear Functions to Data
Dear Teacher
•
On a sheet of paper, write to your teacher what you
know about best fit lines and what you hope to learn
after today’s lesson.
4.2.4: Fitting Linear Functions to Data
2
Before you can find the line of
best fit…..
•
Graph your data
•
Determine if the data can be represented using a linear
model…does the data look linear???
•
Draw a line through the data that is close to most points.
Some values should be above the line and some values
should be below the line.
•
Now you can write the equation of the line.
Let’s try one together.
4.2.4: Fitting Linear Functions to Data
3
4
4.2.4: Fitting Linear Functions to Data
Pablo’s science class is growing
plants. He recorded the height
of his plant each day for 10 days.
The plant’s height, in cm, over
time is in the scatter plot.
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
E
x
a
m
p
l
e
(7, 14), (8, 16)
4.2.4: Fitting Linear Functions to Data
5
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
E
x
a
m
p
l
e
(7, 14), (8, 16)
4.2.4: Fitting Linear Functions to Data
6
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
E
x
a
m
p
l
e
(7, 14), (8, 16)
4.2.4: Fitting Linear Functions to Data
7
y = 2(x – 7) + 14
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
4. Simplify
E
x
a
m
p
l
e
(7, 14), (8, 16)
4.2.4: Fitting Linear Functions to Data
8
y = 2(x – 7) + 14
y = 2x – 14 +14
y = 2x
9
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
E
x
a
m
p
l
e
1
A weather team records the
weather each hour after
sunrise one morning in May.
The hours after sunrise and
the temperature in degrees
Fahrenheit are in the table
to the right.
C
a
n
t
h
e
t
e
m
p
e
r
a
t
u
r
e
0
–
7
h
o
u
r
s
a
f
t
e
r
s
u
n
r
i
s
e
b
e
r
e
p
r
e
s
e
n
t
e
d
b
y
a
l
i
n
e
a
r
f
u
n
c
t
i
o
n
?
I
f
y
e
s
,
f
i
n
d
t
h
e
e
q
u
a
t
i
o
n
o
f
t
h
e
f
u
n
c
t
i
o
n
.
10
10
4.2.4: Fitting Linear Functions to Data
Graph the points!!!
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
1
,
c
o
n
t
i
n
u
e
d
1.
C
r
e
a
t
e
a
s
c
a
t
t
e
r
p
l
o
t
o
f
t
h
e
d
a
t
a
.
Let the
x
-axis represent
hours after sunrise and
the
y
-axis represent
the temperature in
degrees Fahrenheit.
11
11
4.2.4: Fitting Linear Functions to Data
T
e
m
p
e
r
a
t
u
r
e
(
°
F
)
H
o
u
r
s
a
f
t
e
r
s
u
n
r
i
s
e
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
1
,
c
o
n
t
i
n
u
e
d
2.
D
e
t
e
r
m
i
n
e
i
f
t
h
e
d
a
t
a
c
a
n
b
e
r
e
p
r
e
s
e
n
t
e
d
b
y
a
l
i
n
e
a
r
f
u
n
c
t
i
o
n
.
The graph of a linear equation is a line. If the data
looks like it could fit a line, then a linear equation
could be used to represent the data.
The temperatures appear to increase in a line, and a
linear equation could be used to represent the data
set.
12
12
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
1
,
c
o
n
t
i
n
u
e
d
3.
D
r
a
w
a
l
i
n
e
t
o
e
s
t
i
m
a
t
e
t
h
e
d
a
t
a
s
e
t
.
Two points in the data set can be used to draw a line
that estimates that data. When the line is drawn,
some of the data values should be above the line,
and some should be below the line.
A line through (2, 56) and (6, 64) looks like a good fit
for the data.
13
13
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
1
,
c
o
n
t
i
n
u
e
d
14
14
4.2.4: Fitting Linear Functions to Data
GO Best Fit Line
S
t
e
p
s
1.
2.
3.
4.
E
x
a
m
p
l
e
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2.
3.
4.
E
x
a
m
p
l
e
(2, 56), (6, 64)
4.2.4: Fitting Linear Functions to Data
16
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3.
4.
E
x
a
m
p
l
e
(2, 56), (6, 64)
4.2.4: Fitting Linear Functions to Data
17
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
4.
