objective - to find the equation of the line of best fit for a given set of data
DESCRIPTION
Objective - To find the equation of the line of best fit for a given set of data. Brain Weight (g). Max. Life (yr.). Animal. y. 0.4. 3.2. Mouse. 50 40 30 20 10. 50.4. 9.8. Fox. 157. 22.4. Jaguar. Max. Life (yrs.). 175. 20. Sheep. 180. 27. Pig. 325. 41. Seal. x. - PowerPoint PPT PresentationTRANSCRIPT
0 100 200 300 400 500 600
Objective - To find the equation of the line of best fit for a given set of data.
Animal BrainWeight (g)
Max. Life (yr.)
Mouse
Fox
Jaguar
Sheep
Pig
Seal
Donkey
Chimp
0.4
50.4
157
175
180
325
419
440
3.2
9.8
22.4
20
27
41
40
50
x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10
Trend is increasing
Scatterplot - a coordinategraph of data points.
Line of Best Fit-Points act like magnets attracting the line.
Trend looks linear
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10Line of Best Fit-Points act like magnets attracting the line.
Trend is increasing
Trend looks linear
Scatterplot - a coordinategraph of data points.
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10Line of Best Fit-Points act like magnets attracting the line.
Trend is increasing
Trend looks linear
Scatterplot - a coordinategraph of data points.
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10Line of Best Fit-Points act like magnets attracting the line.
Trend is increasing
Trend looks linear
Scatterplot - a coordinategraph of data points.
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10Line of Best Fit-Points act like magnets attracting the line.
Trend is increasing
Trend looks linear
Scatterplot - a coordinategraph of data points.
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10
Steps1) Plot the points.
2) Draw the lineof best fit.
3) Take two pointsoff the line.
(50, 10)
(450, 50)
(50, 10) (450, 50)
0 100 200 300 400 500 600x
y
Brain Weight (g)
Max
. Lif
e (y
rs.)
50
40
30
20
10
Steps1) Plot the points.
2) Draw the lineof best fit.
3) Take two pointsoff the line.
(50, 10)
(450, 50)
(50, 10) (450, 50)
4) Find the equationof the line using thetwo points.
Steps1) Plot the points.
2) Draw the lineof best fit.
3) Take two pointsoff the line.
(50, 10) (450, 50)
4) Find the equationof the line using thetwo points.
my y
x x=
−−
2 1
2 1
m ≈−−
50 10450 50
m ≈40400
m ≈01.
y x b≈ +01.
10 ≈0.1 50( ) + b10 5≈ +b
5≈b
y x≈ +01 5.
Actualy x≈ +0097 5432. .
ScatterplotsWhich scatterplots below show a linear trend?
a) c) e)
b) d) f)
Finding the Line of Best Fit
Outlier
x
y Line of Best Fit• Ignore outliers.
Finding the Line of Best Fit
x
y
No
Line of Best Fit
• Equal # of points above and below the line.
• Does not have to go through any points.
• Ignore outliers.
Finding the Line of Best Fit
x
yNo
Line of Best Fit
• Equal # of points above and below the line.
• Does not have to go through any points.
• Ignore outliers.
• Points attract the line like magnets to a metal rod.
Finding the Line of Best Fit
x
y
Yes
Line of Best Fit
• Equal # of points above and below the line.
• Does not have to go through any points.
• Ignore outliers.
• Points attract the line like magnets to a metal rod.
Choosing Two Points
x
y
Yes
Chosen points are too close together.
Choosing Two Points
x
y
Yes
Chosen points have sufficient spread.
Year
Find the equation of the line of best fit forthe data below.
Sport Utility Vehicles(SUVs) Sales in U.S.
Sales (in Millions)
19911992
199319941995
1996
19971998
1999
0.91.1
1.41.61.7
2.1
2.42.7
3.2
1991 1993 1995 1997 1999 1992 1994 1996 1998 2000
x
y
Year
Veh
icle
Sal
es (
Mil
lion
s)
5
4
3
2
1
Find the equation of the line of best fit forthe data below.
1991 1993 1995 1997 1999 1992 1994 1996 1998 2000
x
y
Year
Veh
icle
Sal
es (
Mil
lion
s)
5
4
3
2
1
Steps1) Plot the points.
2) Draw the lineof best fit.
3) Take two pointsoff the line.
(1992, 1.1)
(1999, 3)
(1992, 1.1) (1999, 3)
4) Find the equationof the line using thetwo points.
Find the equation of the line of best fit forthe data below.
Steps1) Plot the points.
2) Draw the lineof best fit.
3) Take two pointsoff the line.
(1992, 1.1) (1999, 3)
4) Find the equationof the line using thetwo points.
my y
x x=
−−
2 1
2 1
m ≈−−
3 1199 92
.
m ≈197.
m ≈0271.
y x b≈ +0271.
( )1.1 0.271 1992 b≈ +
11 540. ≈ +b− ≈539 b
y x≈ −0271 539.
Actualy x≈ −0275 547.
Find the equation of the line of best fit forthe data below.
1991 1993 1995 1997 1999 1992 1994 1996 1998 2000
x
y
Year
Veh
icle
Sal
es (
Mil
lion
s)
5
4
3
2
1(1992, 1.1)
(1999, 3)
y x≈ −0271 539.If this trend continues,predict the sales forthe year 2004.
( )y 0.271 2004 539≈ −
y x≈ −0271 539.
y ≈ −543 539
yehicles
≈4 million v
The data below shows the gold medal perform-ance in high jump in some of the past Olympics
Year HighJump (in.)
19481956
196419721980
1988
7883.25
85.7587.7592.75
93.5
1948 1956 1964 1972 1980 1988x
y
Year
Hig
h Ju
mp
(in.
)
100
80
60
40
20
The data below shows the gold medal perform-ance in high jump in some of the past Olympics
1948 1956 1964 1972 1980 1988x
y
Year
Hig
h Ju
mp
(in.
)
100
80
60
40
20
(1948, 78)
(1988, 94)(1948, 78) (1988, 94)
The data below shows the gold medal perform-ance in high jump in some of the past Olympics
(1948, 78) (1988, 94)
my y
x x=
−−
2 1
2 1
m ≈−−
94 781988 1948
m ≈1640
m ≈04.
y x b≈ +04.
( )78 0.4 1948 b≈ +
78 779≈ +b− ≈701 b
y x≈ −04 701.
Actualy x≈ −0386 672.
The data below shows the gold medal perform-ance in high jump in some of the past Olympics
1948 1956 1964 1972 1980 1988x
y
Year
Hig
h Ju
mp
(in.
)
100
80
60
40
20
(1948, 78)
(1988, 94)If this trend continues,predict the gold medal height in 2004.
( )y 0.4 2004 701≈ −
y x≈ −04 701.
y ≈ −8016 701.
y ≈100 6. inches