Warm UpWarm Up

1) Determine whether the point (2, 7) 1) Determine whether the point (2, 7) is on the line y = 3x + 1.is on the line y = 3x + 1.

2) Find the equation of the line 2) Find the equation of the line containing the points (4,2) and (7, 5).containing the points (4,2) and (7, 5).

3) Find the equation of the line with 3) Find the equation of the line with slope 3 and containing the point (2, slope 3 and containing the point (2, 5).5).

2.52.5CorrelationCorrelation

And And

Best-Fitting lineBest-Fitting line

The Essential 55The Essential 55by Ron Clarkby Ron Clark

Rule # 15:Rule # 15: Do not ask for a Do not ask for a reward.reward.

AgendaAgenda 8/28/058/28/05

Warm-upWarm-up Go over HWGo over HW Answer any questions Answer any questions

from worksheet and from worksheet and quizquiz

Notes 2.5Notes 2.5 HomeworkHomework

Steps to find the best Steps to find the best fitting line:fitting line:

Carefully draw a scatter plot of the dataCarefully draw a scatter plot of the data

Sketch the line that appears to follow most Sketch the line that appears to follow most closely the pattern given by the points. closely the pattern given by the points. There should be as many pts above and There should be as many pts above and below the linebelow the line

Choose 2 pts on the line and find the slope of Choose 2 pts on the line and find the slope of themthem

Then find the equation of the line using pt-Then find the equation of the line using pt-slope formulaslope formula

Let’s get some dataLet’s get some data

Each person needs a piece of scratch Each person needs a piece of scratch paper.paper.

On the following slide is a list of the Top On the following slide is a list of the Top Ten Grossing Films of 2002.Ten Grossing Films of 2002.

Copy the titles of the movies on your paper.Copy the titles of the movies on your paper. Rank the movies in your order of Rank the movies in your order of

preference.preference. (#1 favorite - #10 least favorite)(#1 favorite - #10 least favorite)

Top 10 Grossing Films of 2002Top 10 Grossing Films of 2002 Spider-ManSpider-Man PG-13PG-13 The Lord of the Rings:The Lord of the Rings: The Two TowersThe Two Towers PG-13 PG-13 Star Wars: Episode IIStar Wars: Episode II - Attack of the Clones- Attack of the Clones PGPG Harry PotterHarry Potter and the Chamber of Secretsand the Chamber of Secrets PGPG My Big Fat Greek WeddingMy Big Fat Greek Wedding PGPG SignsSigns PG-13PG-13 Austin Powers in GoldmemberAustin Powers in Goldmember PG-13PG-13 Men in Black IIMen in Black II PG-13PG-13 Ice AgeIce Age PGPG Die Another DayDie Another Day – James Bond– James Bond PG-13PG-13

#1 favorite – #1 favorite – #10 least #10 least favoritefavorite

Source: Internet Movie Database (imdb.com)

Top 10 Movies of 2002Top 10 Movies of 2002 On your paper make an x and y-On your paper make an x and y-

axis. axis. Only the first quadrant needs to be Only the first quadrant needs to be

shown.shown. Number each axis 1 – 10Number each axis 1 – 10

Top 10 Movies of 2002Top 10 Movies of 2002 Pair your rankings for each movie Pair your rankings for each movie

with a partner; this makes an with a partner; this makes an ordered pair.ordered pair.

One student should plot his/her One student should plot his/her rankings on the x-axis and the rankings on the x-axis and the other on the y-axis.other on the y-axis.

for examplefor example

Kevin’s Kevin’s RankingsRankings

Jeff’s Jeff’s RankingsRankings

Spider ManSpider Man 22 44Lord of the RingsLord of the Rings 77 22Star WarsStar Wars 44 11Harry PotterHarry Potter 88 88Greek WeddingGreek Wedding 99 1010SignsSigns 33 77Austin PowersAustin Powers 1010 99Men In BlackMen In Black 66 66Ice AgeIce Age 55 55Die Another DayDie Another Day 11 33

for examplefor example

1 10

1

10

Kevin’s rankings

Jeff

’s r

anki

ngs

Austin Powers

M in B 2

Signs

6

3 6

7

9

Kevin’Kevin’ss

Jeff’sJeff’s

Spider ManSpider Man 22 44Lord of the Lord of the RingsRings

77 22

Star WarsStar Wars 44 11Harry PotterHarry Potter 88 88Grk WeddingGrk Wedding 99 1010SignsSigns 33 77Austin Austin PowersPowers

1010 99

Men In BlackMen In Black 66 66Ice AgeIce Age 55 55Die Another Die Another DayDay

11 33

Top 10 Films of 2002Top 10 Films of 2002

Should you and your partner go to Should you and your partner go to the movies together?the movies together?