E
x
a
m
p
l
e
(2, 56), (6, 64)
4.2.4: Fitting Linear Functions to Data
18
y = 2(x – 2) + 56
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
4. Simplify
E
x
a
m
p
l
e
(2, 56), (6, 64)
4.2.4: Fitting Linear Functions to Data
19
y = 2(x – 2) + 56
y = 2x – 4 +56
y = 2x +52
20
20
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
-
E
x
a
m
p
l
e
2
21
21
4.2.4: Fitting Linear Functions to Data
Can the speed between 0
and 8 seconds be represented
by a linear function? If yes,
find the equation of the
function.
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
2
,
c
o
n
t
i
n
u
e
d
1.
C
r
e
a
t
e
a
s
c
a
t
t
e
r
p
l
o
t
o
f
t
h
e
d
a
t
a
.
Let the
x
-axis represent
time and the
y
-axis
represent speed.
22
22
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
2
,
c
o
n
t
i
n
u
e
d
2.
D
e
t
e
r
m
i
n
e
i
f
t
h
e
d
a
t
a
c
a
n
b
e
r
e
p
r
e
s
e
n
t
e
d
b
y
a
l
i
n
e
a
r
f
u
n
c
t
i
o
n
.
23
23
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
-
E
x
a
m
p
l
e
3
Automated tractors can mow
lawns without being driven by
a person. A company runs
trials using fields of different
sizes, and records the
amount
of time
it takes the tractor to
mow each field. The field sizes
are measured in acres.
24
24
4.2.4: Fitting Linear Functions to Data
Can the time to mow acres of a
field be represented by a linear
function? If yes, find the equation
of the function.
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
3
,
c
o
n
t
i
n
u
e
d
1.
C
r
e
a
t
e
a
s
c
a
t
t
e
r
p
l
o
t
o
f
t
h
e
d
a
t
a
.
Let the
x
-axis represent
the acres and the
y
-axis
represent the time
in hours.
25
25
4.2.4: Fitting Linear Functions to Data
T
i
m
e
A
c
r
e
s
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
3
,
c
o
n
t
i
n
u
e
d
2.
D
e
t
e
r
m
i
n
e
i
f
t
h
e
d
a
t
a
c
a
n
b
e
r
e
p
r
e
s
e
n
t
e
d
b
y
a
l
i
n
e
a
r
f
u
n
c
t
i
o
n
.
The graph of a linear equation is a line. If the data
looks like it could fit a line, then a linear equation
could be used to represent the data.
T
h
e
t
i
m
e
a
p
p
e
a
r
s
t
o
i
n
c
r
e
a
s
e
i
n
a
l
i
n
e
,
a
n
d
a
l
i
n
e
a
r
e
q
u
a
t
i
o
n
c
o
u
l
d
b
e
u
s
e
d
t
o
r
e
p
r
e
s
e
n
t
t
h
e
d
a
t
a
s
e
t
.
26
26
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
3
,
c
o
n
t
i
n
u
e
d
3.
D
r
a
w
a
l
i
n
e
t
o
e
s
t
i
m
a
t
e
t
h
e
d
a
t
a
s
e
t
.
Two points in the data set can be used to draw a
line that estimates the data. When the line is drawn,
some of the data values should be above the line,
and some should be below the line.
A line through (7, 10) and (40, 112) looks like a
good fit for the data.
27
27
4.2.4: Fitting Linear Functions to Data
G
u
i
d
e
d
P
r
a
c
t
i
c
e
:
E
x
a
m
p
l
e
3
,
c
o
n
t
i
n
u
e
d
28
28
4.2.4: Fitting Linear Functions to Data
GO Best Fit Line
S
t
e
p
s
1.
2.
3.
4.
E
x
a
m
p
l
e
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2.
3.
4.
E
x
a
m
p
l
e
(7, 10) and (40, 112)
4.2.4: Fitting Linear Functions to Data
30
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3.
4.
E
x
a
m
p
l
e
(7, 10) and (40, 112)
4.2.4: Fitting Linear Functions to Data
31
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
4.
E
x
a
m
p
l
e
(7, 10) and (40, 112)
4.2.4: Fitting Linear Functions to Data
32
y = 3.09(x – 7) + 10
GO Best Fit Line
S
t
e
p
s
1.
