objective - to find the equation of the line of best fit for a given set of data

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