Do your rankings have a positive Do your rankings have a positive or negative relationship?or negative relationship?

Could you draw a straight line Could you draw a straight line through your data and touch most through your data and touch most of your data points?of your data points?

Draw a scatter plot and Draw a scatter plot and tell whether the data has tell whether the data has a positive, negative or no a positive, negative or no correlationcorrelation

XX 11 22 33 44 55 66 77 88

yy 66 66 55 55 66 55 44 33

Approximate the best Approximate the best fitting linefitting line

Linear Modeling ProjectLinear Modeling Project

Chlorofluorocarbons (CFC’s) Chlorofluorocarbons (CFC’s) are gasses that are highly are gasses that are highly

stable and non-toxic. When stable and non-toxic. When they break down, they release they break down, they release chlorine atoms which attack chlorine atoms which attack the ozone layer. The ozone the ozone layer. The ozone

layer protects the earth from layer protects the earth from ultra violet rays. ultra violet rays.

The chart gives The chart gives information on the information on the concentration of CFC-11 concentration of CFC-11 in parts per trillion (ppt)in parts per trillion (ppt)

YEARYEAR CFC_11CFC_11

19791979 167167

19831983 205205

19871987 247247

19881988 263263

Plot the data on a time, Plot the data on a time, CFC-11 axisCFC-11 axis

How many lines can you draw How many lines can you draw thru two points?thru two points?

A

B

C

D

1. AB2. AC3. AD4. BC5. BD6. CD

6 lines

Let time t=0 be 1979.Let time t=0 be 1979.Now find the equations Now find the equations for all the 6 lines (we’ll do for all the 6 lines (we’ll do AB together)AB together)

We have 2 points so find the slope We have 2 points so find the slope and use the point slope formula.and use the point slope formula.

A = (0,167) B = (4,205)A = (0,167) B = (4,205) m=(167-205)/(0-4) = -38/-4 = 9.5m=(167-205)/(0-4) = -38/-4 = 9.5 y - 167 = 9.5 ( x – 0)y - 167 = 9.5 ( x – 0) y – 167 = 9.5xy – 167 = 9.5x y = 9.5x + 167y = 9.5x + 167

Now we’ll do the error Now we’ll do the error chart for this equationchart for this equation

Time in Time in YearsYears

Actual Actual CFCCFC

Data Data AB CFCAB CFC

Error ABError AB

Abs(actuAbs(actual – al –

Data)Data)

00 167167 9.5(0) + 167 = 9.5(0) + 167 =

16716700

44 205205 9.5(4) + 167 =9.5(4) + 167 =

20520500

88 247247 9.5(8) + 167 =9.5(8) + 167 =

24324344

99 263263 9.5(9) + 167 = 9.5(9) + 167 =

252.5252.510.510.5

Total Error AB = 14.5

Do this with all of the 6 sets of Do this with all of the 6 sets of data points.data points.

The equation with the The equation with the least least errorerror is the BEST FIT equation. is the BEST FIT equation.

Linear Regression Linear Regression Instructions:Instructions:

22ndnd, mem(+), 4 (clr all lists), enter, mem(+), 4 (clr all lists), enter Stat, edit, enterStat, edit, enter Input the years in L1 and the data in Input the years in L1 and the data in

L2L2 22ndnd, quit to get out, quit to get out Stat, over to calc, 4 (linReg(ax+b))Stat, over to calc, 4 (linReg(ax+b)) EnterEnter This gives you the a & b for a linear This gives you the a & b for a linear

equation, plug this in and do an error equation, plug this in and do an error chart for this equation.chart for this equation.