Identify two points on the
line of best fit
2. Find the slope of the line
using the points
3. Substitute into
y = m(x – x
1
) + y
1
4. Simplify
E
x
a
m
p
l
e
(7, 10) and (40, 112)
4.2.4: Fitting Linear Functions to Data
33
y = 3.09(x – 7) + 10
y = 3.09x – 21.63 + 10
y = 3.09x – 11.63
34
34
4.2.4: Fitting Linear Functions to Data
Resource
http://www.shodor.org/interactivate/activities/Regression/
35
35
T
h
e
I
m
p
o
r
t
a
n
t
T
h
i
n
g
On a sheet of paper, write down three things you learned
today. Out of those three, write which one is most
important and why.
36
36
Exploring the concept of best fit lines in data analysis, this lesson covers how to determine a line of best fit from a scatter plot, interpret the slope and intercept of the line, and fit linear functions to data points. Through examples and steps, students learn to graph data, find the equation of the line of best fit, and understand the significance of slope and intercept in data analysis.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Lesson 4.6 Best Fit Line Concept: Using & Interpreting Best Fit Lines EQs: -How do we determine a line of best fit from a scatter plot? (S.ID.6 a,c) -What does the slope and intercept tell me about the data? (S.ID.7) Vocabulary: Scatter Plot, Slope, Intercept, Line of best fit 1 4.2.4: Fitting Linear Functions to Data
Dear Teacher On a sheet of paper, write to your teacher what you know about best fit lines and what you hope to learn after today s lesson. 4.2.4: Fitting Linear Functions to Data 2
Before you can find the line of best fit .. Graph your data Determine if the data can be represented using a linear model does the data look linear??? Draw a line through the data that is close to most points. Some values should be above the line and some values should be below the line. Now you can write the equation of the line. Let s try one together. 4.2.4: Fitting Linear Functions to Data 3
Pablos science class is growing plants. He recorded the height of his plant each day for 10 days. The plant s height, in cm, over time is in the scatter plot. 4 4.2.4: Fitting Linear Functions to Data
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 14), (8, 16) 4.2.4: Fitting Linear Functions to Data 5
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 14), (8, 16) m = 16 14 8 7=2 1= 2 2. Find the slope of the line using the points 4.2.4: Fitting Linear Functions to Data 6
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 14), (8, 16) m = 16 14 8 7=2 1= 2 2. Find the slope of the line using the points y = 2(x 7) + 14 3. Substitute into y = m(x x1) + y1 4.2.4: Fitting Linear Functions to Data 7
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 14), (8, 16) m = 16 14 8 7=2 1= 2 2. Find the slope of the line using the points y = 2(x 7) + 14 3. Substitute into y = m(x x1) + y1 y = 2x 14 +14 y = 2x 4. Simplify 4.2.4: Fitting Linear Functions to Data 8
(Write this below your GO) Interpret the slope and y-intercept ? = 2? Slope value: ____ Slope units: _______ Y-intercept value: ____ Y-intercept unit: ______ Interpretation: ___________________ ____________________ ___________________ 9 4.2.4: Fitting Linear Functions to Data
Guided Practice Example 1 A weather team records the weather each hour after sunrise one morning in May. The hours after sunrise and the temperature in degrees Fahrenheit are in the table to the right. Can the temperature 0 7 hours after sunrise be represented by a linear function? If yes, find the equation of the function. Graph the points!!! Hours after sunrise 0 1 2 3 4 5 6 7 Temperature in F 52 53 56 57 60 63 64 67 10 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 1, continued 1. Create a scatter plot of the data. Let the x-axis represent hours after sunrise and the y-axis represent the temperature in degrees Fahrenheit. F) Temperature ( Hours after sunrise 11 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 1, continued 2. Determine if the data can be represented by a linear function. The graph of a linear equation is a line. If the data looks like it could fit a line, then a linear equation could be used to represent the data. The temperatures appear to increase in a line, and a linear equation could be used to represent the data set. 12 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 1, continued 3. Draw a line to estimate the data set. Two points in the data set can be used to draw a line that estimates that data. When the line is drawn, some of the data values should be above the line, and some should be below the line. A line through (2, 56) and (6, 64) looks like a good fit for the data. 13 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 1, continued F) Temperature ( 14 Hours after sunrise 4.2.4: Fitting Linear Functions to Data
GO Best Fit Line Steps Example 1. 2. 3. 4.
