Objective - To find the line of best fit for a given set of data in a scatter plot.

AnimalBrain

Weight (g)Max.

Life (yr.)

Mouse

Fox

J

0.450.4157

3.29.8

22 4

y

yrs.)

50

40

0 100 200 300 400 500 600

Jaguar

Sheep

Pig

Seal

Donkey

Chimp

157175180325419440

22.42027414050

x

Brain Weight (g)

Max

. Life

(y 30

20

10

y

yrs.)

50

40Trend is increasing

Scatterplot - a coordinategraph of data points.

0 100 200 300 400 500 600x

Brain Weight (g)

Max

. Life

(y 30

20

10Line of Best Fit-Points act like magnets attracting the line.

Trend looks linear

y

yrs.)

50

40Trend is increasing

Scatterplot - a coordinategraph of data points.

0 100 200 300 400 500 600x

Brain Weight (g)

Max

. Life

(y 30

20

10Line of Best Fit-Points act like magnets attracting the line.

Trend looks linear

y

yrs.)

50

40Trend is increasing

Scatterplot - a coordinategraph of data points.

0 100 200 300 400 500 600x

Brain Weight (g)

Max

. Life

(y 30

20

10Line of Best Fit-Points act like magnets attracting the line.

Trend looks linear

y

yrs.)

50

40Trend is increasing

Scatterplot - a coordinategraph of data points.

0 100 200 300 400 500 600x

Brain Weight (g)

Max

. Life

(y 30

20

10Line of Best Fit-Points act like magnets attracting the line.

Trend looks linear

y

yrs.)

50

40Trend is increasing

Scatterplot - a coordinategraph of data points.

0 100 200 300 400 500 600x

Brain Weight (g)

Max

. Life

(y 30

20

10Line of Best Fit-Points act like magnets attracting the line.

Trend looks linear

Lesson 4-4

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Finding the Line of Best Fity Line of Best Fit

• Ignore outliers.

Outlier

x

Finding the Line of Best Fity

No

Line of Best Fit

• Equal # of points

• Does not have to go through any points.

• Ignore outliers.

x

• Equal # of points above and below the line.

Finding the Line of Best Fity

NoLine of Best Fit

• Equal # of points

• Does not have to go through any points.

• Ignore outliers.

x

• Equal # of points above and below the line.• Points attract the line like magnets to a metal rod.

Finding the Line of Best Fity Line of Best Fit

• Equal # of points

• Does not have to go through any points.

• Ignore outliers.

x

Yes

• Equal # of points above and below the line.• Points attract the line like magnets to a metal rod.

The data below shows the gold medal performance in high jump in some of the past Olympics. Plot the data on a graph and draw the line of best fit.

Year HighJump (in.)

194819561964

7883.2585 75

y

(in.)

100

80

1964197219801988

85.7587.7592.7593.5

1948 1956 1964 1972 1980 1988xYear

Hig

h Ju

mp

( 60

40

20

Test Scores vs. Homework

60

80

100

120

iz S

core

%

0

20

40

60

0 20 40 60 80 100 120% Homework Turned In

Test

& Q

u

Lesson 4-4 (cont.)

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

ScatterplotsWhich scatterplots below show a linear trend?

a) c) e)NegativeCorrelation

PositiveCorrelation

NoCorrelation

b) d) f)

ConstantCorrelation

NoCorrelation

NoCorrelation

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis..

StudentTime SpentWatching TV

Time Spenton Homework

Sam

Jon

30 min.

45 min.

180 min.

150 min.

Lara

Darren

Megan

Pia

Crystal

120 min.

240 min.

90 min.

150 min.

180 min.

90 min.

30 min.

90 min.

90 min.

90 min.

Plot the data on the graph such that homework timeis on the y-axis and TV time is on the x-axis.

TV Homework

30 min.

45 min.

120 i

180 min.

150 min.

90 i n ork

240210180150120 min.

240 min.

90 min.

150 min.

180 min.

90 min.

30 min.

120 min.

120 min.

90 min.

Time Watching TV

Tim

e on

Hom

ewo

30 90 150 210 60 120 180 240

150120906030

Describe the relationship between time spent onhomework and time spent watching TV.

n ork

240210180150

Trend is decreasing.

Trend appears linear.

Time Watching TV

Tim

e on

Hom

ewo

30 90 150 210 60 120 180 240

150120906030

Negative correlation.

Time on TV ↑Time on HW ↓

State the type of correlation you would expect to see between the following.

1) The height of a candle and the number of hours it has been burning.

2) The grade received on a test and the number ofNegative correlation.

2) The grade received on a test and the number ofhomework problems completed.

3) The level of fuel in a gas tank of a vehicle andthe top speed of that vehicle.

Positive correlation.

No correlation.

Lesson 4-4 (cont.)

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010