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) 2. 3. 4. 4.2.4: Fitting Linear Functions to Data 16
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) m = 64 56 =8 4= 2 2. Find the slope of the line using the points 6 2 3. 4. 4.2.4: Fitting Linear Functions to Data 17
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) m = 64 56 =8 4= 2 2. Find the slope of the line using the points 6 2 y = 2(x 2) + 56 3. Substitute into y = m(x x1) + y1 4. 4.2.4: Fitting Linear Functions to Data 18
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) m = 64 56 =8 4= 2 2. Find the slope of the line using the points 6 2 y = 2(x 2) + 56 3. Substitute into y = m(x x1) + y1 y = 2x 4 +56 y = 2x +52 4. Simplify 4.2.4: Fitting Linear Functions to Data 19
Interpret the slope and y-intercept ? = 2? + 52 Slope value: ____ Slope units: _______ Y-intercept value: ______ Y-intercept unit: ________ Interpretation: ______________________ __________________________________ 20 4.2.4: Fitting Linear Functions to Data
Guided Practice - Example 2 Can the speed between 0 and 8 seconds be represented by a linear function? If yes, find the equation of the function. 21 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 2, continued 1. Create a scatter plot of the data. Let the x-axis represent time and the y-axis represent speed. 22 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 2, continued 2. Determine if the data can be represented by a linear function. 23 4.2.4: Fitting Linear Functions to Data
Guided Practice - Example 3 Automated tractors can mow lawns without being driven by a person. A company runs trials using fields of different sizes, and records the amount of time it takes the tractor to mow each field. The field sizes are measured in acres. Time in hours 15 10 22 32.3 46.8 34 39.6 75 70 112 Acres 5 7 10 17 18 20 22 25 30 40 Can the time to mow acres of a field be represented by a linear function? If yes, find the equation of the function. 24 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 3, continued 1. Create a scatter plot of the data. Let the x-axis represent the acres and the y-axis represent the time in hours. Time 25 Acres 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 3, continued 2. Determine if the data can be represented by a linear function. The graph of a linear equation is a line. If the data looks like it could fit a line, then a linear equation could be used to represent the data. The time appears to increase in a line, and a linear equation could be used to represent the data set. 26 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 3, continued 3. Draw a line to estimate the data set. Two points in the data set can be used to draw a line that estimates the data. When the line is drawn, some of the data values should be above the line, and some should be below the line. A line through (7, 10) and (40, 112) looks like a good fit for the data. 27 4.2.4: Fitting Linear Functions to Data
Guided Practice: Example 3, continued Time 28 Acres 4.2.4: Fitting Linear Functions to Data
GO Best Fit Line Steps Example 1. 2. 3. 4.
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) 2. 3. 4. 4.2.4: Fitting Linear Functions to Data 30
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) m = 112 10 =102 33=3.09 2. Find the slope of the line using the points 40 7 3. 4. 4.2.4: Fitting Linear Functions to Data 31
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) m = 112 10 =102 33=3.09 2. Find the slope of the line using the points 40 7 y = 3.09(x 7) + 10 3. Substitute into y = m(x x1) + y1 4. 4.2.4: Fitting Linear Functions to Data 32
GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) m = 112 10 =102 33=3.09 2. Find the slope of the line using the points 40 7 y = 3.09(x 7) + 10 3. Substitute into y = m(x x1) + y1 y = 3.09x 21.63 + 10 y = 3.09x 11.63 4. Simplify 4.2.4: Fitting Linear Functions to Data 33
Interpret the slope and y-intercept ? = 3.09? 11.63 Slope value: ____ Slope units: _______ Y-intercept value: ______ Y-intercept unit: ________ Interpretation: ______________________ __________________________________ 34 4.2.4: Fitting Linear Functions to Data
Resource http://www.shodor.org/interactivate/activities/Regression/ 35
The Important Thing On a sheet of paper, write down three things you learned today. Out of those three, write which one is most important and why. 36
